Ct reconstruction with k-edge filtering

Abstract

Data processing and reconstruction techniques that enhance the practical utility of Ross spectrometers, by addressing the issues of long acquisition times and / or high degrees of noise associated with Ross spectrometers. By applying these techniques to noisy data, it is possible to generate low-noise spectral images, which can significantly increase the practical utility of the spectrometers.

Description

CT RECONSTRUCTION WITH K-EDGE FILTERINGRELATED APPLICATIONS

[0001] This application claims the benefit under 35 U.S.C. § 119(e) of U.S. Provisional Application No. 63 / 563,084, filed on March 8, 2024, which is incorporated herein by reference in its entirety.BACKGROUND OF THE INVENTION

[0002] X-ray computed tomography (CT) is a non-destructive technique for inspecting and analyzing internal structures of samples. In general, X-rays are absorbed or scattered as the X-rays travel through the sample. The X-rays not absorbed or scattered away are then detected by a detector system. The image formed at the detector system is known as an X-ray projection. Tomographic volume data sets are then reconstructed from a series of these projections at different angles via standard CT reconstruction algorithms such as Filtered Back Projection (FBP), FDK (Feldkamp, Davis and. Kress) reconstruction, and iterative reconstruction.

[0003] Some X-ray CT systems utilize polychromatic X-ray sources to generate the X- ray projections. Common polychromatic X-ray sources include X-ray tubes (laboratory sources), white synclirotron beams, or accelerator-based sources. Other examples exist, hi general, poly chromic X-ray beams emitted from the sources contain X-rays having many different energies. The distribution of the X-rays as a function of energy is typically referred to as the beam's spectrum. Polychromatic X-ray beams are distinguished from monochromatic beams that contain X-rays of only a single energy or very narrow ranges of energies.

[0004] White synchrotron beams are one type of polychromatic X-ray source. As electrons accelerate through the synchrotron, the electrons emit an intense "white" beam of polychromatic radiation at a narrow angle tangential to the ring. The beam includes radiation ranging from soft ultraviolet to hard X-rays. Monochromatic X-ray sources can be created from the white polychromatic beam by applying filters such as monochromator crystals and / or X-ray mirrors which pass / reflect radiation of selected energies.

[0005] Laboratory sources such as X-ray tubes also produce polychromatic X-ray beams typically using either fixed or rotating anodes. Within an evacuated tube, a filament(e.g. tungsten) acts as a cathode and a metal target acts as an anode. A high (acceleration) voltage is applied to the cathode, creating a high potential between the cathode and anode. This causes electrons to flow and accelerate across the vacuum from the cathode to the anode. Electrons collide with the anode material and accelerate other electrons, ions and nuclei within the anode material. This process generates X-rays. The spectra of the X-rays produced by X-ray tubes are a function of the anode target material and the acceleration voltage. The spectra are characterized by a continuous spectrum of bremsstrahlung ("braking radiation") X-rays, and secondary X-ray emissions at specific frequencies produced due to ionization and de-excitation of core electrons of the anode material, also known as X-ray fluorescence (XRF). The secondary X-ray emissions, or lines, are characteristic of the metal used in the anode material. The bremsstrahlung radiation is the dominant source of X-rays and can be used as a polychromatic X-ray source, while X-ray filters and / or X-ray mirrors can be applied to the characteristic X-ray emissions and / or the bremsstrahlung radiation to produce monochromatic X-rays, in examples.

[0006] Use of polychromatic X-ray beams in X-ray CT systems has advantages and disadvantages. The main advantage of using polychromatic X-ray beams is that they are typically more powerful than monochromatic X-ray beams for a given source.Disadvantages, however, impede the use of the technology analytically. X-ray detectors are sensitive to X-rays across a broad range of energies, which restricts the ability to differentiate between X-ray energy variances and the compositions of materials. In addition, unlike a monochromatic beam, the X-ray absorption of a polychromatic X-ray beam is generally not proportional to the sample material thickness. This is because lower X-ray energies of the polychromatic X-ray beam are absorbed more by the sample than higher X-ray energies as the beam transverses the sample. As a result, a process known as beam hardening ( BH) occurs when polychromatic X-ray beams are used to generate X-ray projections. Beam hardening is associated with a change in X-ray spectrum towards higher X-ray energies as the X-rays pass through the sample.

[0007] Beam hardening often yields artifacts in tomographic reconstructions from polychromatic X-rays. Typical artifacts include cupping artifacts and streak artifacts, hi general, elements within the sample having a higher atomic number (Z) such as metals yield more BH artifacts in the tomographic reconstructions images than do low-Z elements.

[0008] In order to reduce or prevent artifacts in tomographic reconstructions created from polychromatic X-ray beams, it is important to have a priori knowledge of the exact energy spectra of the X-rays emitted from the X-ray source of the system and of the sensitivities of one or more detectors of the detector system at different X-ray energies. Thus, X-ray source spectrum measurement or estimation is typi cal 1 y the key issue in artifact reduction in tomographic reconstructions of a sample created from X-ray CT systems using polychromatic X-ray sources.

[0009] A priori knowledge of the exact energy spectra of the X-rays also enables spectroscopy. Different elements have different attenuation spectra, particularly around the discrete X-ray "edges" associated with particular electron orbitals. By differentiating attenuation coefficients at different energies it is often possible to uniquely identify the material components of an object.

[0010] There are other techniques for dealing with these phenomena. K-edge filters are used to selectively absorb X-rays at specific energy levels, particularly around the K- edge energy of an element in a sample. K-edge energy or absorption edge, refers to the specific energy level at which the absorption of X-rays by that material sharply increases. This phenomenon is a result of the photoelectric effect, a process in which X-rays are absorbed by electrons in the innermost electron shells (K-shell) of atoms. These filters are employed to tailor the X-ray spectrum for various applications, such as medical imaging and industrial non-destructive testing and spectroscopy. When X-rays with energies close to the K-edge of a specific element pass through that element, they experience a sharp increase in absorption due to the photoelectric effect, hi this way, the filters can be used to analyze the distribution of specific elements in the sample.

[0011] K-edge filters are an important tool in X-ray analysis, allowing for better control of the X-ray beam’s energy spectrum and optimizing image quality for analytical purposes. By combining various X-ray projections filtered through these filters, it becomes possible to extract the impact of X-rays within a relatively narrow energy range.Additionally, multiple pairs or sets of K-edge filters can be employed to generate a spectral response from a sample.SUMMARY OF THE INVENTION

[0012] Ross spectrometers are a type of spectrometer that utilizes techniques such as the K-edge filters to discriminate X-ray energies. See On the Theory and Use of Ross Filters, Paul Kirkpatrick, American Institute of Physics, Vol. 10, Page 186 June 1939. These techniques are well understood, but their use is limited due to the long acquisition times and / or associated noise. This is because Ross spectrometers are only sensitive to those photons in the range differentially absorbed between the K-edge filters, which can result in limited sensitivity and spectral resolution. As a result, they are not widely utilized in imaging and analytical applications.

[0013] The invention relates to processing and reconstruction techniques that can be used to enhance the practical utility of Ross spectrometers and also perform spectroscopic analysis generally. Specifically, the techniques aim to address the issues of long acquisition times and / or high degrees of noise associated with Ross spectrometers. By applying these techniques to noisy data, it is possible to generate low-noise spectral images, which can significantly increase the practical utility of the spectrometers and process the data to modulate the k-edge filter coefficients to remove artefacts.

[0014] In general, according to one aspect, the invention features a method for image registration in an X-ray CT system. The method comprises acquiring projections with multiple different hardware filters, reconstructing the projections into volume datasets for each of the filters, registering the volume datasets to each other, forward projecting with the registered volume datasets to create images for the filters, and combining the forward projected images for the different filters to create combined images.

[0015] hr examples, the different filters are K-edge filters. In addition, loss can be computed in a projection domain. Moreover, in a further step, the combined images can be reconstructed to create a combined volume dataset.

[0016] The above and other features of the invention including various novel details of construction and combinations of parts, and other advantages, will now be more particularly described with reference to the accompanying drawings and pointed out in the claims. It will be understood that the particular method and device embodying the invention are shown by way of illustration and not as a limitation of the invention. The principles and features of this invention may be employed in various and numerous embodiments without departing from the scope of the invention.BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In the accompanying drawings, reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale; emphasis has instead been placed upon illustrating the principles of the invention. Of the drawings;

[0018] Fig. l is a schematic diagram of an X-ray CT system to which the methods of the present invention are applicable:

[0019] Fig. 2 is a schematic view of an exemplary filter wheel of the X-ray CT system;

[0020] Fig. 3 is a plot of attenuation as a function of energy in kilo electron Volts showing differentially sensitive range for balanced K-edge filters;

[0021] Fig. 4 is a 2D histogram showing the reference mapping;

[0022] Fig. 5 is a flow diagram illustrating a workflow for creating combined images for K-edge filters;

[0023] Fig. 6 is a flow’ diagram illustrating a workflow for creating combined volume datasets for K-edge filters;

[0024] Fig. 7 is a plot of system response as a function of energy in kilo electron Volts for different K-edge filter pairs; and

[0025] Fig. 8 is a flow diagram illustrating a workflow for creating monochromatic representation.DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0026] The invention now will be described more fully hereinafter with reference to the accompanying drawings, in which illustrative embodiments of the invention are shown. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the inventi on to those skil led in the art.

[0027] As used herein, the term “and / or” includes any and all combinations of one or more of the associated listed items. Also, all conjunctions used are to be understood in the most inclusive sense possible. Thus, the word “or” should be understood as having the definition of a logical “or” rather than that of a logical “exclusive or” unless the context clearly necessitates otherwise. Further, the singular forms and the articles “a”, “an” and“the” are intended to include the plural forms as well, unless expressly stated otherwise. It will be further understood that the terms: includes, comprises, including and / or comprising, when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. Further, it will be understood that when an element, including component or subsystem, is referred to and / or shown as being connected or coupled to another element, it can be directly connected or coupled to the other element or intervening elements may be present.

[0028] It will be understood that although terms such as “first” and “second” are used herein to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element from another element. Thus, an element discussed below could be termed a second element, and similarly, a second element may be termed a first element without departing from the teachings of the present invention.

[0029] Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.

[0030] Fig. 1 is a schematic diagram of an X-ray CT system 100 to which the methods and workflows of the present invention is applicable.

[0031] In general, the X-ray CT system 100 includes an X-ray source system 102 that generates a polychromatic X-ray beam 104 and a rotation stage 110 with sample holder 112 for holding the sample 114 in the X-ray beam 104 from the X-ray source system 102. Images or X-ray projections are captured by a detector system 118. The X-ray source system 102, the rotation stage 110, and the detector system 118 are mounted to a base 108 of the X-ray CT system 100. A computer system 200 typical ly receives and processes these projections and provides general control of the system 100. The computer system 200 other computer will typically perform tomographic reconstruction using the X-ray projections to create volume datasets.

[0032] The X-ray source 102, in one example, is a polychromatic X-ray source. The polychromatic X-ray source is preferably a laboratory X-ray source because of its ubiquity and relatively low cost. Nonetheless, synchrotron sources or accelerator-based sources are other alternatives.

[0033] Common laboratory X-ray sources include an X-ray tube, in which electrons are accelerated in a vacuum by an electric field and shot into a target piece of metal, with X-ravs being emitted as the electrons decelerate in the metal.

[0034] In one example, the X-ray source 102 is a rotating anode type or microfocused source, with a Tungsten target. Targets that include Molybdenum, Gold, Platinum, Silver or Copper also can be employed. Preferably, a transmissive-target configuration of the X- ray source 102 is used in which the electron beam strikes the thin target 103 from its backside. The X-rays emitted from the other side of the target 103 are then used as the beam 104.

[0035] hi another, more specific example, source 102 is a structured anode X-ray source such as described in U.S. Patent No. 7,443,953 issued to Yun, et al. (“Yun”) on October 28, 2008, the contents of which are mcoqiorated herein by reference in their entirety. In Yun, the source has a thin top layer made of the desired target material and a thicker bottom layer made of low atomic number and low density materials with optimal thermal properties. The anode can include, for instance, a layer of copper with an optimal thickness deposited on a layer of beryllium or diamond substrate.

[0036] X-ray lasers producing radiation having an energy suitable for the tomographic applications described herein also can be employed.

[0037] The X-ray beam 104 generated by source 102 has an energy spectrum that is controlled typically by the operating parameters of the source. In the case of a laboratory source, important parameters include the material of the target and the acceleration voltage (kVp). The energy spectrum is also dictated by any conditioning filters that suppress unwanted energies or wavelengths of radiation. For example, undesired wavelengths present in the beam can be eliminated or attenuated using, for instance, an energy filter (designed to select a desired X-ray wavelength range / bandwidth).

[0038] In addition to the X-ray source 102, the present invention relies on the availability of filters that filter the X-ray beam 104 typically before interaction with thesample 114 (pre -filters). It should be noted that in other examples, the filters are postfilters filtering the beam between the sample 114 and the detector system 118.

[0039] In more detail, the filter wheel 150 is controlled by the controller 210 of the computer system 200. The filter wheel 150 includes a frame 155 that rotates on axle 154 under control of the controller 210 via its control interface 130. Via the control interface 130 of the filter wheel 150, an operator can rotate the filter wheel 150 to bring one of the filters of the wheel 150 to be adjacent to the exit aperture on the target 103 of the X-ray source system 102. In this way, the selected filter (in one example, an air pre-filter) is aligned to filter the beam 104 prior to interaction with the sample 114.

[0040] Fig. 2 shows one embodiment of the filter wheel 150. The filter wheel 150 includes 16 separate pre-filters that are installed in ports 156 of frame 155. These prefilters are selected based on the K-edge energies of eight different elements in or potentially in the sample 114. For example, filters E1+ and El- are the K-edge filters associated with a first element in the sample. Filter EI+ is the K-edge fi lter provides a filter transfer function with sharp transition above the K-edge energy of the first element, and Filter El - is the K-edge filter provides a filter transfer function with sharp transition below the K-edge energy of the first element, hi a similar way, seven more filter pairs E2+ and E2-, E3+ and E3-, E4+ and E4-, E5+ and E5-, E6+ and E6-, E7+ and E7-, E8+ and E8- , are provided for 7 other elements of the sample.

[0041] Returning to Fig. 1 , when the sample 114 is exposed to the X-ray beam 104, the X-ray photons transmitted through the sample form an attenuated X-ray beam 106 that is received by the detector system 118. In some other examples, an objective lens such as a zone plate lens is used to form an image onto the detector system 118 of the X-ray imaging system 100. In alternative embodiments the detector system is a flat panel detector.

[0042] hi the most common configuration of the detector system 118, a magnified projection image of the sample 1 14 is formed on the detector system 118 with a geometrical magnification that is equal to the inverse ratio of the source-to-sample distance and the source-to-detector distance. Generally, the geometrical magnification provided by the X-ray stage is between 2x and 1 OOx, or more. In this case, the resolution of the X-ray image is limited by the focus spot size or virtual size of the X-ray source system 102.

[0043] To achieve high resolution, an embodiment of the X-ray CT system 100 further utilizes a very high resolution detector 124-1 of the detector system 118 in conjunctionwith positioning the sample 114 close to the X-ray source system 102. In one implementation of the high- resolution detector 124-1, a scintillator is used in conjunction with a microscope objective to provide additional magnification in a range between 2x and 100x, or more.

[0044] Other possible detectors can be included as part of the detector system 118 m the illustrated X-ray CT system 100. For example, the detector system 118 can include a lower resolution detector 124-2, as shown in the illustrated embodiment of Fig. 1. This could be a flat panel detector or a detector with a lower magnification microscope objective, in examples. Configurations of one, two, or even more detectors 124 of the detector system 118 are possible.

[0045] Preferably, two or more detectors 124-1 , 124-2 are mounted on a rotating turret 122 of the detector system 118, so that they can be alternately rotated into the path of the attenuated beam 106 from the sample 114.

[0046] Typically, based on operator defined parameters, the controller 210 of the computer system 200 instincts the rotation stage 110 via the control interface 130 to move the sample 114 out of the beam path during X-ray source system 102 calibration. After completion of the cali bration portion, the controller 210 moves the sample 114 back into the beam path and rotates the sample 114 relative to the beam 104 to perform the CT scan of the sample 114.

[0047] The detector system 118 creates an image representation, in pixels, of the X-ray photons from the attenuated X-ray beam 106 that interact with a scintillator in the detectors 124-1, 124-2 of the detector system 118, in one example. The image formed at the detector system 118 is also known as an X-ray projection or X-ray projection image.

[0048] hi one example, the computer system 200 includes an image processor 220 that analyzes the X-ray projections and possibly performs the calculations necessary for tomographic reconstructions created from the X-ray projections. A display device 240, connected to the computer system 200, displays information from the X-ray CT system 100. An input device 250 such as a touch screen, keyboard, and / or computer mouse enables interaction between the operator, the computer system 200, and the display device 240.

[0049] The computer system 200 loads information from and saves information to a database 260 connected to the computer system 200.

[0050] Using user interface applica tions executing on the computer system 200 that display their interfaces on the display device 240, in one example, the operator defines / selects CT scan or calibration parameters. These include X-ray acceleration voltage setings, selected filter, and settings for defining the X-ray energy spectrum of the scan and exposure time on the X-ray source system 102. The operator also typically selects other settings such as the number of X-ray projection images to create for the sample 114, and the angles to rotate the rotation stage 1 10 for rotating the sample 114 for an X-ray CT scan in the X-ray beam 104.

[0051] The computer system 200, often with the assistance of image processor 220, accepts the image or projection information from the detector system 118 associated with each rotation angle of the sample 114. The image processor 220 creates a separate projection image for each rotation angle of the sample 114, and combines the projection images using CT reconstruction algorithms to create 3D tomographic reconstructed volume information for the sample.

[0052] The technique described here generally involves selecting a pair of filters E1-E8 with K-edges that differ in energy by a value AE. The scaling of material X-ray atenuation as a function of energy is well-defined for the photo-electric effect and primarilydeviates from this scaling by large shifts associated with the K-edge. By designing the thickness and / or density of the filters such that the spectral attenuation curve matches both below and above the two respective K-edges, the difference between the images acquired using those filters corresponds only to the photons within the range where the curves differ, which is a relatively narrow spectral band.

[0053] Fig. 3 illustrates the differentially sensitivity ranges for balanced K-edge filters.

[0054] Traditionally, X-ray images are corrected from raw data obtained from a detector by dividing the subject image / , by a reference image R, to obtain a transmission representation It.Eq . 1

[0055] Consider two images, 4 and / 2, acquired with filters 1 and 2, along with their corresponding reference images RLand R2. Spectral-band restricted transmission images Itcare computed by calculating the difference between the raw images and their respective references by using the following transformation:Eq . 2

[0056] This transformation will decrease the effective signal -to-noise ratio SNR as the detected signal is only the difference between 4 and / 2, while the noise variance will increase linearly. Assume that the SNR of each individual measurement is given by:Eq . 3

[0057] Then the expected SNR of the numerator is. For an ideal reference(with 0 noise) the noise would thereby be scaled by their relative difference:Eq . 4

[0058] The process of combining the two images can greatly increase image noise (compared to the uncombined datasets). When combining images acquired with different filters, the signal-to-noise ratio SNR decreases as the difference between the intensities in the numerator of the SNR equation becomes smaller, while the denominator increases relative to the un-combined datasets. This is an inherent drawback associated with Ross spectrometers. One way of interpreting this is that the combined image corresponds to the photons differentially absorbed by the more absorbing filter - this is necessarily less than the complete photon spectrum, so the effective dose in the combined image is correspondingly smaller. The extent of this effect depends on the initial noise levels and the difference in intensities between the filtered images, which must be balanced against the size of the spectral bin. Choosing filters with K — edges that are very close results in low SNR due to their similar intensities, but a small spectral bin. Increasing imageintegration time is the traditional method for increasing SNR, but this may not be practical in many applications.

[0059] The solution here involves several techniques for constructing the imaging workflow, as well as data reconstruction and post-processing, to achieve low noise, spectrally sensitive data.

[0060] Reduced artifact image construction

[0061] The above analysis reveals that combining image data significantly reduces the combined image’s signal-to-noise ratio SNR. However, by using pre-corrected transmission images, the combinatoric function can bypass the need for direct processing of the reference images. The noise impact is relatively small, but because the processing occurs in the transmission domain (rather than the raw data) the artifacts tend to be reduced.

[0062] The pre-corrected transmission images can still be modulated by the relative changes in intensity associated with the reference images but using the means of the reference image instead of the absolute value (pixel by pixel) can reduce the magnitude of noise amplification in the resulting images.Eq . 5

[0063] This is preferably further extended by realizing that the specific reference intensities (modulated by a shared exposure, or scaled by their relative exposures) are not important, it is the ratio between Ri and R? (how the two references correlate) that is of importance. The reference R? can be approximated to be a simple linear mapping of Rl: Rr= aR2. The resulting mapping reference mapping can be visualized on a 2D histogram as shown in Fig. 4.

[0064] The above equation reduces to this :Eq . 6

[0065] Where a is defined as a scalar found by the linear regression of R1 and R2.

[0066] The previous equation can be considered as a special case of the following equation:Eq . 7

[0067] Where in the special case the system is designed to have balanced filter thicknesses, assumed to have perfectly conformant filter spectra, and the coefficients a and p are derived analytically. Another possible approach is to derive the coefficients through system level simulation where the values are chosen to maximize the polychromatic spectral contribution within an energy bin while minimizing the contribution outside of the bin.

[0068] An example optimization equation for the spectral bin dependent coefficients anand / >„ for spectral bin n could be considered below. All the below equations are shown as example optimization equations using simple linear combinations for clarity:

[0069] Eq . 8

[0070] Or alternativelyEq . 9

[0071] Where V i and V2 are two energy dependent view vectors through different filtration conditions and I and u are the lower and upper bounds of the target energy bin. Such an approach would need an accurate system simulator, but would have the advantage of being able to be tuned to the specific filter thicknesses used, rather than assuming the thicknesses used in the system design give maximal energy differentiation.

[0072] An alternative approach, in the absence of an accurate system simulator, would be an experimental approach that used a phantom of known materials. A coefficient optimization can be performed such that (for example) the reconstructed data from the view combinations maximizes flatness inside objects known to be of a single material.

[0073] It should be noted that practical spectrometer designs must give a balance between an optimal filter thickness and a filter thickness that can be easily / practically commercially obtained. An optimal design may choose for a thickness of 37.26pm but a thickness of 40pm may be chosen for the system as it is “close enough” and may be much more easily commercially obtained. This may break the assumption of maximal energy localization made with the analytically defined image combination, however a simulation approach to coefficient determination may be able to compensate for this thickness variation.

[0074] This can be extended by using the optimization equations as a w'ay of optimizing the filter thicknesses, or both thickness and coefficient (as shown below7):

[0075] OrEq . 10Where ti and t? are the thicknesses of filter 1 and 2 respectively.

[0076] It should be noted that the foregoing equations generally use simple linear combinations for clarity. Nevertheless, they can be extended to non-linear combinations (e.g. quadratic or higher order).

[0077] The other advantage of this approach is that it can be extended to use more than one view in the synthetic image construction. Two filters are theoretically sufficient in the case of filters whose attenuation is dominated by the photo-electric effect and the impact of discrete orbital edges (such as the k-edge, as shown in Fig. 3), however if more information is available from other spectral bins, this could be used to compensate for the other physical processes contributing to total attenuation (e.g. elastic and inelastic scatter) (see below').

[0078] Model based image registration

[0079] For combining data, it is important to register the images and especially the images for the K-edge filters. However, at high resolutions, drifts in the X-ray CT system 100 cause misaligned datasets even under the same nominal system conditions. This is particularly challenging to solve because the projection differences are associated with a change in projective geometry relative to the sample, which cannot be easily solved by spatially registering the projection images.

[0080] Fig. 5 shows a workflow to address the problem of system drift / image registration for different K-edge filters executed by the computer system 200.

[0081] In step 310, the image datasets or projections associated with both K-edge filters are reconstructed into corresponding volume datasets from their raw data using properly scaled analytical back projection or an iterative technique.

[0082] In step 312, the two or more datasets are registered to each other in the volume domain using a loss or registration metric or other similarity metric insensitive to scaling, such as mutual information.

[0083] In step 314, the datasets are used to forward project using the same nominal projective geometry. This can be done either to the projective geometry used for the first dataset and then compute the above spectral bin isolation, as shown by Fig. 4. This is typically accomplished from the original raw data or by projecting both volumes from their registered datasets and computing the subtraction.

[0084] Alternatively, the projective geometry of one of the datasets is employed to compute the loss in the projection domain. A single reconstruction is then used, and the projective geometry varied until a best fit is found using classical non-linear optimization techniques (e.g., simplex, LBFGS, Powell) or modern gradient-based optimizers (e.g. ADAM, Adagrad, FTRL (Module: tf.keras. optimizers | TensorFlow v2.14.0) tensorflow.org / api_docs / python / tt7keras / optimizers).

[0085] hi step 316, the projected images are combined and spectral bins isolated without losing image resolution. Then, in step 318, these images are then back projected to create the final isolated volumes using for example equation 6 above.

[0086] Al based denoising and reconstruction

[0087] The resulting spectral window could be further processed using state-of-the-art artificial intelligence (Al ) based reconstruction techniques such as those disclosed e.g. inU.S. Appl. Pub. No. US 2023 / 0009951. which is incorporated herein by the reference in its entirety.

[0088] Combined Al and projection synthesis workflows

[0089] While the neural network techniques mentioned above can be applied after the data is synthesized, they can also be applied before data synthesis or even both.

[0090] Fig. 6 shows another exemplary workflow executed by the computer system 200.

[0091] In step 330, image datasets are reconstructed using Al-based noise-free and artifact- free reconstruction as described in U.S. Appl. Pub. No. US 2023 / 0009951, for example.

[0092] In step 334, the noise-free datasets are registered. This registration can be performed either in the volume domain or through the optimization of a projective geometry.

[0093] In step 336, the noise-free datasets are then forward projected.

[0094] In step 338, the forward projected, noise-free images are combined as mentioned earlier.

[0095] Finally, in step 340, the forward projected images are back projected using either traditional tomographic reconstruction techniques or Al-based reconstruction, as mentioned above.

[0096] Projection synthesis via polynomial regression

[0097] The aforementioned techniques require multiple independent images to be taken, leading to an increase in total acquisition time in proportion to the number of spectral designs desired. However, it is possible to predict the image data at differential acquisition energies, i.e., taken with different K-edge filters, from a single acquisition at one energy (or a finite set) using a subset of projections (keyframes) that allow for the transfer function to be fitted for that view using the computer system 200, for example.

[0098] Generally, projections for some of the filters can be synthesized. For example, instead of acquiring 7 full projection sets, 1 full projection set is acquired, and 6 projection sets are acquired at reduced projection numbers at keyframes with other balanced filters. A polynomial is then fit to predict these reduced projection sets from the full projection set bythe computer system 200. Those polynomials (using interpolated coefficients) are then applied to the projections from the full projection set that do not have matched projections with other balanced filters. This greatly reduces acquisition time, as instead of having to acquire 7 full projection sets; only one full projection set and 6 much reduced projection sets are needed.

[0099] Also note that in some cases it is important to acquire the differential data for every view. With two datasets at a limited number of views, the mapping of the projections from filter 1 to filter 2 can be synthesized. This can greatly reduce noise or increase acquisition time, or both. As the polynomial regression is anchored in a way that is view dependent (albeit sparsely sampled) the image reconstruction can then be quite robust.

[0100] Another advantage when taking the sparse multi-projection views at the same time with an automated filter wheel is that the requirement to do image registration is removed. This would be impractical if for every view, as it takes time to change between filters. However for a small number of sparse views, it can be made practical.

[0101] The function parameters that map from one energy to another is interpolated between these keyframes. An example of this transfer function would be the polynomial function used for beam-hardening correction.

[0102] Where I is the input attenuation, 0 is the output (corrected) attenuation, a, b, c, d and e are coefficients to be fitted, and ft corresponds to a constant absorption value, which in turn typically corresponds to an effective energy for the nominal effective energy desired for the reconstruction.

[0103] In this formulation, the correction parameters (a, b, c, d, e) are fitted using a limited subset of projections (keyframes) to map the input attenuation / to the corrected output attenuation 0.

[0104] The constant absorption value ft typically corresponds to an effective energy for the desired reconstruction. The fitted coefficients at each projection of the subset are then interpolated between the keyframes, with the interpolation weighting given by the relative projection angle between each keyframe. For instance, if IT is the intermediate anglebetween two keyframes at angles rq^ and iq,. the coefficients (a, b, c, etc) used for the projection at n would be determined by:

[0105] For example, if keyframes were taken every 10 degrees (0 ,10,20, ... ,340,350,360) the coefficient taken for a projection at 17 degrees would be:

[0106] While acquiring a whole projection set is necessary for at least one energy bin, the remaining energy bins can be synthesized from a very limited set of keyframes. The total acquisition time for all the projection sets required for a full spectral series would only be slightly longer than the acquisition time for a single energy bin in the projection set. For example, to acquire a spectrum with six bins, traditionally, seven whole projection series would be needed, with a total acquisition time of 7 times that of a single projection set. However, with transfer function projection synthesis, a whole projection set is only required at six sets of keyframes. If keyframes are taken every 10 projections, the total acquisition time would be 1,6 times that of a single tomography series, resulting in an effective speedup of 4.4 times.

[0107] The predicted spectral bin data could also reduce impact of relative nonlinearities in the reconstructed image. The differential image is subject to differential nonlinear attenuation corresponding to e.g. non-uniform filter material or scintillator material. This is not effectively corrected by reference correction, even if reference linear mapping is used (although this helps). By using a transformation function from either one or both spectral bins the images will not be sensitive to differential nonlinearities and will also not be subject to the noise amplification as described above.

[0108] This transformation could be a simple polynomial, as described above, but more complex non-linear functions (such as deep neural networks) could also be executed by the computer system 200. One downside of using a polynomial prediction is that it is possible that some non-linear / non-continuous / non-monotonic transforms (such as those arisingfrom the strong variation in attenuation associated with the k-edge of high-Z materials) are not properly accounted for using the polynomial. For these applications a non-linear trainable transform (such as a neural network) might be beneficial.

[0109] Sub-spectral tweaking using simulated transmission modulation

[0110] One issue in the design of the spectrometer is that its design is predicated in the correlation between attenuation coefficients across energies between materials, except for the specific K-edge position of each filter material. This is strictly true for the portion of an attenuation coefficient that corresponds to the photo-electric effect, but the photo-electric effect is not the only source of material attenuation. Of particular interest is incoherent (or Compton) scattering. This can lead to differential attenuation behavior between K-edge filters well balanced across spectra for the photo-electric effect. See Kirkpatrick supra.

[0111] Another approach is to remove or reduce balance errors by the use of simulated views. To address errors associated with the spectral regions outside of the differential pass band with differential spectral sensitivity, there is a functional modification of attenuation values. The workflow executed by the computer system 200 simulates differential views from a realistic balanced Ross filter pair, and differential views from an idealized Ross filter pair (i.e. without differential attenuation outside of the target energy band). Then some function (e.g. a polynomial) is used to map from the realistic simulated balanced ross filter pair to an ideal filter pair, reducing errors.

[0112] Fig. 7 is a plot of system spectral response as function of energy showing an example spectrometer design.

[0113] As shown, a perfectly balanced filter pair would be exactly 0 outside its window of differential behavior. In reality, however, scattering effects and other nonuniformities lead to non-zero or even negative spectral behavior. For most bins this is a relatively minor contribution that may lead to some imaging anomalies. In the less sensitive (e.g. higher kV) bins the difference can be significant, however.

[0114] Simulation can be used modulate each projection set to remove only this component. If we consider a modulation function f with parameters p operating on attenuation image A, converting it into image B (once again, this function can range from a simple polynomial to a non-linear network):

[0115] The computer system 200 simulates a series of polychromatic views through an object of a nominal material, both with the actual filter material and a nominal filter material with a set of attenuation coefficients equal to the second material without its K- edge increase (i.e. continuing the ~Z’ / E3trend without a k-edge increase). Let this view simulation operation be g, giving attenuation values corresponding to a material m and set of thicknesses t:

[0116] Then the function parameters p can be fit between these two simulated values:

[0117] Other loss functions than the L2 norm could be used. This correction is dependent on the simulated material, but should be fairly minor (the nominal simulation will only vary slightly from the actual filter). As and so can be viewed as a first order correction for the residual out-of-bin attenuation differences between the actual filter coefficients and the filter coefficients of a nominal filter with perfectly matched attenuation values.

[0118] A slight modification to tlris would be to fit the parameters of the modulation function such that both projection sets of the pair are modulated to have attenuation coefficients only corresponding to the photoelectric effect (which has a shared attenuation profile in a balanced design, apart for in the range between their respective k-edges, removing the impact of other attenuation physics such as Compton scattering.

[0119] At high energies other interaction physics beyond the photo-electric effect, such as scattering effects, may become significant or even come to dominate. This leads to “tails” in the spectrometer’s sensitivity’ bands - i.e. non-zero spectral sensitivity outside the target energy range.

[0120] By combining more energy views (i.e. more than 2) it may be possible to reduce the presence of these tails while maintaining significant sensitivity in the target spectral range of interest. The inclusion of these extra datasets may also increase signal to noise as it utilizes extra data.

[0121] The above equation 7 can thereby be naturally extended to include an arbitrary number (u) of views:Or

[0122] This reduces the impact of differential non-linearities between the different scans - a significant issue when using imperfect filters with an imperfect detector response system. It should be noted that while error reduction through the use of additional hardware features is common, the present approach uses the data through optimization.

[0123] K-edges for automatic beam hardening correction

[0124] K — edge imaging can be used for automatic beam hardening correction in X- ray imaging. Beam hardening occurs when the X-ray beam passes through an object, and the lower energy X-ray photons are absorbed more than the higher energy photons, leading to an increase hi the mean energy of the beam. This can result in artifacts and inaccurate image reconstruction. K — edge imaging involves acquiring images at two different X-ray energies, with one energy above and the other below the K — edge of the material of interest. The K — edge is the energy level at which the material absorbs X-rays most strongly, leading to a sharp increase in the attenuation coefficient. By using K — edge imaging, it is possible to correct for beam hardening by subtracting the two images acquired at different energies. This can improve image quality and reduce artifacts, particularly when imaging materials with high atomic numbers, such as bone or metal. This workflow can be used to create a true quasi-monochromatic representation, but the narrower the spectral window used the greater the degree of noise amplification experienced.

[0125] Fig. 8 is a flow diagram showing a method for creating monochromatic representation.

[0126] In step 370, X-ray CT system 100 is used to acquire a small number (maybe just 1) of projection pairs with Z-edge filters at a very narrow energy window. The leads to a large noise amplification.

[0127] Then in step 372, a polynomial transformation function is fit to rescale the data to the monochromatic projection.

[0128] Once again, a polynomial function could be used, as well as a non-linear transfer function such as deep neural network.

[0129] While this invention has been particularly shown and described with references to preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the invention encompassed by the appended claims.

Claims

CLAIMSWhat is claimed is:

1. A method for tomographic reconstruction from image datasets obtained using K- edge filters in an X-ray computed tomography system, the method comprising: acquiring projections with different filters; reconstructing the projections into volume datasets for each of the filters; forward projecting with the registered volume datasets to create images; and combining the forward projected images to create combined images.

2. The method of claim 1, wherein the different filters are K-edge filters.

3. The method of either of claims 1 or 2, further comprising reconstructing the combined images to create a combined volume dataset.

4. The method of any of claims 1-3, wherein the projections for each of the filters are reconstructed into the volume datasets for each of the filters using neural networks.

5. The method of any of claims 1-4, further comprising computing loss in a projection domain.

6. The method of any of claims 1-5, further comprising combining the forward projected images linearly or non-linearly.

7. The method of any of claims 1-6, further comprising using more than two different filters.

8. The method of any of claims 1-7, further comprising registering the volume datasets to each other using loss or registration metric or other similarity metric insensitive to scaling.

9. The method of any of claims 1-8, further comprising correcting the forward projected images using reference images.

10. The method of any of claims 1-9, further comprising correcting the forward projected images using reference images for each of the different fi lters.

11. The method of claim 10, further comprising correcting the forward projected images using a ratio of the reference images for each of the different filters.

12. The method of any of claims 1-11, wherein at least some of the projections constructed into the volume datasets for each of the filters are synthesized.

13. The method of claim 12, wherein projections for one of the filters are used to simulate projections for a different filter.

14. The method of claim 12, wherein the projections are simulated using a transfer function derived from a beam-hardening correction.

15. The method of any of claims 1-14, further comprising simulating differential views from a realistic balanced Ross filter pair, and differential views from an idealized Ross filter pair and mapping from the realistic simulated balanced Ross filter pair to the ideal filter pair.

16. The method of any of claims 1-14, further comprising employing a polynomial transformation function to rescale to a monochromatic projection.

17. An X-ray computed tomography system, comprising: an X-ray source system that generates a polychromatic X-ray beam: a rotation stage with sample holder for holding a sample in the X-ray beam; a detector system for detecting the X-ray beam after interaction with the sample; and a computer system that receives and processes projections from the detector system, wherein the computer system executes a method as described in any one of claims 1-14.

Images