Estimate background radiation from unknown sources

Abstract

An embodiment includes a method, comprising: receiving measured radiation obtained from a radiation detector that receives radiation passing through an object; simulating the measured radiation obtained from the radiation detector that receives radiation passing through the object; generating an offset based on the measured radiation and the simulated measured radiation; estimating scattered radiation based on the offset; and estimating primary radiation based on the estimated scattered radiation.

Description

Background Art

[0001] Unless otherwise indicated herein, the methods described in this section are not prior art to the claims in the present disclosure and are not admitted to be prior art by inclusion in this section.

[0002] Some x-ray imaging can use a wide area cone beam. An x-ray detector can detect both primary radiation and scattered radiation. Scattered radiation can introduce artifacts in the image or reconstruction. Brief Description of the Drawings

[0003] Figure 1 is a block diagram of an imaging system according to some embodiments.

[0004] Figures 2A - 2B is a flowchart of an image processing technique with scatter correction according to some embodiments.

[0005] Figure 3 is a flowchart of gain estimation in an image processing technique with scatter correction according to some embodiments.

[0006] Figure 4 is a flowchart of multi-pass gain estimation in an image processing technique with scatter correction according to some embodiments.

[0007] Figure 5 is a flowchart of multi-pass gain estimation using a region of interest in an image processing technique with scatter correction according to some embodiments.

[0008] Figure 6 is a flowchart of offset estimation in an image processing technique with scatter correction according to some embodiments.

[0009] Figure 7 is a flowchart of offset estimation across sub-regions in an image processing technique with scatter correction according to some other embodiments.

[0010] Figure 8A Shows the measured radiation image I m .

[0011] Figure 8B Shows the simulated primary radiation image J p .

[0012] Figure 8C Shows the simulated scattered radiation image J s .

[0013] Figure 9A Shows the measured radiation image I m and the first-pass second-order polynomial fit scatter plot with the simulated radiation image J tot .

[0014] Figure 9B Shows the measured radiation image I m And the simulated radiation image J with outliers removed tot Of the second - order polynomial fit scatter plot for the second pass.

[0015] Figure 10 Shows a curve graph of the column vector.

[0016] Figure 11A Shows the offset image.

[0017] Figure 11B Shows the smoothed offset image.

[0018] Figure 12A Shows the reconstructed image without background or external scatter correction.

[0019] Figure 12B Shows the reconstructed image with background or external scatter correction.

[0020] Figure 13 Is a flowchart of gain estimation in an image processing technique with scatter correction according to some other embodiments.

[0021] Figure 14 Is a flowchart of offset estimation in an image processing technique with scatter correction according to some other embodiments.

[0022] Figure 15 Is a flowchart of gain and offset estimation in an image processing technique with scatter correction according to some embodiments.

[0023] Figure 16A Shows the measured radiation image I m .

[0024] Figure 16B Shows the simulated primary radiation image J p .

[0025] Figure 16C Shows the simulated scatter radiation image J s .

[0026] Figure 17 Shows the scatter plot or curve graph of the normalized measured radiation image I m And the simulated measured radiation image J tot Of the scatter plot or curve graph.

[0027] Figure 18A Shows the measured radiation image.

[0028] Figure 18BShows the pixels used in offset calculation.

[0029] Figure 18C Shows the pixels used in gain calculation.

[0030] Figure 19 Is a flowchart of gain and offset estimation in an image processing technique with scatter correction according to some embodiments.

[0031] Figure 20 Shows a block diagram of an exemplary background radiation estimation and correction device. Detailed Description

[0032] Before explaining any embodiments of the present invention in detail, it should be understood that the present invention is not limited in its application to the details of the construction and arrangement of components set forth in the following description or shown in the following drawings. The present invention is capable of other embodiments and of being practiced or carried out in various ways. The numbers provided in the flowcharts and processes are for clarity in illustrating steps and operations and do not necessarily indicate a particular order or sequence. Unless otherwise defined, the term "or" can refer to a selection of options (e.g., the OR operator or the exclusive OR) or a combination of options (e.g., the AND operator, and / or, logical OR, or Boolean OR).

[0033] The disclosed embodiments generally relate to techniques, mechanisms, methods, devices, and systems, collectively referred to as techniques, to estimate background scattered radiation or offsets from unknown sources and object scattering and to correct both the scattered radiation generated by objects in the field of view (FOV) of an imaging detector, background scattered radiation outside the FOV of the imaging detector, and so on. The disclosed embodiments also provide techniques for estimating spatial variations and / or spatially invariant scaling factors (gains) of object scattering and spatial variations and / or spatially invariant offsets of background scattered radiation.

[0034] Figure 1is a block diagram of an imaging system according to some embodiments. Cone beam computed tomography (CBCT) is an imaging technique used to provide three-dimensional (3D or 3-D) volumetric information of an object. The imaging system 100 generally includes a radiation source 102 such as an x-ray source and a radiation detector 106, also referred to as a flat panel detector, an imaging detector, or a detector. Using an x-ray source as an example, the radiation source 102 is configured to emit a divergent cone 103 of x-ray radiation that, after passing through the object 108, generates a signal on the radiation detector 106, thereby generating a projection image. By rotating the system 100 completely or partially around the object 108 (e.g., via a gantry), or equivalently by rotating the object 108 within a fixed stationary imaging system 100 and then applying an appropriate reconstruction algorithm, a 3D reconstruction of the internal structure of the object 108 can be obtained. Although rotation is used as an example, in other embodiments, different acquisition trajectories or techniques such as helical, circle + line, saddle, tomosynthesis, tomography, "inverse geometry CT", etc. can be used. Due to the high isotropic spatial resolution and high throughput of CBCT, CBCT is a powerful tool for industrial applications such as dimensional metrology, non-destructive testing, defect identification, general quality control, and part inspection on assembly lines. CBCT is also a powerful tool for other applications such as medical imaging and security inspections.

[0035] When a wide area cone beam 103 passes through a material, a large amount of scattered radiation can be generated, resulting in an undesirable and sometimes severe degradation of image quality that can even produce artifacts such as cupping, shading, streaks, non-uniformities, and inaccurate material density.

[0036] The system 100 can be coupled to a processor 112. The processor 112 can be a general-purpose processor, a digital signal processor (DSP), a graphics processing unit (GPU), an application-specific integrated circuit, a microcontroller, a programmable logic device, discrete circuitry, a combination of such devices, etc. Although only one processor 112 is shown in the system 100, there can be multiple processors 112. In addition, other interface devices such as memories, logic chip sets, hubs, memory controllers, communication interfaces, etc. can be part of the processor 112.

[0037] The processor 112 can be configured to perform various image processing techniques on one or more images received from the image detector 106. Some image processing techniques can mitigate scattering problems, particularly addressing scattering caused by the object itself. For example, kernel-based scattering estimation methods can be fast and effective, but may have some medium accuracy. In another example, the CBCT scattering correction algorithm uses a fast finite element deterministic photon transport solver running on a GPU. The fast finite element deterministic photon transport solver can quickly calculate the non-scattered (primary) and scattered x-ray photons transmitted through a 3D voxel representation of the object, which is typically generated from a processed first-pass CBCT reconstruction. Then, the estimated or calculated scattering (which approximates the actual scattering) from the kernel method or the transport-based method can be subtracted from the measured original projections to reconstruct a more accurate image.

[0038] Because anything actually in the x-ray beam path can generate scattering, there can be more scattering sources than those within the object 108. For example, if the x-ray beam is wide open, as is the case in some industrial applications, any additional object 114 that is not within the field of view 103a (FOV) of the radiation detector 106 but is within the irradiation field 103 can also generate scattered radiation 110a that reaches the detector. Depending on the specific setup of the scanning system and the location of the additional object 114, this scattering (or "background") component can be significant. Unfortunately, because this type of scattering source is not observed by the radiation detector 106, it is practically impossible for any conventional software-based scattering estimation / correction algorithm (including the two methods described above and many other methods in the literature) to address and correct the intensity of this background scattering.

[0039] Correction of background radiation is a prevalent problem in industrial CBCT because the beam is typically not collimated. Some of the embodiments described herein can heuristically address the problem of estimating scattering from unknown sources outside the radiation detector FOV 103a.

[0040] In x-ray imaging, the signal reaching the detector has two components, a primary component and a scattered component, as represented by Expression 1:

[0041] I m = I p + I s Expression 1

[0042] I m is the (measured) signal reaching the detector, I p is the primary, and I s is the scattered. The primary I pRepresents unscattered photons whose spatial distribution carries information about the internal structure of object 108 and is considered the "true" signal. I m is the measured signal. A scatter correction technique or algorithm is performed to obtain the unknown I m from the known I p .

[0043] In some embodiments, scattered I s radiation and primary I p radiation are calculated from a first-pass reconstruction of a given object using the underlying physical laws that describe radiation transport. This calculation or process is referred to as simulation. The simulation starts with the spectrum of the x-ray source, models the conical radiation, attenuates the modeled radiation through a 3D matrix of materials that are similar to the object in composition and density, and calculates the primary intensity and the scattered intensity separately. The simulated signal is represented by Expression 2:

[0044] J tot = J p + J s Expression 2

[0045] J p is the simulated primary radiation, J s is the simulated scattered radiation, and J tot is the combined simulated measured radiation.

[0046] When the various components including the x-ray spectrum, source distribution, scanner geometry, object properties (such as material composition and density), and detector response are correctly modeled, the simulated measured radiation J tot should closely match the measured radiation I m . The difference between the simulated measured radiation J tot and the measured radiation I m should include a gain or scaling constant and noise. The gain results from the fact that the number of photons represented in the simulation does not necessarily represent the measurement result (e.g., the difference may be caused by various unmodeled effects such as analog-to-digital converter (ADC) scaling, electronic gain, detector capacitor selection, tube current setting (e.g., mA setting), tube filtration, or inaccurate source for distance measurement). Let the gain be represented as λ, and initially ignoring noise sources such as photon noise and electronic noise (discussed later), the relationship between the simulated measured radiation J tot and the measured radiation I m can be represented by Expression 3:

[0047]

[0048] Combining Expression 1 and Expression 3, the primary radiation I p can be represented by Expression 4:

[0049] I p = I m - λJ s Expression 4

[0050] The CBCT scatter correction method does not directly use λJ p as I p , because the main signal is usually a high-frequency signal and is difficult to model based on a rough first-pass reconstruction. Since the scatter signal is a low-frequency signal, its calculation error in the first-pass reconstruction is usually robust. Subtracting the scatter estimate from the measured signal results in a more accurate main signal I p .

[0051] The scaling factor λ can be inferred from two known quantities I m and J tot as a direct proportion of the two, as represented by Expression 5:

[0052] λ = I m / J tot Expression 5

[0053] J tot and I m are images (or matrices in mathematical terms). In some embodiments, λ is a scalar applied to all pixels, and the value of λ generated is a value that may be a good compromise for each pixel. For example, the value of λ can be obtained by averaging, and the averaging can be done before calculating Expression 5 (e.g., averaging the pixel values in I m and J tot , and then generating the scaling factor λ based on the ratio of the averages of I m and J tot (λ = I m,AVG / J tot,AVG )) or after calculating Expression 5 (e.g., calculating the ratio of the values of each pixel in I m and J tot , and then generating the scaling factor λ based on the average of the ratios (λ = (average(I m / J tot ,)))). In other words, one method is to calculate Expression 5 for each pixel and then aggregate the results by taking the average of these ratios to obtain λ. Another method is to first aggregate the pixel values by taking the average of the J tot pixels and the average of the I m pixels, and then apply Expression 5 to obtain λ. As another example, λ can be a weighted average instead of a simple average, giving smaller weights to data points with more noise or lower credibility. As yet another example, λ can be calculated using the median instead of the average.

[0054] Note that, in addition to what is described by the gain λ, the simulated measured radiation J tot and the measured radiation I m can also be different. In other words, the simulated measured radiation J tot may not be similar to the measured radiation I measured by the radiation detector 106 m . The existence of such differences can have many causes, including any assumptions that deviate from physical reality in the simulation. For example, it may be extremely difficult to perfectly model the energy spectrum of the x-ray source, the accuracy of the material and density estimates of the object 108 model, and the detector's response to x-ray incidence. Although errors in the simulation model can be sources of error, these errors are generally small relative to the added external scattering component from sources other than the object being imaged.

[0055] Not taking the added external scattering component into account in the simulation model can be problematic because the proportional relationship between measurement and simulation is no longer maintained. If the object is part of the model, the disclosed method without background compensation is effective. If unknown objects 114 exist outside the FOV 103a and these unknown objects 114 are not considered, image processing without background compensation will significantly underestimate scatter.

[0056] In the case where an object near the detector is irradiated but does not produce a direct image (mainly) on the detector but imparts scatter to the image, this signal is referred to herein as "background scatter" or "external scatter". Expression 3 can be rewritten, enhanced, and / or extended to include the background component, which can be represented by Expression 6:

[0057]

[0058] where the additional variable b represents background scatter and is unknown.

[0059] The embodiments described herein can use information from I m and J tot to estimate λ and b. Note that each of λ and b can be spatially varying (matrix) or spatially constant (scalar). The embodiments can include several algorithms, including a first algorithm, a second algorithm, and a third algorithm. In the first algorithm, the gain λ is a scalar and the offset b is a matrix. In the second algorithm, the gain λ is a scalar and the offset b is a scalar. And the third algorithm has a framework for supporting spatial variation in both the gain λ and the offset b. Other embodiments can include different algorithms. In some embodiments, the gain λ associated with J tot , J p and J s can be the same or different.

[0060] As used herein, the offset b may be interchangeably referred to as "external scatter", "background", "additional scatter", or "offset". And λ is referred to as the "scaling factor" or "gain".

[0061] Figures 2A - 2B is a flowchart of an image processing technique with scatter correction according to some embodiments. Figure 1 The system 100 of will be used as an example. Figure 1 The processor 112 of may be configured to perform the various techniques described herein; however, in other embodiments, the processor 112 may be configured to perform some operations while other operations are performed by other processors. See Figure 1 、 Figure 2A and Figure 2B In some embodiments, at 200, the measured radiation I obtained from the radiation detector 106 is received m , where the radiation detector receives the radiation 103 that has passed through the object 108. The processor 112 may generate a two-dimensional data array representing the intensity of the received radiation based on the data received from the radiation detector 106. In some embodiments, the radiation detector 106 may be configured to generate data. In other embodiments, the processor 112 may be configured to receive the measured radiation I from a different source m .

[0062] At 202, the measured radiation I obtained from the radiation detector 106 that has received the radiation passing through the object 108 m is simulated as J tot . In some embodiments, the processor 112 performs the simulation, while in other embodiments, other systems may perform the simulation and provide the results to the processor 112. Various photon transport simulation techniques may be used to perform the simulation. 3DVSHARP is an example of such a technique; however, in other embodiments, other techniques may be used.

[0063] In some embodiments, at 204, based on the measured radiation I m and the simulated measured radiation J tot a gain λ is generated. However, in other embodiments, the generation of the gain may be omitted, assuming a constant such as 1, or not based on the measured radiation I m and the simulated measured radiation J totOne or both of them. In some embodiments, the gain λ can be generated as part of an earlier calibration process. A scan without the object 108 can be performed. The gain can be λ, and can be generated by using the measured and simulated data from this scan rather than the data when generating the offset b. In some embodiments, the gain λ can be generated before obtaining the data of the desired scan from the object 108. In other embodiments, the gain λ can be generated by scaling the gain λ by an appropriate factor based on the source imager distance, source flux, etc. In some embodiments, the gain λ can be analytically generated by simulating the components of the system 100 to generate the gain λ.

[0064] In 206, based on the measured radiation I m and the simulated measured radiation J tot generate the offset b. The gain λ and the offset b can be generated by the processor 112. As described below, a variety of techniques can be used to generate the gain λ and the offset b. Each of the gain λ and the offset b can be a matrix or a scalar. In operations 204 and 206, by using a part of the simulated measured radiation J tot such as the simulated primary radiation J p or the simulated scattered radiation J s ), based on the simulated measured radiation J tot generate the gain λ and the offset b.

[0065] In 208 or 208', estimate the scattered radiation I s respectively based on the offset b or the gain λ and the offset b. In 210, based on the estimated scattered radiation I s estimate the primary radiation I p . The estimated primary radiation can also be referred to as the corrected primary radiation. Or correct the measured radiation I m . In some embodiments, once both the gain λ and the offset b are generated, the estimate of the scattered radiation I s can be calculated as the simulated scattered radiation J s plus the external scattering represented by the offset b, as represented by Expression 7:

[0066] I s = λJ s + b Expression 7

[0067] For completeness, it should be noted that the measured primary radiation or the primary radiation I p is just the difference between the measured radiation I m and the measured scattered radiation I s , but in some embodiments, to reduce noise, estimate the primary radiation I p , as represented by Expression 8:

[0068]

[0069] Actually, the terms multiplied by I can then be filtered and / or clipped to reduce noise. In other embodiments, the measured primary radiation I is calculated by subtracting only an estimate of the scattered radiation I from the measured radiation I. m from the measured radiation I. m subtracting the estimated scattered radiation I s to calculate the measured primary radiation I. p .

[0070] In some embodiments, the calculated offset b may not have the same magnitude as J, and if necessary, the magnitude can be adjusted to that of J. In some embodiments, it may be necessary to adjust the magnitude of I again to match the magnitude of I. s and if necessary, the magnitude can be adjusted to that of J. s In some embodiments, it may be necessary to adjust the magnitude of I again to match the magnitude of I. s to match the magnitude of I. m .

[0071] Figure 3 is a flowchart of gain estimation in an image processing technique with scatter correction according to some embodiments. In some embodiments, the gain λ can be estimated based on various operations on the measured radiation and the simulated measured radiation. Operations 204-1 and 204-2 are examples of operations that can be included in operation 204 of Figure 2B .

[0072] In 204-1, a polynomial is fit to a first vector of pixel values of the measured radiation I m and a second vector of pixel values of the simulated measured radiation J tot . In 204-1, the gain λ is based on the polynomial. For example, the gain λ can be a scalar value that is the linear component of the polynomial.

[0073] In some embodiments, the polynomial can be a first-order or linear polynomial. However, in other embodiments, the polynomial can be a higher-order polynomial. In some embodiments, a polynomial that is at least second-order can better accommodate errors in the simulation model, such as residual beam hardening effects, inaccurate detector response, etc. Thus, the linear term may be less affected by the corresponding non-linearity in the simulation-measurement mapping.

[0074] The fit will also produce a zero-order term, which is considered the total offset (or scalar offset b) of the entire projection. As described below, additional operations can be performed to generate the offset b for estimating the scattered radiation.

[0075] Figure 4 is a flowchart of multi-pass gain estimation in an image processing technique with scatter correction according to some other embodiments. Operations 204-1, 204-3, 204-4, and 204-5 are operations that can be included inFigure 2B An example of an operation in operation 204.

[0076] In 204-1, a first polynomial is fitted to a first vector of pixel values of the measured radiation and a second vector of pixel values of the simulated measured radiation. This operation can be the same as Figure 3 that of 204-1 as described above.

[0077] In 204-3, the magnitudes of the first vector and the second vector are reduced to remove pixels for which the error of the first polynomial is greater than a threshold. In some embodiments, the threshold can be infinity or a sufficiently large number. Thus, no pixels will be removed. In other embodiments, the threshold can be set such that outlying pixels are removed. Thus, the first vector and the second vector will have fewer pixels. In a particular example, the threshold for the error can be about 40%-60%. In some embodiments, the threshold is 50%.

[0078] In 204-4, a second polynomial is fitted to the reduced first vector and the reduced second vector. The fitting operation can be the same as or similar to the operation in 204-1. If the operations in 204-1 and 204-3 remove pixels that are outliers (i.e., have a higher error relative to the first polynomial), then the second polynomial can have a better fit. In some embodiments, the operation in 204-4 can use a polynomial of a different order as the second polynomial.

[0079] In 204-5, a gain λ is generated based on the second polynomial. The generation of the gain λ can be the same as or similar to that in 204-2, but using the second polynomial.

[0080] In some embodiments, operations similar to 204-1 and 204-3 can be repeated to further reduce the number of pixels in the first vector and the second vector. The same or different error thresholds can be used to remove pixels. However, after multiple iterations, a final polynomial can be fitted similar to 204-4, and a gain λ can be generated as in 204-5.

[0081] Figure 5 is a flowchart of multi-pass gain estimation using a region of interest in an image processing technique with scatter correction according to some other embodiments. Operations 204-6 to 204-12 are examples of operations that can be included in Figure 2B operation 204.

[0082] In 204-6, the measured radiation I m and / or the simulated measured radiation J tot are resized such that the measured radiation I m and the simulated measured radiation J totHave the same resolution. The measured radiation I m Can be resized, and the simulated measured radiation J tot Can be resized, or both can be resized. After resizing, the measured radiation I m And the simulated measured radiation J tot Pixels of can have a one-to-one association.

[0083] In 204-7, determine the region of interest (ROI) of the measured radiation I m In some embodiments, the ROI can be the entire image, while in other embodiments, the ROI can be a sub-region of the image. In a specific example, the ROI can be the region where the signal is generally the lowest and thus the scattering effect is the greatest. The image region with the lowest signal can include the region corresponding to the central region of the object 108 projected onto the radiation detector 106. As another example, several ROIs can be placed around the volume, either at fixed intervals or at specific features of interest identified by computer vision. In some specific examples, the ROI can be determined by: registering the volume with a manually identified ROI on a CAD model; automatically searching for several large, wide, flat regions; automatically searching for flat regions with certain desired path lengths (e.g., longer paths, or medium paths, paths greater than a quarter of the image, etc.); automatically searching for regions with different path length distributions; finding some edges or corners in the image and analyzing the ROI around the edges or corners; finding the centroid of a cylinder block or circuit board and drawing an ROI around it; placing the ROI on a mixed material region or between dense objects, and so on.

[0084] In 204-8, generate a first vector of the pixel values of the measured radiation in the region of interest where the values are less than a first threshold. The first threshold can be selected such that all pixels of the ROI are selected. In other embodiments, the first threshold can be selected such that only pixels with values less than a specific signal level are selected. These pixel values are collected into the first vector.

[0085] In 204-9, generate a second vector of the pixel values of the simulated measured radiation corresponding to the first vector. As in 204-6, the measured radiation I m And / or the simulated measured radiation J tot Are resized, and the second vector of pixel values corresponding to the first vector of pixel values can be selected on a one-to-one basis.

[0086] In 204-10, a first polynomial is fitted to a first vector and a second vector. In 204-11, pixel values with a relative error of the first polynomial greater than a second threshold are removed from the first vector and the second vector. In 204-12, a second polynomial is fitted to the remaining pixel values of the first vector and the second vector. In 204-13, the gain includes the linear term of the second polynomial. The operations in 204-10 to 204-13 can be similar to the operations 204-1, 204-3, 204-4, and 204-5 described above regarding Figure 4 the operations 204-1, 204-3, 204-4, and 204-5.

[0087] Figure 6 is a flowchart of offset estimation in an image processing technique with scatter correction according to some embodiments. Operations 206-1 to 206-3 are examples of operations that can be included in Figure 2A or Figure 2B the operation 206. In some embodiments, for each row, a region with the lowest intensity (and where the influence of external scatter is significant) is determined, and then the simulated signal is compared with the measurement result to obtain a difference. The amount of the difference is the offset b. A threshold is used to determine whether the intensity is low enough. The threshold is the row minimum multiplied by a constant.

[0088] In some embodiments, operations 206-1 to 206-3 are performed for each of a plurality of sub-regions of the measured radiation I m . In 206-1, a threshold is generated based on the minimum value of the sub-region. For example, the minimum value within the sub-region can be scaled by a factor greater than 1 such as 1.1, 1.5, etc. As will be described in further detail below, this threshold can be used to divide pixels into pixels for which the offset b is calculated separately and pixels for which the offset b is calculated based on other separately calculated offset bs.

[0089] Specifically, in 206-2, a pixel offset is generated for each pixel in the sub-region having a value below the threshold. In some embodiments, the offset b can be calculated by Expression 9:

[0090] b(i, sub-region) = I m (i, sub-region) - λ × J tot (i, sub-region) Expression 9

[0091] In 206-3, the pixel offsets of the pixels in the sub-region having values below the threshold are combined into a default offset for the pixels in the sub-region having values greater than the threshold. For example, the offset b from 206-2 can be averaged to generate an offset b for other pixels. In other embodiments, other techniques such as median, weighted average, etc. can be used to combine the offset b.

[0092] Using a threshold greater than 1 allows for the partitioning of pixels used to generate the individual offset b to be controlled. For example, a threshold can be selected such that multiple pixels with lower values within a sub-region rather than a single pixel (i.e., the pixel with the minimum value) can be used to reduce the impact of noise.

[0093] As described above, an offset b can be generated for each pixel. Thus, the offset b is an offset image that includes the offset b of pixels having values below the threshold in the sub-region and a default offset. In some embodiments, the offset image can be smoothed based on the sub-region or based on the offset image as a whole. Smoothing can soften any discontinuities that may arise due to the different processing of certain pixels. Smoothing can be performed by applying a median filter, a box filter, a bilateral filter, a spline, a Gaussian filter, a low-pass filter, or other types of filters. Some filters such as the median filter have the advantage of using only one parameter and provide consistent results and improved image quality. In some embodiments, the size of the filter can be based on the size of the image. For example, the filter can have a size of 50 millimeters (mm), while the image has a size of approximately 2000 mm.

[0094] In some embodiments, the offset image can be clamped to have a limit. For example, the offset image can be clamped at a lower limit such that the offset image does not go below that lower limit. In a specific example, the lower limit can be zero or a negative number. Thus, large negative numbers can be clamped.

[0095] In some embodiments, by calculating the gain λ, there is a fundamental mapping between the simulated measured radiation J tot and the measured radiation I m and the offset b can be determined. In some embodiments, the offset b can include external scatter. It is desirable for the offset b to vary in a smooth manner between pixels. For example, in industrial imaging, the turntable commonly used to rotate the object 108 often generates external scatter, so the external scatter typically has a greater variation between rows than between columns (where the rows are orthogonal to the axis of rotation), so the external scatter can be estimated row by row. That is, the rows can define the sub-region. However, in other embodiments, the sub-region can be defined by the orientation of the radiation detector 106 relative to the object 114 that generates the external scatter. The sub-region can include columns, diagonal regions of pixels, curved regions of pixels, etc.

[0096] Figure 7 is a flowchart of offset estimation across a sub-region in an image processing technique with scatter correction according to some other embodiments. Operations 206-4 to 206-7 are examples of operations that can be included in Figure 2A or Figure 2B the operation 206 of

[0097] In 206-4, a third vector is generated that includes the minimum value of each of a plurality of sub-regions from the measured radiation I m For example, for each row in the measured radiation I m find the minimum value. Create a third vector that contains the minimum values from each row. The length of the third vector is the number of rows in the measured radiation I m .

[0098] In 206-5, the third vector is smoothed to generate a fourth vector. Multiple techniques can be used to perform the smoothing, such as by applying a median filter, box filter, bilateral filter, spline, Gaussian filter, low-pass filter, or other types of filters. The filter can typically operate over a length of several pixels. Thus, the fourth vector can include the smoothed minimum values row by row. In some embodiments, the median filter reduces noise without causing signal spillover or overshoot from adjacent rows to a single row, which can be helpful when the attenuation of the object in its axial direction (i.e., from row to row) has a sudden change

[0099] In 206-6, the fourth vector is scaled by a value greater than 1 to generate a fifth vector. As described above with respect to operation 206-1, the minimum value can be scaled by a factor greater than 1. Scaling the fourth vector generates a threshold similar to that in 206-1, but for each row. The scaling can be optimized for different applications by taking into account the trade-off between offset accuracy and noise reduction. Smaller values tend to give a more accurate offset b, while larger values that result in more pixels in the calculation can help reduce noise

[0100] In 206-7, an offset matrix is generated as offset b, where for each pixel of each sub-region of the measured radiation I m if the pixel value is lower than the value of the fifth vector associated with the sub-region, the corresponding pixel of the offset matrix is the difference between the pixel value of the measured radiation and the corresponding pixel value of the simulated measured radiation scaled by the gain λ. Additionally, for other pixels, the corresponding pixel value of the offset matrix is generated based on the other pixel values of the offset matrix for the sub-region. This operation 206-7 can be similar to operations 206-2 and 206-3 described above for each row

[0101] Figure 8A Shows the measured radiation image I m . Figure 8B Shows the simulated primary radiation image J p . Figure 8C Shows the simulated scattered radiation image J s . The simulated primary radiation J p and the simulated scattered radiation J s can be combined to form the simulated measured radiation Jtot 。

[0102] Figure 9A Shows the measured radiation I under the full-image ROI m and the corresponding simulated radiation image J tot of the first-pass second-order polynomial fit. According to Figures 8A - 8C , the y-axis represents the measured radiation I m , and the x-axis represents the simulated measured radiation J tot , where each pixel is a red dot and the fit curve is blue. The fit curve can be the result of operation 204-1 or other similar operations.

[0103] Figure 9B Shows the measured radiation image I with outliers having an error greater than 50% (>50%) excluded m and the corresponding simulated radiation image J tot of the second-pass second-order polynomial fit. After excluding the outliers, according to Figures 8A - 8C , the y-axis represents the measured radiation I m , and the x-axis represents the simulated measured radiation J tot , where each pixel is a red dot and the fit curve is blue. The linear term is 0.608, which is the gain λ of the projection shown here. The fit curve can be the result of operation 204-4 or other similar operations.

[0104] Figure 10 Shows a graph of a column vector. The blue dashed line is the vector with the minimum value for each row, as in operation 206-4. Then, before using the vector to generate the offset image, the vector is smoothed with one of the above filters to show the noise-reduced vector represented by the red solid line, as in operation 206-5.

[0105] Figure 11A Shows the offset image before smoothing from operation 206-7, and Figure 11B shows the offset image after smoothing. Since a threshold T is used for each row, only a part of the image has a direct calculation of the offset. As Figure 11A shown, the rest of the image is filled with the average of the available offsets from each row. After filtering with a box filter (e.g., a 50 mm filter), the offset becomes smooth and becomes the calculated external scatter.

[0106] Figure 12A Shows the reconstructed image without background or external scatter correction. Figure 12B Shows the reconstructed image with background or external scatter correction using the described technique. As shown, the image uniformity is improved.

[0107] As described above, some embodiments include a scalar gain λ and a spatially varying offset b. In other embodiments, the gain λ can remain scalar and the offset b is changed to a scalar. The scalar offset b can be referred to as a static offset or a static background. Both the offset b and the gain λ can be calculated differently. For example, high-intensity regions such as air regions can be used for gain calculation, and the region with the maximum attenuation (or low-intensity region) can be used for offset calculation.

[0108] Figure 13 is a flowchart of gain estimation in an image processing technique with scatter correction according to some embodiments. Operations 204-13 to 204-15 are examples of operations that can be included in Figure 2A operation 204.

[0109] In 204-13, the measured radiation I m and the simulated measured radiation J tot pixels are selected, where each pixel value tuple has an Euclidean magnitude higher than a threshold. For example, for the measured radiation I m and the simulated measured radiation J tot for each pixel value tuple, the Euclidean magnitude r can be calculated as in expression 10.

[0110]

[0111] g1 is a rough gain estimate. In some embodiments, g1 can be generated based on the measured radiation I m and the simulated measured radiation J tot ; however, in other embodiments, g1 can be 1. The higher intensity values of the measured radiation I m may have higher intensity values in the corresponding pixels of the simulated measured radiation J tot . These higher intensity values can give a better estimate of the gain λ.

[0112] This threshold is used to select the higher intensity values. For example, the threshold can be 95% of the maximum value of r (referred to as m3). 95% is just an example and can be any number close to 1 to select the desired amount of higher intensity pixels.

[0113] In 204-14, an intermediate gain g2 is generated based on the selected pixels. For example, the intermediate gain g2 can be generated using expression 11:

[0114] where all k satisfy the r(k)>0.95m3 expression 11

[0115] In 204-15, a gain λ is generated based on an offset and a second intermediate gain g2. As will be described in further detail below, an offset b can be generated and then used to further refine the gain λ.

[0116] Figure 14 is a flowchart of offset estimation in an image processing technique with scatter correction according to some other embodiments. In 206-10, pixels of the measured radiation and the simulated measured radiation are selected, where each pixel value tuple has an Euclidean magnitude below a threshold. Similar to operation 204-13, in 206-10, a threshold can be used to select pixels; however, the selection and threshold are implemented to select pixels with a lower Euclidean magnitude. The threshold can be based on a minimum Euclidean magnitude (m4). For example, the threshold can be 1.1 times m4. The value 1.1 is an example and can be any value greater than 1 to select a desired amount of lower-intensity pixels.

[0117] In 206-11, an offset b is generated based on the selected pixels. Expression 12 is an example of the selection criterion and the generation of the offset b.

[0118] b = average(I m (k) - g2J tot (k)) where all k satisfy r(k) < 1.10m4 Expression 12

[0119] Here, for the selected pixels, the scaled simulated measured radiation J m is subtracted from the measured radiation I tot . The scaling of the simulated measured radiation J tot is the intermediate gain g2. The offset b is the average of those values over all the selected pixels.

[0120] Figure 15 is a flowchart of gain and offset estimation in an image processing technique with scatter correction according to some embodiments. In 204-20, a first intermediate gain is generated based on the maximum value of the measured radiation and the maximum value of the simulated measured radiation. For example, the maximum value (m1) of the measured data I m and the maximum value (m2) of the simulated measured radiation J tot are found. The first intermediate gain g1 is estimated as m1 / m2. The rough gain estimate g1 may not be accurate but can be used as a starting point to generate an effective final gain λ and offset b.

[0121] In 204-21, the simulated measured radiation is normalized to the measured radiation I m with the first intermediate gain. In some embodiments, the simulated measured radiation J totScale by a first intermediate gain g1, as shown in expression 10 above. However, the calculation of the first intermediate gain g1 can be inverted. The simulated measured radiation J can be scaled by the reciprocal of the first intermediate gain g1 tot , and the measured radiation I can be scaled by the first intermediate gain g1 m , and so on. In any case, the simulated measured radiation J tot is normalized to the measured radiation I m .

[0122] In 204-22, the Euclidean magnitude of the normalized simulated measured radiation and the measured radiation is calculated for each pixel. The Euclidean magnitude can be calculated similar to operation 204-13 described above or the normalization techniques given appropriately

[0123] In 204-23, a first pixel of the measured radiation and the simulated measured radiation is selected, the first pixel corresponding to the normalized simulated measured radiation J tot and the measured radiation I m whose Euclidean magnitude is higher than a first threshold. In 204-24, a second intermediate gain g2 is generated based on the selected first pixel of the measured radiation I m and the simulated measured radiation J tot . These operations can be similar to the operations in 204-13 and 204-14 above

[0124] In 206-20, a second pixel of the measured radiation I m and the simulated measured radiation J tot is selected, the second pixel corresponding to the normalized simulated measured radiation J tot and the measured radiation I m whose magnitude is lower than a second threshold. This operation can be similar to operation 206-10

[0125] In 206-21, an offset is generated based on the selected second pixel of the measured radiation I m and the simulated measured radiation J tot . This operation can be similar to operation 206-11

[0126] In 204-25, a gain is generated based on the offset and the second intermediate gain g2. In some embodiments, the second intermediate gain g2 is adjusted to account for the presence of the offset b to arrive at a final gain g3 (or λ), and expression 13 is used to calculate this final gain

[0127]

[0128] The same threshold used above in Expression 11 (0.95 in this example) can be used here as the selection criterion for the pixels of the simulated measured radiation J in Expression 13. tot

[0129] In some embodiments, the static background offset can be calculated as in Expression 14.

[0130] b = I m (r == m4) – g2 * J tot (r == m4) Expression 14

[0131] In some embodiments, in the gain calculation described above with respect to Figures 3 - 5 the 0th term from the polynomial fit represents the total offset of the image. This value is not used as a static, scalar, or invariant offset because the total offset value is derived from most (if not all) of the pixels in the ROI. In some examples, it is more accurate to use only the darkest pixels for the static offset calculation (i.e., the intercept at the ordinate) compared to using all pixels with all intensities because they are closer to the ordinate.

[0132] Figure 16A shows the measured radiation image I m . FIG. 16 shows the simulated primary radiation image J p . Figure 16C shows the simulated scattered radiation image J s . Thus, the first intermediate gain g1 is calculated to be 0.518. The first intermediate gain g1 is used to scale the simulated total gain to plot a graph of the measured radiation versus the simulated radiation points. The distance of each data point from the origin is calculated. Those data points located within 5% of the farthest point (and used for calculating the gain) and those data points located within 10% of the closest point (and used for calculating the offset) are selected. The 5% and 10% thresholds are merely examples and can be different percentages, different values, etc. in other embodiments.

[0133] Figure 17 shows the normalized measured radiation image I m versus the simulated measured radiation image J tot . The y-axis represents the measured radiation I m , and the x-axis represents the simulated measured radiation J tot , where each pixel is a red dot and the fitted curve is blue. The green dot cluster in the upper right corner represents the data used in 204 - 23 (for gain), and the green dot cluster in the lower left corner represents the data used in 206 - 20 (for offset).

[0134] Figure 18A Shows the measured radiation image I m For reference. Figure 18B Shows the pixels (shown in white) used in the offset calculation in 206 - 20, and Figure 18C Shows the pixels (shown in white) used in the gain calculation in 204 - 23. Figures 18B - 18C Shows the image of the pixels showing the green dots in the scatter plot corresponding to Figure 17 .

[0135] Once the near and far data points are identified, these points can be used to calculate the gain λ and the offset b as described above. In this example, the gain λ is 0.488 and the offset b is 139.

[0136] In some embodiments, both the gain λ and the offset b can vary spatially. Having a spatially - dependent gain λ can be useful in many different applications. In particular, there can be many possible sources of inaccuracy in a model or simulation, including x - ray spectra, target composition, inherent filtration, heel effect, material composition and density of the object, scintillator response, detector linearity, etc., and many of these factors can manifest as non - linearities in the data. Using a Taylor series approximation, many of these non - linear effects can be at least partially compensated for by a spatially - varying gain λ. However, estimating a spatially - varying gain λ can pose some technical hurdles, which will be described below.

[0137] One challenge in simultaneously estimating both the gain and the background can be summarized as aiming to solve the third equation in Expression 6 (i.e., I m = λJ tot + b) for many pixels simultaneously, which can be reformulated as Expression 15:

[0138] I m [i]= λ[i]J tot [i]+ b[i] Expression 15

[0139] i is a positive integer and is a pixel index. If there are N pixels, then i ranges from 1 to N. Then expression 15 represents a system of equations with N equations, where N is typically large. If b and λ are independent of i (i.e., both b and λ are scalars), then there are N equations and two unknowns, so it is generally expected that the system of equations has a well-defined solution, and the problem is suitable for using an algorithm such as the above. If λ is a matrix but b is a scalar, then there are N equations with N + 1 unknowns and cannot be directly solved, but the above algorithm solves the problem by first using polynomial fitting (N equations, and the number of unknowns is equal to the number of polynomial coefficients, much less than N) to solve for the scalar λ, and then fixing λ and solving a selected set of b (N equations with at most N unknowns). However, if both λ and b are matrices, then without additional assumptions, there are N equations with 2N unknowns, so expression 14 is an ill-posed problem. For example, these degenerate solutions are all technically valid in expressions 16 - 18, but none of them are particularly meaningful:

[0140] For all pixels, λ[i] = 0 and b[i] = I m [i] Expression 16

[0141] For all pixels, λ[i] = I m [i] / J tot [i] and b[i] = 0 Expression 17

[0142] For all pixels, λ[i] = 1 and b[i] = I m [i] - J tot [i] Expression 18

[0143] Therefore, some additional assumptions or constraints can be used to define the problem well. Some embodiments include methods similar to the above methods, except that instead of finding λ for all pixels, λ is found for local sub-regions of the pixels, and the process is repeated for a set of sub-regions of the pixels.

[0144] Figure 19 is a flowchart of gain and offset estimation in an image processing technique with scatter correction according to some embodiments. In 204 - 30, an intermediate gain matrix is generated, including an intermediate gain for each of a plurality of sub-regions of the measured radiation. The intermediate gain can be calculated as described above, such as in operation 204 - 11. In 204 - 30, an offset for each sub-region is generated based on the associated intermediate gain. For example, the offset b can be generated as described above, such as in operation 206 - 11. Thus, even when the gain λ or the offset b is a scalar in a sub-region, the gain λ and the offset b can vary spatially at least across sub-regions.

[0145] Some embodiments incorporate smoothness criteria in both the gain λ and the offset b. The reason for using smoothness is that it has been observed that most non-ideal situations should be expected to vary slowly. Consider the cost function of Expression 19:

[0146]

[0147] A = J tot , m = I m , obtaining the vector norm for all i, ▽ is the gradient (i.e., the spatial derivative) operator, and α and β are scalar parameters. Thus, the first term on the right side of Expression 19 (i.e., represents the total squared error obtained by summing over all pixels in Expression 14, while the second term (i.e., ) penalizes the roughness of λ (i.e., the opposite of smoothness), and the third term (i.e., ) penalizes the roughness of b. Note that λ is spatially constant if and only if ▽λ = 0 for all i, and thus if and only if the second term on the right side of Expression 19 is zero. Additionally, when minimizing E, the larger α is, the more likely the second term is to be close to zero. Thus, α serves as the smoothness control for the gain λ, where minimizing E using a larger value of α will result in a smoother λ, and minimizing E using a smaller value of α will result in a rougher λ. Similarly, β serves as the smoothness control for the offset b.

[0148] The first-order optimality criteria for Expression 19 are in Expressions 20 - 21:

[0149]

[0150]

[0151] Rewriting Expressions 20 - 21 in matrix form, minimizing Expression 19 is equivalent to solving for λ and b in Expression 22:

[0152]

[0153] Expression 22 has 2N equations and 2N unknowns and can be solved using a well-known linear system solver, or Expression 19 can be directly solved using least squares or a quadratic optimization solver.

[0154] There are many reasonable variations of the cost function in expression 18, including non - quadratic error terms, or other ways of representing gain and offset values. For example, the gain and offset values can be represented by lower - order splines (or other transforms), where λ = Fc and b = Gd, where F and G are the spline (or transform) bases, and c and d are the spline (or transform) coefficients. Then, expression 18 can be represented by lower - order splines as expression 22 or expression 23, either of which can be solved by a similar technique used to solve expression 19:

[0155]

[0156] After solving for c and d, apply λ = Fc and b = Gd to obtain the desired gain λ and offset b values.

[0157] In some embodiments, offset extrapolation can be performed using other more complex methods, including but not limited to linear interpolation or extrapolation, expansion of edge pixels, splines, pixel repair, sparse image recovery, etc.

[0158] In some embodiments, the calculated offset b can have a negative value. Negative offset b values can be caused by different reasons, such as reasonable errors in calculations, beam hardening effects that are not fully accounted for, other inconsistencies in the measured data, or other pre - processing steps with inaccuracies or over - corrections. Accepting negative scatter as it is may be preferred or desirable because even if a negative offset may not be physically realistic, a negative offset b can often provide a good mathematical approximation to correct other non - ideal situations in the data. However, in other examples, applying a lower limit to clamp the negative scatter to a fixed minimum value may be preferred or desirable. This can be achieved, for example, by using quadratic optimization to solve expression 19 and incorporating the linear constraint b ≥ 0.

[0159] A scalar offset or static background can be useful when external scatter is fairly uniform across the detector, or when a constant offset is left intentionally or unintentionally in the offset calibration of the detector. The described methods and techniques are effective when the attenuation in the air region or regions with very small attenuation in the projection (which is common in many scans) is considered. The computational steps involved are robust and can be performed quickly, and in some examples, in real - time.

[0160] Some embodiments can be used with spatially varying backgrounds or static backgrounds, and can also be used to correct data without offset correction. In an example, if there is external scatter, the offset b term represents the sum of the offset value plus the external scatter. If there is no external scatter, the offset b represents only the offset value.

[0161] The 3D voxelized representation of the object usually comes from a first-pass CBCT reconstruction without correction or with some less accurate scatter correction such as kernel-based scatter estimation. However, the 3D voxelized representation of the object can alternatively come from a CAD model, or a registered reconstruction of different products of the same object design. These latter possibilities seem to be good candidates for online inspection.

[0162] CBCT reconstruction can be iterated, where the described techniques are used to correct a set of projection images and used to make a new reconstruction, which is then used to calculate material and density images for another pass of the CBCT reconstructed images. This correction and reconstruction can be repeated any number of times, but in some examples, sufficiently good image quality appears after two passes.

[0163] The described techniques can be used in conjunction with FDK to reconstruct data (where FDK is a cone-beam algorithm proposed by Feldkamp, Davis, and Kress—a widely used filtered backprojection [or backprojection] algorithm for 3D CBCT reconstruction, see LA Feldkamp et al., "Practical cone-beam algorithm", J. Opt. Soc. Am. Al, 612-619, 1984), which is incorporated by reference in its entirety. However, the described techniques are not dependent on any particular reconstruction algorithm. The described techniques can be used with a variety of algorithms, including filtered backprojection, backprojection filtering, Hilbert's method, pi-lines, Katzevich's method, machine learning methods, or various iterative schemes.

[0164] Figure 20 1 shows a block diagram of an exemplary background radiation estimation and correction device. Background radiation estimation and correction device 300 may include a background radiation estimator 310. Background radiation estimator 310 may be configured to generate a gain λ and an offset b as described above. Background radiation estimator 310 may include a processor configured to receive the measured radiation I as described above. m The background radiation estimator 310 may include a model simulator 314 and an optional object modeler 316. The model simulator 314 may be configured to generate simulations as described above.

[0165] The background radiation estimator 310 may include an offset estimator 340 and a gain estimator 320. The gain estimator 320 and the offset estimator 340 may be configured to generate the gain λ and the offset b as described above. For example, the gain estimator 320 may be configured to perform the above Figure 2B , Figures 3 - 5 , Figure 13 , Figure 15 and Figure 19Operations such as operation 204, operations 204-1 to 204-25, and operation 204-30, etc. The offset estimator 340 may be configured to perform the above operations regarding Figure 2A , Figure 2B , Figure 6 , Figure 7 , Figure 14 , Figure 15 and Figure 19 Operations such as operation 206, operations 206-1 to 206-7, 206-10, 206-11, 206-20, 206-21, and 206-30, etc. The gain estimator 320 and the offset estimator 340 may be configured to communicate with each other to implement the above iterative process.

[0166] The gain estimator 320 may include a resizer 322, an ROI generator 324, a threshold selector 326, a vector generator 328, a polynomial fitter 330, a calculator 322, etc. to perform the above operations. The offset estimator 340 may include a resizer 322, a pixel selector 344, a vector generator 328, a smoother 348, a calculator 322, an extrapolator 352, an image generator 354, etc. to perform the above operations. For example, the resizer 322 may be configured to perform operation 204-6, etc. The ROA generator 324 may be configured to perform operation 204-7, etc. The threshold selector 326 may be configured to select thresholds for operations 204-3, 204-8, 204-11, 204-13, 204-23, 206-1, 206-2, 206-10, 206-20, etc. The vector generator 328 may be configured to generate vectors associated with operations 204-1, 204-3, 204-8, 204-9, 204-11, 206-4, 206-5, 206-6, etc. The polynomial fitter 330 may be configured to perform operations 204-1, 204-4, 204-10, 204-12, etc. The calculator 322 may be configured to perform calculations in the above various operations and equations.

[0167] The background estimation radiation estimation and correction device 300 may include a scattered radiation estimator 360 and a primary radiation estimator 362. The scattered radiation estimator 360 may be configured to perform the above operation of generating scattered radiation I s . The primary radiation estimator 362 may be configured to generate primary radiation I p as described above.

[0168] The background estimation radiation estimation and correction device 300 may include a processor such as processor 112, an associated memory, a communication interface, etc. to receive the above data, perform the above processing, and transmit data, such as the estimated or corrected primary radiation I p .

[0169] The foregoing summary is illustrative and not intended to be limiting in any way. In addition to the above examples, other aspects, features, and advantages of the present invention will become apparent by reference to the accompanying drawings, the following detailed description, and the appended claims.

[0170] Some embodiments include a method for estimating background radiation from an unknown source in a tomographic scan, the method comprising: receiving measured radiation (I m ) obtained from a radiation detector, wherein the measured radiation (I m ) includes primary radiation (I p ) passing through an object in the field of view (FOV) of the radiation detector and scattered radiation (I s ) including object scattered radiation from the object in the FOV and background scattered radiation from matter outside the FOV; modeling the object based on the measured radiation (I m ) to generate a modeled object; simulating radiation transmission through the modeled object to obtain simulated primary radiation (J p ) from the modeled object and simulated scattered radiation (J s ) from the modeled object, wherein the combined simulated radiation (J tot ) includes the simulated primary radiation (J p ) and the simulated scattered radiation (J s ) (J tot = J p + J s ); and estimating background scattered radiation (offset or b) based on the measured radiation (I m ) and the combined simulated radiation (J tot ).

[0171] In some embodiments, the estimation of background scattered radiation is spatially varying.

[0172] In some embodiments, estimating background scattered radiation (offset or b) further includes: sizing the measured radiation (I m ) to obtain a measured radiation image and sizing the combined simulated radiation (J tot)An analog radiation image that has been resized to a combination of pixels having a size similar to the measured radiation image; selecting, in each row of the measured radiation image, the pixel having the minimum intensity value, wherein each pixel having the minimum intensity value is a minimum pixel; generating a measured column vector (V1) based on the minimum pixel of each row; smoothing the measured column vector (V1) to generate a smoothed measured column vector (V2); multiplying the smoothed measured column vector (V2) by a multiplier (A) greater than one to generate a threshold column vector having row thresholds (T(row)=V2(row)*A); calculating the offset (offset(i,row)) of each pixel (p(i,row)) in the row having an intensity value below the corresponding row threshold of the row to which the pixel belongs, wherein each pixel offset is equal to the measured pixel value minus the corresponding combined analog radiation pixel value multiplied by a scaling factor (gain or λ) (offset(i,row)=I m (i,row)–λ*J tot (i,row)); extrapolating the offset to each pixel in the row having an intensity value higher than the corresponding row threshold based on the pixel offset; generating an offset image having a size similar to the size of the measured radiation image based on the pixel offset calculation and pixel offset extrapolation; and smoothing the offset image to generate a smoothed offset image, wherein the estimation of background scattered radiation (offset or b) is the smoothed offset image.

[0173] In some embodiments, a box filter, bilateral filter, median filter, or another low-pass filter is used to smooth the measured column vector (V1) to generate a smoothed measured column vector (V2), and a box filter, bilateral filter, Gaussian filter, low-pass filter, median filter, spline, or another low-pass filter is used to smooth the offset image to generate a smoothed offset image.

[0174] In some embodiments, extrapolating the offset for each pixel in the row further includes: averaging the pixel offsets in each row to generate an average row offset for each row; and setting the pixel offset extrapolation to the average row offset for each row.

[0175] In some embodiments, the method further includes setting a lower limit for the offset (offset(i)) for each pixel (p(i)).

[0176] In some embodiments, the method further includes generating a scaling factor (gain or λ) based on the measured radiation (I m ) and (divided by) the combined analog radiation (J tot ) (or λ = I m / J tot ).

[0177] In some embodiments, generating the scaling factor (gain or λ) further includes: subjecting the measured radiation (Im ) is sized to the measured radiation image, and the combined simulated radiation (J tot ) is sized to a combined simulated radiation image having pixels of a size similar to the measured radiation image; similar regions of interest (ROIs) are selected in the measured radiation image and the combined simulated radiation image; and a scaling factor (gain or λ) is calculated for pixels of similar size having similar ROIs.

[0178] In some embodiments, the scaling factor (gain or λ) is a scalar.

[0179] In some embodiments, calculating the scaling factor (gain or λ) for pixels of similar size further includes: selecting an inclusion threshold (T1); generating a first measurement vector (Y1) from each pixel in the measured radiation image having a measurement below the inclusion threshold (T1), wherein each pixel in the first measurement vector (Y1) having a measurement below the inclusion threshold (T1) is an included measurement pixel; generating (adjoint) a first simulated vector (X1) from each pixel in the combined simulated radiation image corresponding to the included measurement pixels; polynomially fitting the first measurement vector (Y1) to the first simulated vector (X1); calculating the relative fitting error of the included measurement pixels in the first measurement vector; selecting an error threshold (T2); generating a second measurement vector (Y2) from each pixel in the first measurement vector (Y1) having a fitting error below the error threshold (T2), wherein each pixel in the second measurement vector (Y2) having a fitting error below the error threshold (T2) is a low error measurement pixel; generating a second simulated vector (X2) from each pixel in the first simulated vector (X1) corresponding to the low error measurement pixels; polynomially fitting the second measurement vector (Y2) to the second simulated vector (X2); and generating the scaling factor (gain or λ) from the linear term coefficient of the polynomial fit of the second measurement vector (Y2) and the second simulated vector (X2).

[0180] In some embodiments, calculating the scaling factor (gain or λ) for pixels of similar size further includes: calculating a gain ratio (λ(i)) of the measured radiation (I m ) to the combined simulated radiation (J tot ) for each pixel (p(i)), and averaging the gain ratios (λ(i)) to generate the scaling factor (gain or λ); or calculating a gain ratio (λ(i)) of the measured radiation (I m ) to the combined simulated radiation (J tot ) for each pixel (p(i)), and generating the scaling factor (gain or λ) based on the median gain ratio; or for each pixel (p(i)) the combined simulated radiation (J tot)Average to generate an average combined simulated radiation, and for each pixel (p(i)), the measured radiation (I m )Average to generate an average measured radiation, and calculate a scaling factor (gain or λ) based on the ratio of the average measured radiation to the average combined simulated radiation.

[0181] In some embodiments, the scaling factor (gain or λ) and the background scattered radiation (offset or b) are each selected from the group consisting of a spatially invariant scalar or a spatially varying matrix.

[0182] In some embodiments, the background scattered radiation (offset or b) is spatially invariant, and the scaling factor (gain or λ) is spatially invariant.

[0183] In some embodiments, generating the scaling factor (gain or λ) uses at least one high-intensity region of a mathematical combination of the measured radiation (I m ), the combined simulated radiation (J tot ), or the measured radiation (I m ) and the combined simulated radiation (J tot ); and estimating the background scattered radiation (offset or b) uses at least one low-intensity region of a mathematical combination of the measured radiation (I m ), the combined simulated radiation (J tot ), or the measured radiation (I m ) and the combined simulated radiation (J tot ).

[0184] In some embodiments, at least one high-intensity region is used for gain calculation, and at least one low-intensity region is used for offset calculation, where: the high-intensity region consists of pixel positions where the pixel value is in the high percentile of the pixel values of all pixels, where optionally, the high percentile is in the range between 80% and 100%, and the low-intensity region consists of pixel positions where the pixel value is in the low percentile of the pixel values of all pixels, where optionally, the low percentile is in the range between 0% and 20%, and the pixel value can be the simulated radiation, the measured radiation, or a mathematical combination of the simulated radiation and the measured radiation.

[0185] In some embodiments, the background scattered radiation (offset or b) is spatially varying, and the scaling factor (gain or λ) is spatially varying.

[0186] In some embodiments, the parameters of the modeled object are selected from the group consisting of object density, linear attenuation coefficient, object chemical composition, and object atomic number.

[0187] In some embodiments, simulating radiative transfer through a modeled object and scattered radiation from the object includes using a kernel-based scatter estimator, a (linear) Boltzmann equation solver (LBES), other finite element deterministic photon transport solvers, or Monte Carlo simulators.

[0188] In some embodiments, the estimation of scattered radiation (I s ) is a scaling factor (gain or λ) multiplied by the simulated scattered radiation (J s ) plus an estimate of the background scattered radiation (offset or b) (or I s = λJ s + b).

[0189] Some embodiments include a method for correcting a tomographic scan with background radiation from an unknown source, the method comprising: generating a scaling factor (gain or λ) as described above and estimating the background scattered radiation (offset or b); estimating the scattered radiation (I s ) according to the scaling factor (gain or λ) multiplied by the simulated scattered radiation (J s ) plus the estimate of the background scattered radiation (offset or b) (or I s = λJ s + b); estimating the primary radiation (I m ) by subtracting the estimate of the scattered radiation (I s ) from the measured radiation (I p ).

[0190] Some embodiments include a method for correcting a tomographic scan with background radiation from an unknown source, the method comprising: receiving the measured radiation (I m ) from a radiation detector, wherein the measured radiation (I m ) includes the primary radiation I p passing through an object in the field of view (FOV) of the radiation detector and scattered radiation (I s ) including object scattered radiation from the object in the FOV and background scattered radiation from matter outside the FOV (I m = I p + I s ); receiving the combined simulated radiation (J m ) from a radiation simulator of a model object generated from the measured radiation (I tot ), wherein the combined simulated radiation J tot ) includes the simulated primary radiation (J p ) from the modeled object and the simulated scattered radiation (J s ) from the modeled object (J tot = J p + J s); Generate a scaling factor (gain or λ); Estimate the background scattered radiation (offset or b); Estimate the scattered radiation (I s ) by multiplying the simulated scattered radiation (J s ) by the scaling factor (gain or λ) and adding the estimated background scattered radiation (offset or b) (or I s = λJ s + b); Estimate the primary radiation (I m ) by subtracting the estimated scattered radiation (I s ) from the measured radiation (I p ).

[0191] In some embodiments, the method further includes presenting an estimate of the primary radiation (I p ); or wherein estimating the primary radiation (I p ) performs a simple subtraction of the estimated scattered radiation (I m ) from the measured radiation (I s ) (or I p = I m - I s ); or wherein estimating the primary radiation (I p ) performs a smoothed subtraction (I p = I m (1 - smooth(I s / I m )).

[0192] Some embodiments include a method for estimating background radiation from an unknown source in a tomographic scan, the method comprising: measuring radiation using a radiation detector, wherein the measured radiation (I m ) includes primary radiation (I p ) passing through an object in the field of view (FOV) of the radiation detector and scattered radiation (I s ) including object scattered radiation from the object in the FOV and background scattered radiation from material outside the FOV; modeling the object based on the measured radiation (I m ) to obtain a modeled object; simulating radiation transmission through the modeled object to obtain simulated primary radiation (J p ) from the modeled object and simulated scattered radiation (J s ) from the modeled object, wherein the combined simulated radiation (J tot ) includes the simulated primary radiation (J p ) and the simulated scattered radiation (J s ) (J tot = J p + J s ); and based on the measured radiation (I m ) and the combined simulated radiation (Jtot ) to estimate background scattered radiation (offset or b).

[0193] Some embodiments include a method for estimating background radiation from an unknown source in a tomographic scan, the method comprising: receiving measured radiation (I m ) obtained from a radiation detector, wherein the measured radiation (I m ) includes primary radiation (I p ) passing through an object in the field of view (FOV) of the radiation detector and scattered radiation (I s ) including object scattered radiation from the object in the FOV and background scattered radiation from matter outside the FOV; receiving combined simulated radiation (J m ) modeling the object based on the measured radiation (I tot ), wherein the combined simulated radiation (J tot ) includes simulated primary radiation (J p ) and simulated scattered radiation (J s ) (J tot = J p + J s ); and estimating background scattered radiation (offset or b) based on the measured radiation (I m ) and the combined simulated radiation (J tot ).

[0194] Some embodiments include at least one non - transitory machine - readable storage medium including a plurality of instructions adapted to be executed to implement the methods described herein.

[0195] Some embodiments include a background radiation estimator 310, including: a receiver 312 for obtaining measured radiation (I m ) from a radiation detector, wherein the measured radiation (I m ) includes primary radiation (I p ) passing through an object in the field of view (FOV) of the radiation detector and scattered radiation (I s ) including object scattered radiation from the object in the FOV and background scattered radiation from matter outside the FOV; a model simulator 314 for simulating radiation transmission through a modeled object based on the measured radiation (I m ) of the object to obtain simulated primary radiation (J p ) from the modeled object, simulated scattered radiation (J s ) from the modeled object, wherein the combined simulated radiation (J tot ) includes the simulated primary radiation (J p ) and the simulated scattered radiation (Js )(J tot = J p + J s ); and an offset estimator 340 configured to estimate background scattered radiation (offset or b) based on the measured radiation (I m ) and the combined simulated radiation (J tot ).

[0196] In some embodiments, the offset estimator 340 further includes: a sizing adjuster 322 configured to size the measured radiation (I m ) into a measured radiation image and size the combined simulated radiation (J tot ) into a combined simulated radiation image having pixels of a similar size to the measured radiation image; or a pixel selector 344 configured to select pixels having minimum intensity values in each row of the measured radiation image, wherein each pixel having a minimum intensity value is a minimum pixel; a vector generator 328 configured to generate a measured column vector (V1) based on the minimum pixels of each row; a smoother 348 configured to smooth the measured column vector (V1) to generate a smoothed measured column vector (V2) and configured to smooth the offset image to generate a smoothed offset image, wherein the estimation of the background scattered radiation (offset or b) is the smoothed offset image; a calculator / processor 332 configured to multiply the smoothed measured column vector (V2) by a multiplier (A) greater than one to generate a threshold column vector with row thresholds (T(row) = V2(row) * A) and configured to calculate the offset (offset(i, row)) of each pixel (p(i, row)) in the row having an intensity value lower than the corresponding row threshold of the row to which the pixel belongs, wherein each pixel offset is equal to the measured pixel value minus the corresponding combined simulated radiation pixel value multiplied by a scaling factor (gain or λ) (offset(i, row) = I m (i, row) – λ * J tot (i, row)); an extrapolator 352 configured to extrapolate the offset to each pixel in the row having an intensity value higher than the corresponding row threshold based on the pixel offset; and an imaging generator 354 configured to generate an offset image having a similar size to the measured radiation image based on the pixel offset calculation and pixel offset extrapolation.

[0197] In some embodiments, the background radiation estimator 310 further includes a gain estimator 320 configured to generate a scaling factor (gain or λ) from the measured radiation (I m ) and the combined simulated radiation (J tot ).

[0198] In some embodiments, the gain estimator 320 further includes a size adjuster 322 configured to adjust the measured radiation (I m ) is resized to become the measured radiation image, and the combined simulated radiation (J tot ) is resized to become a simulated radiation image having a combination of pixels of similar size to the measured radiation image; a region of interest (ROI) generator 324, the ROI generator being configured to select a similar region of interest (ROI) in the measured radiation image and the combined simulated radiation image; a threshold selector 326, the threshold selector being configured to select an inclusion threshold (T1), and being configured to select an error threshold (T2); a vector generator 328, the vector generator being configured to generate a first measurement vector (Y1) based on each pixel in the measured radiation image having a measurement result lower than the inclusion threshold (T1), wherein each pixel in the first measurement vector (Y1) having a measurement result lower than the inclusion threshold (T1) is an included measurement pixel, and being configured to generate (accompany) a first simulation vector (X1) based on each pixel in the combined simulated radiation image corresponding to the included measurement pixel; a polynomial fitter 330, the polynomial fitter being configured to convert A first measurement vector (Y1) is polynomially fitted to the first simulation vector (X1) and a second measurement vector (Y2) is polynomially fitted to the second simulation vector (X2); a calculator / processor 332, which is configured to calculate the relative fitting error of the measurement pixels contained in the first measurement vector; and wherein the vector generator 328 is also configured to generate a second measurement vector (Y2) based on each pixel in the first measurement vector (Y1) having a fitting error lower than an error threshold (T2), wherein each pixel in the second measurement vector (Y2) having a fitting error lower than the error threshold (T2) is a low-error measurement pixel, and is also configured to generate a second simulation vector (X2) based on each pixel in the first simulation vector (X1) corresponding to a low-error measurement pixel; and wherein the calculator / processor 332 is also configured to generate a scaling factor (gain or λ) based on the coefficient of the linear term of the polynomial fit from the second measurement vector (Y2) and the second simulation vector (X2).

[0199] In some embodiments, the background radiation estimator 310 also includes a scattered radiation estimator 360, which is configured to multiply the simulated scattered radiation (J) by a scaling factor (gain or λ). s ) plus an estimate of the background scattered radiation (offset or b) to estimate the scattered radiation (I s )(or I s =λJ s + b); and a primary radiation estimator 362, the primary radiation estimator being configured to be measured by the radiation (Im ) subtracts the scattered radiation (I s ) estimate to estimate the primary radiation (I p ).

[0200] Some embodiments include a background radiation estimator for estimating background radiation from an unknown source in a tomographic scan, including: a measurement radiation receiving device for obtaining measurement radiation (I m ) from a radiation detector, wherein the measured radiation (I m ) includes primary radiation (I p ) passing through an object in the field of view (FOV) of the radiation detector and scattered radiation (I s ) including object scattered radiation from an object in the FOV and background scattered radiation from matter outside the FOV; a model simulation device for simulating radiation transmission through a modeled object based on the measured radiation (I m ) of the object to obtain simulated primary radiation (J p ) from the modeled object, simulated scattered radiation (J s ) from the modeled object, wherein the combined simulated radiation (J tot ) includes the simulated primary radiation (J p ) and the simulated scattered radiation (J s )(J tot = J p + J s ); and an offset estimation device for estimating background scattered radiation (offset or b) based on the measured radiation (I m ) and the combined simulated radiation (J tot ).

[0201] In some embodiments, the background radiation estimator further includes an object modeling device for generating a modeled object based on the measured radiation (I m ); or a gain estimation device for generating a scaling factor (gain or λ) based on the measured radiation (I m ) and the combined simulated radiation (J tot ).

[0202] In some embodiments, the background radiation estimator further includes: a sizing device for sizing the measured radiation (I m ) into a measured radiation image and sizing the combined simulated radiation (J tot)An analog radiation image that has been size-adjusted to be a combination of pixels having a size similar to the measured radiation image; or a pixel selection device for selecting the pixels having the minimum intensity value in each row of the measured radiation image, wherein each pixel having the minimum intensity value is a minimum pixel; or a vector generation device for generating a measured column vector (V1) from the minimum pixels of each row; or a smoothing device for smoothing the measured column vector (V1) to generate a smoothed measured column vector (V2), and smoothing the offset image to generate a smoothed offset image, wherein the estimate of the background scattered radiation (offset or b) is the smoothed offset image; or a calculation / processing device for multiplying the smoothed measured column vector (V2) by a multiplier (A) greater than one to generate a threshold column vector having row thresholds (T(row)=V2(row)*A), and calculating the offset (offset(i,row)) of each pixel (p(i,row)) in the row having an intensity value lower than the corresponding row threshold of the row to which the pixel belongs, wherein each pixel offset is equal to the measured pixel value minus the corresponding combined analog radiation pixel value multiplied by a scaling factor (gain or λ) (offset(i,row)=I m (i,row)–λ*J tot(i, row)); or an extrapolation device for extrapolating the offset to each pixel in the row having an intensity value higher than the corresponding row threshold based on the pixel offset; or an imaging generation device for generating an offset image having a size similar to the measured radiation image based on the pixel offset calculation and pixel offset extrapolation; or a threshold selection device for selecting an inclusion threshold (T1) and for selecting an error threshold (T2); or a vector generation device for generating a first measurement vector (Y1) based on each pixel in the measured radiation image having a measurement result lower than the inclusion threshold (T1), wherein each pixel in the first measurement vector (Y1) having a measurement result lower than the inclusion threshold (T1) is an included measurement pixel, and for generating an (adjoint) first simulation vector (X1) based on each pixel in the combined simulated radiation image corresponding to the included measurement pixel; or a polynomial fitting device for polynomially fitting the first measurement vector (Y1) to the first simulation vector (X1) and for polynomially fitting the second measurement vector (Y2) to the second simulation vector (X2); or a calculation / processing device for calculating the relative fitting error of the measurement pixels included in the first measurement vector; or a vector generation device for generating a second measurement vector (Y2) based on each pixel in the first measurement vector (Y1) having a fitting error lower than the error threshold (T2), wherein each pixel in the second measurement vector (Y2) having a fitting error lower than the error threshold (T2) is a low-error measurement pixel, and for generating a second simulation vector (X2) based on each pixel in the first simulation vector (X1) corresponding to the low-error measurement pixel; or a gain estimation device for generating a scaling factor (gain or λ) based on the coefficient of the linear term of the polynomial fitting from the second measurement vector (Y2) and the second simulation vector (X2).

[0203] Some embodiments include a background radiation correction device for correcting a tomographic scan having background radiation from an unknown source, comprising: a background radiation estimator as described above; a scattered radiation estimation device for estimating scattered radiation (I s ) based on multiplying a scaling factor (gain or λ) by simulated scattered radiation (J s ), or I s = λJ s + b), plus an estimate of background scattered radiation (offset or b); and a primary radiation estimation device for estimating primary radiation (I m ) by subtracting an estimate of the scattered radiation (I s ) from the measured radiation (I p)。Some embodiments include a method comprising: receiving measured radiation obtained from a radiation detector that receives radiation passing through an object 200; simulating measured radiation 202 obtained from a radiation detector that receives radiation passing through an object; generating an offset 206 based on the measured radiation and the simulated measured radiation; estimating scattered radiation 208, 208' based on the offset; and estimating primary radiation 210 based on the estimated scattered radiation.

[0204] In some embodiments, the method further comprises generating a gain 204 based on the measured radiation and the simulated measured radiation; wherein estimating the scattered radiation further comprises estimating the scattered radiation 208' based on the gain and the offset.

[0205] In some embodiments, the method further comprises generating estimated scattered radiation based on the gain, the offset, and a simulated scattered radiation component of the simulated measured radiation; and generating the estimated primary radiation based on the estimated scattered radiation and the measured radiation.

[0206] In some embodiments, the method further comprises fitting a polynomial to a first vector of pixel values of the measured radiation and a second vector of pixel values of the simulated measured radiation 204-1; and generating a gain 204-2 based on the polynomial.

[0207] In some embodiments, the gain is a linear term of the polynomial.

[0208] In some embodiments, the polynomial is at least a second-order polynomial.

[0209] In some embodiments, the method further comprises fitting a first polynomial to a first vector of pixel values of the measured radiation and a second vector of pixel values of the simulated measured radiation 204-1; reducing the magnitudes of the first vector and the second vector to remove pixel values for which the error of the first polynomial is greater than a threshold 204-3; fitting a second polynomial to the reduced first vector and the reduced second vector 204-4; and generating a gain 204-5 based on the second polynomial.

[0210] In some embodiments, the method further includes adjusting the magnitude of the measured radiation and / or the simulated measured radiation such that the measured radiation and the simulated measured radiation have the same resolution 204-6; determining a region of interest 204-7 of the measured radiation; generating a first vector 204-8 of pixel values of the measured radiation in the region of interest with values less than a first threshold; generating a second vector 204-9 of pixel values of the simulated measured radiation corresponding to the first vector; fitting a first polynomial to the first vector and the second vector 204-10; removing pixel values from the first vector and the second vector for which the relative error of the first polynomial is greater than a second threshold 204-11; fitting a second polynomial to the remaining pixel values of the first vector and the second vector 204-12; wherein the gain includes the linear term of the second polynomial; generating a third vector 206-4 including a minimum value from each of a plurality of sub-regions of the measured radiation; smoothing the third vector to generate a fourth vector 206-5; scaling the fourth vector by a value greater than 1 to generate a fifth vector 206-6; and generating an offset matrix as an offset, wherein for each pixel of each sub-region of the measured radiation: if the value of the pixel is lower than the value of the fifth vector associated with the sub-region, the value of the corresponding pixel of the offset matrix is the difference between the pixel value of the measured radiation and the pixel value of the corresponding pixel of the simulated measured radiation scaled by the gain; and for other pixels, generating the value of the corresponding pixel of the offset matrix based on the other pixels of the offset matrix of the sub-region 206-7.

[0211] In some embodiments, the method further includes selecting pixels of the measured radiation and the simulated measured radiation, wherein each pixel value tuple has an Euclidean magnitude higher than a threshold 204-13; generating an intermediate gain based on the selected pixels 204-14; and generating a gain based on the offset and a second intermediate gain 204-15.

[0212] In some embodiments, the method further includes generating a first intermediate gain 204-20 based on a maximum value of the measured radiation and a maximum value of the simulated measured radiation; normalizing the simulated measured radiation to the measured radiation having the first intermediate gain 204-21; calculating, for each pixel, an Euclidean metric of the normalized simulated measured radiation and the measured radiation 204-22; selecting a first pixel of the measured radiation and the simulated measured radiation, the first pixel corresponding to a pixel of the normalized simulated measured radiation and the measured radiation for which the Euclidean metric is higher than a first threshold 204-23; generating a second intermediate gain 204-24 based on the selected first pixel of the measured radiation and the simulated measured radiation; selecting a second pixel of the measured radiation and the simulated measured radiation, the second pixel corresponding to a pixel of the normalized simulated measured radiation and the measured radiation for which the metric is lower than a second threshold 206-20; generating an offset 206-21 based on the selected second pixel of the measured radiation and the simulated measured radiation; and generating a gain 204-25 based on the offset and the second intermediate gain.

[0213] In some embodiments, the method further includes generating an intermediate gain matrix that includes an intermediate gain for each of a plurality of sub-regions of the measured radiation 204-30; and generating an offset for each of the sub-regions based on the associated intermediate gain 206-30.

[0214] In some embodiments, for each of a plurality of sub-regions of the measured radiation: generating a threshold 206-1 based on a minimum value of the sub-region; generating a pixel offset for each pixel in the sub-region having a value below the threshold 206-2; and combining the pixel offsets of the pixels in the sub-region having values below the threshold into a default offset for pixels in the sub-region having values greater than the threshold 206-3; wherein the offset is an offset image that includes the pixel offsets of the pixels in the sub-region having values below the threshold and the default offset.

[0215] In some embodiments, the method further includes selecting pixels of the measured radiation and the simulated measured radiation, wherein each pixel value tuple has an Euclidean metric below a threshold 206-10; and generating an offset 206-11 based on the selected pixels.

[0216] Some embodiments include a system comprising: a communication interface; a memory; and a processor configured to: receive measured radiation obtained from a radiation detector that receives radiation passing through an object; simulate the measured radiation obtained from the radiation detector that receives radiation passing through an object; generate an offset based on the measured radiation and the simulated measured radiation; estimate scattered radiation based on the offset; and estimate primary radiation based on the estimated scattered radiation.

[0217] In some embodiments, the processor is further configured to: fit a first polynomial to a first vector of pixel values of the measured radiation and a second vector of pixel values of the simulated measured radiation; reduce the magnitudes of the first vector and the second vector to remove pixel values for which the error of the first polynomial is greater than a threshold; fit a second polynomial to the reduced first vector and the reduced second vector; generate a gain based on the second polynomial; and estimate scattered radiation based on the gain and the offset.

[0218] In some embodiments, the processor is further configured to: select pixels of the measured radiation and the simulated measured radiation, wherein each pixel value tuple has an Euclidean magnitude higher than a threshold; generate an intermediate gain based on the selected pixels; generate a gain based on the offset and a second intermediate gain; and estimate scattered radiation based on the gain and the offset.

[0219] In some embodiments, the processor is further configured to: generate a threshold based on the minimum value of a sub-region; generate a pixel offset for each pixel in the sub-region having a value below the threshold; and combine the pixel offsets of pixels in the sub-region having values below the threshold into a default offset for pixels in the sub-region having values greater than the threshold; wherein the offset is an offset image comprising the pixel offsets of pixels in the sub-region having values below the threshold and the default offset.

[0220] In some embodiments, the processor is further configured to: select pixels of the measured radiation and the simulated measured radiation, wherein each pixel value tuple has an Euclidean magnitude below a threshold; and generate an offset based on the selected pixels.

[0221] Some embodiments include a system comprising: means for receiving measured radiation obtained from a radiation detector that receives radiation passing through an object; means for simulating measured radiation obtained from a radiation detector that receives radiation passing through an object; means for generating an offset based on the measured radiation and the simulated measured radiation; means for estimating scattered radiation based on the offset; and means for estimating primary radiation based on the estimated scattered radiation.

[0222] In some embodiments, the system further includes means for generating a gain based on the measured radiation and the simulated measured radiation, wherein the means for estimating the scattered radiation includes means for estimating the scattered radiation based on the gain; means for generating the measured scattered radiation based on the gain, the offset, and the simulated scattered radiation component of the simulated measured radiation; and means for generating the measured unscattered radiation based on the measured scattered radiation and the measured radiation.

[0223] Some embodiments include a non-transitory computer-readable medium that includes instructions that, when executed by a computer, cause the computer to perform the operations described herein. The circuitry may include hardware, firmware, program code, executable code, computer instructions, and / or software. The non-transitory computer-readable storage medium may be a computer-readable storage medium that does not include a signal.

[0224] It should be understood that many of the functional units described in this specification are labeled as modules to more particularly emphasize their implementation independence. For example, a module may be implemented as a hardware circuit including custom very large scale integration (VLSI) circuits or gate arrays, including but not limited to logic chips, transistors, or other components. A module may also be implemented in a programmable hardware device, including but not limited to a field programmable gate array (FPGA), programmable array logic, programmable logic device, or similar device.

[0225] References to "example" or "embodiment" throughout the specification mean that a particular feature, structure, or characteristic described in connection with the example is included in at least one embodiment of the invention. Thus, the appearances of the words "example" or "embodiment" in various parts of this specification are not necessarily all referring to the same embodiment.

[0226] In addition, the described features, structures, or characteristics may be combined in a suitable manner in one or more embodiments. In the following description, numerous specific details (such as examples of layouts and designs) are provided to provide a thorough understanding of the embodiments of the invention. However, those skilled in the relevant art will recognize that the invention may be practiced without one or more of the specific details or using other methods, components, layouts, etc. In other instances, well-known structures, components, or operations are not shown or described in detail to avoid obscuring aspects of the invention.

[0227] The claims following this written disclosure are hereby expressly incorporated into this written disclosure, with each claim independently serving as a separate embodiment. This disclosure includes all permutations of the independent claims and their dependent claims. Additionally, further embodiments that can be derived from the subsequent independent and dependent claims are expressly incorporated into this written description. These further embodiments are determined by replacing the dependency of a given dependent claim with the phrase "any of the claims beginning with claim [x] and ending with the claim immediately preceding said claim", where the term "[x]" within the brackets is replaced with the number of the most recently cited independent claim. For example, for a first set of claims beginning with independent claim 1, claim 4 can depend on either claim 1 or claim 3, where these separate dependencies result in two different embodiments; claim 5 can depend on any of claim 1, claim 3, or claim 4, where these separate dependencies result in three different embodiments; claim 6 can depend on any of claim 1, claim 3, claim 4, or claim 5, where these separate dependencies result in four different embodiments; and so on.

[0228] The recitation of the term "first" with respect to a feature or element in a claim does not necessarily imply the existence of a second or additional such feature or element. An element, if any, recited in apparatus-plus-function format is intended to be construed to cover the corresponding structure, material, or acts described herein, as well as equivalents thereof. Embodiments of the present invention that claim exclusive attributes or characteristics are defined as follows.

Claims

1. A method, comprising: Receiving measured radiation obtained from a radiation detector that receives radiation passing through an object, wherein the measured radiation includes primary radiation and scattered radiation, the primary radiation passes through the object within a field of view (FOV) of the radiation detector, and the scattered radiation includes object scattered radiation from the object within the FOV and background scattered radiation from matter outside the FOV; Simulating radiation transmission through a model of the object to obtain simulated primary radiation from the model of the object and simulated scattered radiation from the model of the object, wherein the combined simulated radiation includes the simulated primary radiation and the simulated scattered radiation; Estimating the background scattered radiation based on the measured radiation and the combined simulated radiation; Estimating scattered radiation based on the estimated background scattered radiation; And Estimating primary radiation based on the estimated scattered radiation.

2. The method according to claim 1, further comprising: Generating a gain based on the measured radiation and the combined simulated radiation; Wherein estimating the scattered radiation further includes estimating the scattered radiation based on the gain and the estimated background scattered radiation.

3. The method according to claim 2, further comprising: Generating the estimated scattered radiation based on the gain and the estimated background scattered radiation; And Generating estimated primary radiation based on the estimated scattered radiation and the measured radiation.

4. The method according to any one of claims 2 - 3, further comprising: Fitting a polynomial to a first vector of pixel values of the measured radiation and a second vector of pixel values of the combined simulated radiation; And Generating the gain based on the polynomial.

5. The method according to claim 4, wherein: The gain is a linear term of the polynomial.

6. The method according to claim 5, wherein: The polynomial is at least a second - order polynomial.

7. The method according to any one of claims 2 - 3, further comprising: Fitting a first polynomial to a first vector of pixel values of the measured radiation and a second vector of pixel values of the combined simulated radiation; Reducing the sizes of the first vector and the second vector to remove pixel values for which the error of the first polynomial is greater than a threshold; Fitting a second polynomial to the reduced first vector and the reduced second vector; And Generating the gain based on the second polynomial.

8. The method according to any one of claims 2 - 3, further comprising: Adjusting the sizes of the measured radiation and / or the combined simulated radiation such that the measured radiation and the combined simulated radiation have the same resolution; Determining a region of interest of the measured radiation; Generating a first vector of pixel values of the measured radiation in the region of interest that are less than a first threshold; Generating a second vector of pixel values of the combined simulated radiation corresponding to the first vector; Fitting a first polynomial to the first vector and the second vector; Remove pixel values from the first vector and the second vector for which the relative error of the first polynomial is greater than a second threshold; Fit a second polynomial to the remaining pixel values of the first vector and the second vector; wherein the gain includes the linear term of the second polynomial; Generate a third vector including a minimum value from each of a plurality of sub-regions of the measured radiation; Smooth the third vector to generate a fourth vector; Scale the fourth vector by a value greater than 1 to generate a fifth vector; and Generate an offset matrix as the estimated background scattered radiation, wherein for each pixel of each sub-region of the measured radiation: If the value of the pixel is lower than the value of the fifth vector associated with the sub-region, the value of the corresponding pixel of the offset matrix is the difference between the pixel value of the measured radiation and the pixel value of the corresponding pixel of the combined simulated radiation scaled by the gain; and For other pixels, generate the value of the corresponding pixel of the offset matrix based on other pixels of the offset matrix of the sub-region.

9. The method according to any one of claims 2-3, further comprising: Select pixels of the measured radiation and the combined simulated radiation, wherein each pixel value tuple has an Euclidean magnitude higher than a threshold; Generate an intermediate gain based on the selected pixels; and Generate the gain based on the estimated background scattered radiation and the intermediate gain.

10. The method according to any one of claims 2-3, further comprising: Generate a first intermediate gain based on the maximum value of the measured radiation and the maximum value of the combined simulated radiation; Normalize the combined simulated radiation to the measured radiation having the first intermediate gain; Calculate the Euclidean magnitude of the normalized combined simulated radiation and the measured radiation for each pixel; Select a first pixel of the measured radiation and the combined simulated radiation, the first pixel corresponding to a pixel of the normalized combined simulated radiation and the measured radiation for which the Euclidean magnitude is higher than a first threshold; Generate a second intermediate gain based on the selected first pixel of the measured radiation and the combined simulated radiation; Select a second pixel of the measured radiation and the combined simulated radiation, the second pixel corresponding to a pixel of the normalized combined simulated radiation and the measured radiation for which the magnitude is lower than a second threshold; Generate the estimated background scattered radiation based on the selected second pixel of the measured radiation and the combined simulated radiation; and Generate the gain based on the estimated background scattered radiation and the second intermediate gain.

11. The method according to any one of claims 2-3, further comprising: Generate an intermediate gain matrix including an intermediate gain for each of a plurality of sub-regions of the measured radiation; and Generate the estimated background scattered radiation for each of the sub-regions based on the associated intermediate gain.

12. The method according to any one of claims 1-3, wherein for each of a plurality of sub-regions of the measured radiation: generating a threshold based on the minimum value of the sub-region; generating a pixel offset for each pixel in the sub-region having a value below the threshold; and combining the pixel offsets of the pixels in the sub-region having the values below the threshold into a default offset for pixels in the sub-region having values greater than the threshold; wherein the estimated background scattered radiation is an offset image including the pixel offsets of the pixels in the sub-region having the values below the threshold and the default offset.

13. The method according to any one of claims 1-3, further comprising: selecting pixels of the measured radiation and the combined simulated radiation, wherein each pixel value tuple has an Euclidean magnitude below a threshold; and generating the estimated background scattered radiation based on the selected pixels.

14. A system comprising: a communication interface; a memory; and a processor configured to: receive the measured radiation obtained from a radiation detector that receives radiation passing through an object, wherein the measured radiation includes primary radiation and scattered radiation, the primary radiation passes through the object in the field of view (FOV) of the radiation detector, and the scattered radiation includes object scattered radiation from the object in the FOV and background scattered radiation from matter outside the FOV; simulating the radiation transmission of a model passing through the object to obtain the simulated primary radiation of the model from the object and the simulated scattered radiation of the model from the object, wherein the combined simulated radiation includes the simulated primary radiation and the simulated scattered radiation; estimating the background scattered radiation based on the measured radiation and the combined simulated radiation; estimating the scattered radiation based on the estimated background scattered radiation; and estimating the primary radiation based on the estimated scattered radiation.

15. The system according to claim 14, wherein the processor is further configured to: fit a first polynomial to a first vector of pixel values of the measured radiation and a second vector of pixel values of the combined simulated radiation; reducing the magnitudes of the first vector and the second vector to remove pixel values for which the error of the first polynomial is greater than a threshold; fitting a second polynomial to the reduced first vector and the reduced second vector; generating a gain based on the second polynomial; and estimating the scattered radiation based on the gain and the estimated background scattered radiation.

16. The system according to claim 14, wherein the processor is further configured to: select pixels of the measured radiation and the combined simulated radiation, wherein each pixel value tuple has an Euclidean magnitude above a threshold; generating an intermediate gain based on the selected pixels; generating a gain based on the estimated background scattered radiation and the intermediate gain; and estimating the scattered radiation based on the gain and the estimated background scattered radiation.

17. The system according to any one of claims 14 - 15, wherein the processor is further configured for a sub-region of the measured radiation: Generate a threshold based on the minimum value of the sub-region; Generate a pixel offset for each pixel in the sub-region having a value below the threshold; and Combine the pixel offsets of the pixels in the sub-region having the values below the threshold into a default offset for pixels in the sub-region having values greater than the threshold; Wherein the estimated background scattered radiation is an offset image including the pixel offsets and the default offset of the pixels in the sub-region having the values below the threshold.

18. The system according to any one of claims 14 - 15, wherein the processor is further configured to: Select pixels of the measured radiation and the combined simulated radiation, wherein each pixel value tuple has an Euclidean magnitude below a threshold; and Generate the estimated background scattered radiation based on the selected pixels.

19. A system, comprising: Means for receiving measured radiation obtained from a radiation detector that receives radiation passing through an object, wherein the measured radiation includes primary radiation and scattered radiation, the primary radiation passes through the object in the field of view (FOV) of the radiation detector, and the scattered radiation includes object scattered radiation from the object in the FOV and background scattered radiation from matter outside the FOV; Means for simulating the radiation transport of a model passing through the object to obtain simulated primary radiation of the model from the object and simulated scattered radiation of the model from the object, wherein the combined simulated radiation includes the simulated primary radiation and the simulated scattered radiation; Means for estimating the background scattered radiation based on the measured radiation and the combined simulated radiation; Means for estimating scattered radiation based on the estimated background scattered radiation; And Means for estimating primary radiation based on the estimated scattered radiation.

20. The system according to claim 19, further comprising: Means for generating a gain based on the measured radiation and the combined simulated radiation, wherein the means for estimating scattered radiation includes means for estimating scattered radiation based on the gain; Means for generating measured scattered radiation based on the gain and the estimated background scattered radiation; And Means for generating measured unscattered radiation based on the measured scattered radiation and the measured radiation.

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