Method and system for reconstructing three-dimensional volume of sample based on wide field mode CT scanning

Abstract

A method and system for reconstructing a three-dimensional volume based on truncated X-ray projections acquired in a single rotation wide field mode (SRWFM) computed tomography (CT) scan offsets the axis of rotation of the sample relative to the X-ray propagation optical axis so that the effective field of view is enlarged beyond the nominal size of the detector. Redundant weighting is applied to compensate for incomplete angle sampling in truncated projection, which weighting is performed after ramp filtering and before back projection in an analysis (e.g., back projection after filtering) or iterative reconstruction algorithm. Additional correction includes adjusting the pixel intensity based on an angle between the X-ray optical axis and the detector plane, and remapping the projection data onto a virtual detector plane aligned with the axis of rotation. These techniques mitigate image artifacts, reduce noise and ensure accurate attenuation coefficient representation, ultimately achieving high quality reconstruction of larger or asymmetric positioning samples from a single 360-degree rotation.

Description

Technical Field

[0001] The present invention generally relates to a method and system for reconstructing a three-dimensional volume based on X-ray projection data acquired in a single-rotation wide-field mode (SRWFM) computed tomography (CT) scan. Background Art

[0002] X-ray microtomography systems provide high-resolution, non-destructive imaging of the internal structure of a sample. In examples, these systems are used in a variety of industrial and research applications, such as mining, manufacturing, materials science, clinical research, and failure analysis. These systems provide the ability to visualize features in a sample without the need to cut and slice the sample.

[0003] An X-ray microtomography system includes an X-ray projection system that generates projection data of a sample and a computer system that reconstructs a tomographic volume of the sample based on the projection data. In operation, the X-ray projection system scans the sample at different projection angles to generate projection data. During the scan, X-rays are directed at the sample and are absorbed or scattered by the sample as the X-rays travel through the sample. The X-rays that are not absorbed or scattered pass through the sample and are modulated by the sample. A detector system receives the transmitted X-rays and creates an image representation of the received X-rays in pixels. A series of X-ray projections at different angles generated by the scan forms the projection data of the sample. Then, the computer system accesses the projection data and applies a tomographic reconstruction algorithm to the projection data to reconstruct a volume dataset of the sample. The volume dataset is a three-dimensional (3D) representation of the entire sample, and a slice is a two-dimensional (2D) cross-sectional image of the sample based on the volume dataset.

[0004] The most common reconstruction algorithms belong to a class of reconstruction techniques called analytic reconstruction. The aim is to find a closed-form solution to the problem of reconstructing the internal structure of an object based on its projections. The most common analytic method is filtered backprojection (FBP). First, a high-pass filter (usually a ramp filter) is used to process the projections in the frequency domain or the spatial domain. Then, each filtered projection is "smeared" back onto the imaging plane as if each data point is uniformly emitted back in the shape of the original beam. The backprojections from all angles are added together to produce a reconstructed volume that approximates the internal structure of the object. The filtering and backprojection operations together help obtain a more accurate and less blurred reconstruction of the original object. One type of filtered backprojection is the Feldkamp-Davis-Kress (FDK) reconstruction algorithm. It is often used with X-ray microtomography systems because it reduces the artifacts associated with typical cone-beams. See Practical Cone-Beam Algorithm by Feldkamp, L.A., Davis, L.C. and Kress, J.W. (1984), Journal of the Optical Society of America A, 1, 612-619.

[0005] Iterative reconstruction is another method that estimates the reconstructed volume through forward projection and reconstructs slices continuously based on the projection data. For this purpose, multiple iterations are performed on the estimated projection data for each view. During each iteration, the estimated projection data is compared with the actual (e.g., measured) projection data. The result of each comparison is used to correct the current estimate of the reconstructed volume, thereby creating a new estimate of the reconstructed volume. When the estimated projection data and the measured projection data are close enough (which means the iterative process converges), the volume dataset is reconstructed based on the measured projection data. Exemplary iterative reconstruction algorithms include algebraic reconstruction technique (ART), simultaneous iterative reconstruction technique (SIRT), and iterative least-squares technique (ILST). The algorithms typically differ in the way of comparing the measured projection data and the estimated projection data and the type of correction applied to the current estimate. See Lin, Q., Andrew, M., Thompson, W., Blunt, M. J., and Bijeljic, B., Optimization of image quality and acquisition time for lab-based X-ray microtomography using an iterative reconstruction algorithm, Advances in Water Resources 115, 112 - 124 (2018).

[0006] Analytical reconstruction methods and iterative reconstruction methods have advantages and disadvantages. For example, FBP provides good image quality with relatively low processing overhead, which improves throughput and reduces costs. The disadvantage of FBP is that it is vulnerable to image noise in the projection data. The advantages of iterative reconstruction generally include improved image quality, less sensitivity to image noise, reduced image artifacts, and the ability to reconstruct the best image in the case of incomplete projection data. The disadvantages of iterative reconstruction include the complexity associated with the selection of the regularization parameter applied to the iterative reconstruction algorithm, longer processing time, and increased computational cost.

[0007] The resolution of a high-end X-ray micro-tomography (microscopy) system (x-ray microscopy, XRM) can reach 0.5 μm, which results in a relatively small field of view because the number of pixels is usually fixed (e.g., 1024 by 1024). Currently, many commercial XRM systems can have a wide field mode (WFM) option, which attempts to expand the field of view of the system beyond the detector size. In a conventional arrangement, the WFM scan mode can provide a field of view nearly 2 times larger than that of a conventional scan. In a conventional scan, the rotation axis is projected onto the center of the detector. In one of the current WFM implementations, two scans must be performed. One is to first move the rotation axis to the right side of the detector and then rotate it together with the mounted sample to obtain a scan. The other is to move the rotation axis to the left side of the detector and then obtain another scan of the sample. After the two scans, the original projection data from the two scans are stitched together to form a projection much larger than the detector size (e.g., for a 1024 by 1024 pixel detector, the stitched projection size can be 1906 by 1906 pixels). The stitched data set from the two rotation axis movement scans is treated as a conventional scan with the rotation axis projected onto the center of the detector in the FDK reconstruction. However, one drawback is that this dual-scan WFM method requires very accurate mechanical calibration to avoid image artifacts. Another method of performing the WFM mode is to move the rotation axis only once and perform a scan, which is generally referred to as the single rotation wide field mode (SRWFM). Note that for the rotation axis movement mode, the sample only rotates around this moving rotation axis; for the detector offset system, the detector will maintain the same offset for all projections. Generally, a full 360-degree scan is required to obtain sufficient raw data to perform 3D volume reconstruction.

[0008] In Cho, P.S., Rudd, A.D. and Johnson, R.H.'s Cone-beam CT from width-truncated projections, Computerized Medical Imaging and Graphics, 20, 49-57 (1996), a cone-beam CT technique that allows reconstruction based on width-truncated projections is described. Summary of the Invention

[0009] The present invention relates to analytical reconstruction and iterative reconstruction for micro-tomography X-ray scanning, so-called single rotation wide field mode (SRWFM) scanning using cone-beam X-ray computed tomography.

[0010] Use the SRWFM mode. It involves the possibility of moving the rotation axis once, but also possibly multiple times, and performing one or more scans, which can be reconstructed using the proposed reconstruction method as described later. An imaging configuration is adopted in which the rotation axis of the sample and / or the detector is offset from the center of the X-ray beam of the system. This allows imaging of larger samples (wide field). A set of X-ray projections from different angles is obtained by rotating the sample only (such as once) in a 360-degree angular range. For SRWFM, the sample rotates only around this moving rotation axis; for the detector offset system, the detector will maintain the same offset for all projections. Generally, a full 360-degree scan is required to obtain sufficient raw data for 3D volume reconstruction. Importantly, a reconstruction method is applied to weight different regions of the projection data to improve the reconstruction and reduce artifacts.

[0011] Generally, according to one aspect, the present invention features a method for reconstructing a three-dimensional volume of a sample based on projection data obtained by X-ray microtomography. The method includes: obtaining X-ray projections of the sample by a detector by rotating the sample around a rotation axis offset relative to the X-ray propagation axis, and processing the obtained projections by applying redundant weighting to correct for incomplete angular sampling in regions of the projection data to account for the offset rotation axis, wherein the redundant weighting is performed before backprojection in analytical reconstruction or before an equivalent backprojection operation in iterative reconstruction.

[0012] Preferably, a ramp filter is applied to the projection data before redundant weighting, and the redundant weighting is performed on the ramp-filtered data.

[0013] Redundant weighting can be applied to regions around the projection of the rotation axis on the detector, and may employ a position-dependent weighting function that corrects the projection without the need for multiple scans.

[0014] The projection data can be adjusted by scaling the pixel intensity according to the angle formed between the optical axis of the X-ray beam and the plane of the detector, and the scaling corrects for geometric distortion introduced by the offset axis configuration.

[0015] In the current example, the projection is remapped onto a virtual detector plane perpendicular to the line connecting the X-ray source and the rotation axis, thereby ensuring a correct attenuation coefficient representation in the reconstructed volume.

[0016] The iterative reconstruction method can include: applying weighting based on a noise model to the difference between the measured data and the forward projection data, and subsequently combining the redundant weighting before backprojection, thereby improving noise handling and artifact reduction.

[0017] Typically, projections are acquired over the entire 360-degree rotation of the sample to ensure sufficient sampling of the region within the magnified field of view, and the projections can be acquired in only a single complete 360-degree rotation.

[0018] Generally, according to one aspect, the invention features a system for reconstructing a three-dimensional volume of a sample based on projection data obtained from a single-rotation wide-field mode (SRWFM) X-ray scan. The system includes: an X-ray source configured to generate an X-ray beam; a rotating stage configured to hold and rotate the sample about a rotation axis offset relative to the X-ray propagation axis, thereby providing X-ray projections with a magnified effective field of view that exceeds the nominal detector size; and a detector configured to receive the X-ray projections of the sample. A processing system is configured to: receive projection data from the detector, apply redundant weighting to correct for incomplete angular sampling in a region of the projection data, where the redundant weighting is performed prior to back-projection in analytical reconstruction or prior to an equivalent back-projection operation in iterative reconstruction. Then, based on the applied redundant weighting, reconstruct the three-dimensional volume of the sample from the projection data.

[0019] The processing system is preferably further configured to apply a ramp filter to the projection data prior to applying the redundant weighting, such that the redundant weighting is performed on the ramp-filtered data. Moreover, the processing system can be configured to apply the redundant weighting in a region on the detector around the projection of the rotation axis.

[0020] The processing system is configured to employ a position-dependent weighting function, which preferably corrects the projection without the need for multiple scans. The processing system is further preferably configured to adjust the projection data by scaling the pixel intensity according to the angle formed between the optical axis of the X-ray beam and the plane of the detector, the scaling correcting for geometric distortion introduced by the offset-axis configuration.

[0021] The processing system can be configured to remap the projections onto a virtual detector plane perpendicular to the line connecting the X-ray source and the rotation axis, thereby ensuring a correct attenuation coefficient representation in the reconstructed volume.

[0022] In one example, the processing system is configured to perform an iterative reconstruction algorithm that includes: applying a weighting based on a noise model to the difference between the measured data and the forward projection data, and subsequently incorporating the redundant weighting prior to back-projection, thereby improving noise handling and artifact reduction.

[0023] A controller is configured to operate the rotating stage and acquire projections over the entire 360-degree rotation of the sample, possibly in only a single rotation, to ensure sufficient sampling of the region within the magnified field of view.

[0024] The above and other features of the present invention, including various novel construction details and combinations of components, and other advantages will now be described more specifically with reference to the accompanying drawings, and the above and other features of the present invention, including various novel construction details and combinations of components, and other advantages will be pointed out in the claims. It will be understood that the specific methods and devices embodying the present invention are shown by way of illustration and not as a limitation of the present invention. The principles and features of the present invention can be used in various and many embodiments without departing from the scope of the present invention.

[0025] Related Applications

[0026] This application claims the benefit of U.S. Provisional Application No. 63 / 623,069, filed on January 19, 2024, under 35 U.S.C.§119(e), which is incorporated herein by reference in its entirety. Brief Description of the Drawings

[0027] In the drawings, the reference numerals refer to the same parts in different views. The drawings are not necessarily drawn to scale, but rather emphasis is placed on illustrating the principles of the present invention. In the drawings:

[0028] Figure 1 is a schematic view of an X-ray microtomography system to which the method of the present invention can be applied;

[0029] Figure 2A and Figure 2B is a schematic top view of the hardware configuration for single-rotation wide-field mode (SRWFM) scanning, showing the detector moved to one side with respect to the X-ray propagation axis ( Figure 2A ) and the rotating table moved to the side of the detector ( Figure 2B );

[0030] Figure 3A and Figure 3B are slices showing image artifacts of SRWFM scans with FDK reconstruction ( Figure 3A ) and iterative reconstruction ( Figure 3B );

[0031] Figure 4 is a flowchart showing a method of FDK filtered back-projection reconstruction based on SRWFM scans;

[0032] Figure 5 is a top view of the SRWFM hardware configuration with the rotation axis moved, where the virtual detector plane is at an angle to the "original" X-ray beam propagation axis;

[0033] Figure 6 shows the two-dimensional extent of the detector on which the projection of the rotation axis of the rotating table lies;

[0034] Figure 7is a flowchart showing a method for iterative reconstruction for SRWFM scanning; and

[0035] Figure 8A and Figure 8B is from Figure 4 the FDK reconstruction ( Figure 8A ) detailed in Figure 7 and the iterative reconstruction ( Figure 8B ) detailed in Slice of

[0036] The present invention will now be described more fully hereinafter with reference to the accompanying drawings, in which illustrative embodiments of the invention are shown. However, the invention may 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 invention to those skilled in the art.

[0037] As used herein, the term "and / or" includes any and all combinations of one or more of the associated listed items. Further, unless otherwise expressly stated, the singular forms and the article "a", "an" and "the" are also intended to include the plural forms. It should also be understood that the terms including, comprising, encompassing and / or incorporating when used in this specification specify the presence of the 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 combinations thereof. Further, it will be understood that when an element including a 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.

[0038] 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 consistent with their meaning in the context of the relevant art and not in an idealized or overly formal sense unless expressly so defined herein.

[0039] Figure 1 is a schematic diagram of an X-ray microtomography system 100 to which the method and workflow of the present invention can be applied.

[0040] Generally, the X-ray microtomography system 100 combines an X-ray microscopy system 101 and a computer system 200 for receiving projections of a sample 114 and calculating a volume dataset 264 based on these projections.

[0041] The X-ray microscopy system 101 includes an X-ray source system 102 that generates a typically polychromatic X-ray beam 104. A rotating stage 110 has a sample holder 112 for holding a sample 114. The rotating stage 110 rotates the sample 114 in the X-ray beam 104 from the X-ray source system 102. An image or X-ray projection is captured by a detector system 118. The X-ray source system 102, the rotating stage 110, and the detector system 118 are all mounted to a base 108 of the X-ray CT system 100. A computer system 200 typically receives and processes these projections and provides overall control of the system 100. The computer system 200 or another computer will typically perform tomographic reconstruction using the X-ray projections to create a volume data set of the sample 114.

[0042] In one example, the X-ray source 102 is a cone beam, polychromatic X-ray source. The polychromatic X-ray source is preferably a laboratory X-ray source because of its prevalence and relatively low cost. Nevertheless, synchrotron sources or accelerator-based sources are other alternatives.

[0043] Common laboratory X-ray sources include X-ray tubes in which electrons are accelerated in a vacuum by an electric field and are shot into a metal target, and X-rays are emitted as the electrons slow down in the metal.

[0044] In one example, the X-ray source 102 is a rotating anode reflection type target or a microfocus source with a tungsten target. Targets including molybdenum, gold, platinum, silver, or copper can also be used. In one embodiment, a transmission type target configuration of the X-ray source 102 is used, in which an electron beam impinges on a thin target 103 from the back side of the thin target 103. Then, the X-rays emitted from the other side of the target 103 are used as the beam 104.

[0045] 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 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 on the detector system 118 of the X-ray imaging system 100.

[0046] In one embodiment of the detector system 118, an enlarged projection image of the sample 114 is formed on the detector system 118 at a geometric magnification that is equal to the inverse ratio of the source-to-sample distance and the source-to-detector distance. Typically, the geometric magnification provided by the X-ray stage is between 2 times and 100 times or greater. In this case, the resolution of the X-ray image is limited by the focal size or virtual size of the X-ray source system 102.

[0047] To achieve high resolution, embodiments of the X-ray microtomography system 100 further utilize a very high resolution detector 124-1 of the detector system 118, preferably in combination with positioning the sample 114 close to the X-ray source system 102. In one embodiment of the high resolution detector 124-1, a scintillator or other X-ray to light conversion device is used in combination with a possible microscope objective to provide additional optical magnification in the range between 2x and 100x, or greater additional optical magnification.

[0048] Other possible detector or detector lens combinations may be included as part of the detector system 118 in the X-ray CT system 100 shown. For example, the detector system 118 may include a lower resolution detector 124-2. In an example, this may be a flat panel detector or a detector with a lower magnification microscope objective. Configurations of one, two, or more detectors 124 of the detector system 118 are possible.

[0049] Preferably, two or more objectives / detectors 124-1, 124-2 are mounted on the rotating turntable 122 of the detector system 118 such that they can be alternately rotated into the path of the attenuated beam 106 from the sample 114. In some embodiments, one image detector may acquire images from different objectives located in the imaging path.

[0050] Typically, based on operator-defined parameters, the controller 210 (acquisition software) of the computer system 200 sends instructions to the control interface 130 to initiate the movement of the rotating table 110 and the rotation and transport motors of the detector, thereby positioning the sample 114 and the detector 124 for the SRWFM setup. The control interface 130 is typically embedded in a program. After completion, the controller 210 rotates the sample 114 relative to the beam 104 to perform a CT scan of the sample 114 and saves the projection data 262 to the data storage 260.

[0051] In one example, the computer system 200 includes a graphics or other acceleration processor 220 that analyzes the X-ray projections and may perform the calculations necessary for tomographic reconstruction represented by the volume dataset 264 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. Input devices 250 such as a touch screen, keyboard, and / or computer mouse enable interaction between the operator, the computer system 200, and the display device 240.

[0052] In one example, using a user interface application that executes on computer system 200 and displays its interface on display device 240, an operator defines / selects CT scan or calibration parameters, which include whether to use SRWFM scanning. These include X-ray acceleration voltage settings, and settings of the X-ray energy spectrum for defining scan and exposure times on X-ray source system 102. The operator typically also selects other settings, such as the number of X-ray projection images created for sample 114, and the angle of rotation of the rotating table 110.

[0053] Computer system 200 receives, with the help of its image processor 220, image or projection information from detector system 118 that is associated with each rotation angle of sample 114. Typically, image processor 220 uses a reconstruction algorithm to combine the projection images to create 3D tomographic reconstruction volume information 264 of sample 114.

[0054] Computer system 200 will typically execute an analytic reconstruction application 254 and / or an iterative reconstruction application 256 for reconstructing a volume dataset of sample 114 based on projection data 262.

[0055] Reconstruction applications 254, 256 run on top of operating system 252. Operating system 252 is in turn executed by the central processing unit (CPU) 250 of the computer.

[0056] Figure 2A and Figure 2B are schematic top views of two hardware configurations for single-rotation wide-field mode scanning. In Figure 2A , detector 124 is moved to one side relative to the center or axis OA of the cone formed by X-ray beam 104. This means that the line passing through the source (point) and perpendicular to the detector is no longer the center or axis (optical axis) of the cone of the X-ray beam. In Figure 2B , rotating table 110 is moved to one side of the detector relative to the optical axis OA of X-ray cone OA 104. This means that rotating table 110 is located outside the line passing through the source and perpendicular to detector 124.

[0057] Due to this movement, the projections acquired by the detector are truncated relative to the moving side, but they are widened relative to the other side. The truncated part is more or less estimated in the following reconstruction.

[0058] Both of these configurations increase the field of view of the reconstructed 3D volume by moving the rotating table or the detector to one side, which is defined as single-rotation wide-field mode (SRWFM), and the reconstructed 3D volume is reconstructed based on the truncated projections acquired using the detector.

[0059] Figure 3A and Figure 3Bare the image artifacts of the SRWFM scan with the FDK reconstruction result ( Figure 3A ) and the iterative reconstruction result ( Figure 3B ).

[0060] Both present artifacts on the reconstructed slices. The ring image artifacts are prominent in the FDK reconstruction but less visible in the iterative reconstruction. However, the artifact problem requires further attention.

[0061] Figure 4 is a flowchart showing the steps of processing the projection data (raw transmission data), which is obtained by the image detector 124 using FDK filtered backprojection for SRWFM and executed by a computer system such as the computer system 200.

[0062] In step 310, two-dimensional Gaussian smoothing can (not necessarily) be performed on the projection data. This is useful for improving the signal-to-noise ratio (SNR) in the final reconstructed volume.

[0063] In step 312, cone-beam correction weighting is performed on the projection characteristics of the FDK reconstruction. This cone-beam correction weighting is a weighting related to the cone-beam CT geometry. In the cone-beam geometry, the density of the rays changes with the distance from the source. This can lead to different contributions of the rays to the variation in the final reconstruction. As described in Feldkamp, L.A., Davis, L.C. and Kress, J.W. (1984), Practical Cone-Beam Algorithm, Journal of the Optical Society of America A, 1, 612 - 619, the cone-beam weighting function is used to compensate for this non-uniformity by adjusting the intensity values before backprojection.

[0064] In step 314, ramp filtering is performed on the projection. This is used to counteract the blurring introduced by the backprojection process. The backprojection operation is essentially a smoothing process, and without any correction, the reconstructed image will become blurred. This blurring effect occurs because each pixel in the reconstructed image is essentially the average of the attenuation line integrals along the rays passing through that pixel.

[0065] In this variant of the FDK algorithm, redundancy weighting of the measurement data is not performed (Cho, P.S., Rudd, A.D. and Johnson, R.H., Cone-beam CT from width-truncated projections, Computerized Medical Imaging and Graphics, 20, 49-57 (1996)). As we know in mathematics, the multiplication of two signals in the spatial domain is equal to the convolution of these two signals in the frequency domain. Therefore, pre-weighting the original measurement data is to multiply the original measurement data by a redundancy weighting function, which is a convolution operation in the frequency domain of the signal. Thus, this step can introduce additional frequency components, which can be amplified by the ramp filtering step because the ramp filter is a high-pass filter. Instead, redundancy weighting is performed after convolution with the ramp filter.

[0066] Specifically, in step 316, the pixel intensity is scaled to 1 / cos(α), where α is the angle as Figure 5 shown. That is, α is the angle between the plane of the detector 124 and the virtual detector plane 124V, which is perpendicular to the vector V passing through the rotation axis RA of the rotating table 110 and the center of the source 102. By making the intensity in the reconstructed volume represent the attenuation coefficient of the sample, this makes the image intensity scaling correct for the SRWFM with rotation axis offset.

[0067] Alternatively, for example, the original projection data can be remapped onto a virtual detector plane that is perpendicular to the line from the source 102 to the rotation axis RA of the rotating table 110 in the main plane of the cone-beam geometry. Then, the reconstruction is performed using the projections on the virtual detector.

[0068] Then, in step 318, redundancy weighting (single-rotation wide-field weighting) of the 2D ramp-filtered projection data is performed before the back-projection step.

[0069] Figure 6 Shows the relationship between the region of the rotation axis RA of the rotating table 110 and the detector 124 when the position of the rotation axis RA of the rotating table is projected onto the detector 124 in the SRWFM configuration as viewed from the perspective of the source 110. This shows how to define the factor σ, which is the distance between the rotation axis RA projected onto the detector 124 and the nearest edge 124-E of the detector 124 that extends parallel to the projected rotation axis RA.

[0070] The redundancy weighting (SRWF weighting) of the ramp-filtered 2D raw data in step 318 is performed according to the following weighting formula:

[0071]

[0072] where σ is defined as in Figure 6 .

[0073] As shown in Figure 6 , this formula is used when the rotation axis of the turntable 110 moves to the left relative to the detector center. If the rotation axis moves to the right relative to the detector, the flipped version of the weighted formula is used.

[0074] Finally, in step 320 of Figure 4 , back-projection is performed, i.e., the pre-processed projection data is "smeared back" to each voxel of the reconstructed volume, i.e., each pixel value of the pre-processed projection data is placed back into the voxel of the reconstructed volume that intersects the X-ray path from the X-ray source to the detector pixel.

[0075] Figure 7 is a flow chart showing a method for iterative reconstruction of SRWFM scans to be performed by a computer system (such as computer system 200).

[0076] In step 330, the reconstructed volume is initialized to zero.

[0077] In step 332, a stopping criterion based on the reconstructed volume is checked. The stopping criterion can be based on a predetermined number of iterations. If the number of iterations reaches a predetermined value, the method stops. Other stopping criteria can be based on the change in the final reconstructed volume, i.e., if the change in voxel values is less than a predefined value between iterations, the method stops. In either case, the final set of reconstructed volumes 264 is saved in step 342.

[0078] In step 334, forward projection is performed.

[0079] In step 336, the raw projection is compared with the forward projection from step 334 to calculate the difference between the raw projection data and the forward projection data, which is used to update the reconstructed volume in the back-projection step.

[0080] In step 338, noise model weighting is performed, which adjusts the contribution of each X-ray line integral measured along the line connecting the source and a given detector pixel to the reconstructed image volume. More specifically, X-ray line integrals with larger attenuation values and thus larger uncertainties (or noise) contribute less to the reconstructed volume compared to X-ray line integrals with smaller attenuation values and less noise.

[0081] Then, in step 318, the previously defined single-rotation wide-field weighting is performed as described in conjunction with Figure 4 .

[0082] This improves the iterative reconstruction image quality and reduces artifacts by adding an additional SRWFM weighting step using a weighting formula in the iterative reconstruction.

[0083] Iterative reconstruction creates an updated reconstructed volume in step 330 by back-projecting 340 with the weighted projections from step 318.

[0084] Figure 8A and Figure 8B shows the image reconstruction results of the FDK-based method ( Figure 4 ) and the iterative reconstruction method ( Figure 8A ) according to Figure 7 . Figure 8B ).

[0085] In an example of SRWFM scans for FDK results and iterative reconstruction results, the proposed method can eliminate image artifacts of both reconstruction methods.

[0086] Although the invention has been specifically shown and described with reference to its preferred embodiments, those skilled in the art will understand that various changes in form and detail may be made therein without departing from the scope of the invention covered by the appended claims.

Claims

1. A method for reconstructing a three-dimensional volume of a sample based on projection data obtained by single-rotation wide-field mode (SRWFM) X-ray microtomography, the method comprising: acquiring X-ray projections of the sample by a detector by rotating the sample about a rotation axis that is offset relative to the X-ray propagation axis; and processing the acquired projections to account for the offset rotation axis by applying redundant weighting to correct for incomplete angular sampling in a region of the projection data, wherein the redundant weighting is performed before backprojection in analytical reconstruction or before an equivalent backprojection operation in iterative reconstruction.

2. The method according to claim 1, further comprising: Before the redundant weighting, a ramp filter is applied to the projection data, and wherein the redundant weighting is performed on the ramp-filtered data.

3. The method according to claim 1, wherein The redundant weighting is applied in a region on the detector around the projection of the rotation axis.

4. The method according to claim 3, wherein The redundant weighting employs a position-dependent weighting function that corrects the projection without the need for multiple scans.

5. The method according to claim 1, further comprising: Adjusting the projection data by scaling pixel intensities according to an angle formed between the optical axis of the X-ray beam and the plane of the detector, the scaling correcting for geometric distortion introduced by the offset-axis configuration.

6. The method according to claim 1, wherein Remapping the projections onto a virtual detector plane perpendicular to the line connecting the X-ray source and the rotation axis, thereby ensuring correct attenuation coefficient representation in the reconstructed volume.

7. The method according to claim 1, wherein The iterative reconstruction method comprises: applying weighting based on a noise model to the difference between the measured data and the forward projection data, and subsequently incorporating the redundant weighting before backprojection, thereby improving noise handling and artifact reduction.

8. The method according to claim 1, further comprising: Acquiring projections over the entire 360-degree rotation of the sample to ensure sufficient sampling of regions within the magnified field of view.

9. The method according to claim 8, further comprising: Acquiring projections only in a single complete 360-degree rotation.

10. A system for reconstructing a three-dimensional volume of a sample based on projection data obtained by single-rotation wide-field mode (SRWFM) X-ray scanning, the system comprising: an X-ray source configured to generate an X-ray beam; a rotating stage configured to hold and rotate the sample about a rotation axis that is offset relative to the X-ray propagation axis, thereby providing X-ray projections with a magnified effective field of view that exceeds the nominal detector size; a detector configured to receive the X-ray projections of the sample; and a processing system configured to: receive projection data from the detector, apply redundant weighting to correct for incomplete angular sampling in a region of the projection data, wherein the redundant weighting is performed before backprojection in analytical reconstruction or before an equivalent backprojection operation in iterative reconstruction, and reconstruct a three-dimensional volume of the sample based on the projection data based on the applied redundant weighting.

11. The system according to claim 10, wherein The processing system is further configured to: apply a ramp filter to the projection data before applying the redundant weighting such that the redundant weighting is performed on the ramp-filtered data.

12. The system according to claim 10, wherein, The processing system is configured to: apply the redundant weighting in a region on the detector around the projection of the rotation axis.

13. The system according to claim 12, wherein, The processing system is configured to: employ a position-dependent weighting function that corrects the projection without the need for multiple scans.

14. The system according to claim 10, wherein, The processing system is further configured to adjust the projection data by scaling pixel intensities according to an angle formed between an optical axis of the X-ray beam and a plane of the detector, the scaling correcting for geometric distortion introduced by the offset axis configuration.

15. The system according to claim 10, wherein The processing system is configured to remap the projection onto a virtual detector plane perpendicular to a line connecting the X-ray source and the rotation axis, thereby ensuring correct attenuation coefficient representation in the reconstructed volume.

16. The system according to claim 10, wherein, The processing system is configured to perform an iterative reconstruction algorithm that includes applying a weighting based on a noise model to a difference between measured data and forward projection data, and subsequently combining the redundant weighting prior to back projection, thereby improving noise handling and artifact reduction.

17. The system according to claim 10, further comprising a controller configured to operate the turntable and acquire projections during a full 360-degree rotation of the sample to ensure sufficient sampling of regions within the enlarged field of view.

18. The system according to claim 17, wherein, The controller is configured to rotate the sample only once during the full 360-degree rotation, thereby eliminating the need for multiple independent scans.

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