WO2021252410A1 - Reducing artifacts in computerized tomography scans - Google Patents

Abstract

A computer system for reducing metal artifacts in computed tomography (CT) images is configured to reconstruct a raw CT image from a CT projection. The CT projection includes a matrix of measurements in a projection domain obtained via a CT scan, and the raw CT image includes a matrix of pixels in an image domain reconstructed from the matrix of measurements in the projection domain. The computer system identifies metal segments in the raw CT image and forward projects the metal segments to generate shadows in the projection domain. The computer system then iteratively adjusts measurements in the shadows in the projection domain to reduce metal artifacts in the raw CT image and reconstructs an improved CT image based on the adjusted measurements in the shadows and measurements not in the shadows in the projection domain.

Description

REDUCING ARTIFACTS IN COMPUTERIZED TOMOGRAPHY SCANS

CROSS-REFERENCE TO RELATED APPLICATIONS [0001] This application claims the benefit of and priority to United States Provisional Patent Application Serial No. 63/036,312, filed June 8, 2020 and titled “SYSTEM FOR REDUCTION OF ARTIFACTS IN COMPUTERIZED TOMOGRAPHY SCANS”, which is herein incorporated by reference in its entirety.

BACKGROUND

[0002] Computers and computing systems have affected nearly every aspect of modem living. Computers are generally involved in work, recreation, healthcare, transportation, entertainment, household management, etc. Computers have developed an increasingly important role in physical security systems. Whereas, digital security systems maintain the security of digital spaces, such as servers and databases, physical security systems assist in maintaining the security of physical spaces, such as airports and large venues.

[0003] An example area where computers are utilized to assist in maintaining physical security is x-ray technology. For example, nearly every airport in the world now uses x- ray scanners, such as CT scanners, to inspect the contents of luggage being brought onto an airplane. While scanning bags provides an important keystone to modem physical security strategies, one will appreciate the significant difficulties involved in scanning luggage. Nearly every item of luggage will be filled with unique items of differing physical compositions and densities. Further, many modem suitcases and bags include metal frame elements that further increase the difficulty of performing meaningful x-ray scans of luggage and its contents.

[0004] The subj ect matter claimed herein is not limited to embodiments that solve any disadvantages or that operate only in environments such as those described above. Rather, this background is only provided to illustrate one exemplary technology area where some embodiments described herein may be practiced.

BRIEF SUMMARY

[0005] Disclosed embodiments include a computer system for reducing metal artifacts in computer tomography (CT) images. The computer system comprises one or more processors and one or more computer-readable storage devices having stored thereon executable instructions that, when executed by the one or more processors, configure the computer system to perform various acts. The computer system is configured to reconstruct a raw CT image from a CT projection (also referred to as a sinogram) generated via a CT scan. The CT projection includes a matrix of measurements obtained via the CT scan in a projection domain, and the raw CT image includes a matrix of pixels in an image domain that are reconstructed from the matrix of measurements in the projection domain. The computer system is also configured to identify one or more metal segments in the raw CT images and forward project the one or more metal segments to generate one or more shadows in the projection domain. The computer system is also configured to iteratively adjust measurements in the one or more shadows in the projection domain to reduce metal artifacts in the raw CT image and reconstruct an improved CT image in the image domain based on the adjusted measurements in the one or more shadows and measurements not in the one or more shadows in the projection domain.

[0006] The disclosed embodiments also include a method implemented at a computer system for reducing metal artifacts in computed tomography (CT) images. The method includes reconstructing a raw CT image from a CT projection. The CT projection includes a matrix of measurements obtained via a CT scan in a projection domain, and the raw CT image includes a matrix of pixels in an image domain that are constructed from the matrix of measurements in the projection domain. The method also includes identifying one or more metal segments in the raw CT image and forward projecting the one or more metal segments to generate one or more shadows in the projection domain. The method further includes iteratively adjusting measurements in the one or more shadows in the projection domain to reduce metal artifacts in the raw CT image and reconstructing an improved CT image based on the adjusted measurements in the one or more shadows and measurements not in the one or more shadows in the projection domain.

[0007] Disclosed embodiments also include a computer system for identifying one or more features associated with a particular type of artifact in CT images and reducing the particular type of artifact in a given CT image. The computer system comprises one or more processors and one or more computer-readable storage devices having stored thereon executable instructions that, when executed by the one or more processors, configure the computer system to perform various acts. The computer system is configured to access a plurality of labeled CT images as training data and access a machine learning network. Each of the plurality of labeled CT images is labeled as having a particular type of artifact or not having the particular type of artifact. The computer system is also configured to identify one or more artifact features that are associated with the particular type of artifact using the machine learning network and the plurality of labeled CT images. When the computer system receives a CT projection, the computer system is configured to reconstruct a raw CT image from the CT projection. The CT projection includes a matrix of measurements obtained via a CT scan in a projection domain, and the raw CT image includes a matrix of pixels in an image domain that are reconstructed from the matrix of measurements in the projection domain. The computer system is also configured to identify one or more artifact segments in the raw CT image and forward projects the one or more artifact segments to generate one or more shadows in the projection domain. The computer system is also configured to iteratively adjust measurements in the one or more shadows in the projection domain to minimize effect of at least one of the one or more artifact features and reconstruct an improved CT image based on the adjusted measurements in the one or more shadows and measurements not in the one or more shadows in the projection domain.

[0008] This Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used as an aid in determining the scope of the claimed subject matter. [0009] Additional features and advantages will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by the practice of the teachings herein. Features and advantages of the invention may be realized and obtained by means of the instruments and combinations particularly pointed out in the appended claims. Features of the present invention will become more fully apparent from the following description and appended claims or may be learned by the practice of the invention as set forth hereinafter.

BRIEF DESCRIPTION OF THE DRAWINGS [0010] In order to describe the manner in which the above-recited and other advantages and features can be obtained, a more particular description of the subj ect matter briefly described above will be rendered by reference to specific embodiments which are illustrated in the appended drawings. Understanding that these drawings depict only typical embodiments and are not therefore to be considered to be limiting in scope, embodiments will be described and explained with additional specificity and detail through the use of the accompanying drawings in which:

[0011] Figure 1A illustrates a first airport bag in a conventional FBP reconstruction;

[0012] Figure IB illustrates the first airport bag in a metal segmentation;

[0013] Figure 1C illustrates the first airport bag in a reconstruction after damaged value recovery based on minimizing a total variation norm described herein;

[0014] Figure ID illustrates the first airport bag in an image-domain TV reconstruction; [0015] Figure 2A illustrates a second airport bag in a conventional FBP reconstruction;

[0016] Figure 2B illustrates the second airport bag in a metal segmentation;

[0017] Figure 2C illustrates the second airport bag in a reconstruction after damaged value recovery based on minimizing a total variation norm described herein;

[0018] Figure 2D illustrates the second airport bag in an image-domain TV reconstruction;

[0019] Figure 3A illustrates a third airport bag in a conventional FBP reconstruction;

[0020] Figure 3B illustrates the third airport bag in a metal segmentation;

[0021] Figure 3C illustrates the third airport bag in a reconstruction after damaged value recovery based on minimizing a total variation norm described herein;

[0022] Figure 3D illustrates the third airport bag in an image-domain TV reconstruction;

[0023] Figure 4A illustrates a fourth airport bag in a conventional FBP reconstruction;

[0024] Figure 4B illustrates the fourth airport bag in a metal segmentation;

[0025] Figure 4C illustrates the fourth airport bag in a reconstruction after damaged value recovery based on minimizing a total variation norm described herein;

[0026] Figure 4D illustrates the fourth airport bag in an image-domain TV reconstruction;

[0027] Figure 5A illustrates a fifth airport bag in a conventional FBP reconstruction;

[0028] Figure 5B illustrates the fifth airport bag in a metal segmentation;

[0029] Figure 5C illustrates the fifth airport bag in a reconstruction after damaged value recovery based on minimizing a total variation norm described herein;

[0030] Figure 5D illustrates the fifth airport bag in an image-domain TV reconstruction;

[0031] Figure 6A illustrates a projection mask for the first airport bag;

[0032] Figure 6B illustrates a projection mask for the second airport bag;

[0033] Figure 6C illustrates a projection mask for the third airport bag;

[0034] Figure 6D illustrates a projection mask for the fourth airport bag;

[0035] Figure 6E illustrates a projection mask for the fifth airport bag;

[0036] Figure 7A illustrates a raw FBP reconstruction of the first airport bag;

[0037] Figure 7B illustrates an improved FBP reconstruction of the first airport bag based on minimizing a sum of squares of values of pixels that have negative values described herein;

[0038] Figure 8A illustrates a raw FBP reconstruction of the second airport bag; [0039] Figure 8B illustrates an improved FBP reconstruction of the second airport bag based on minimizing a sum of squares of values of pixels that have negative values described herein;

[0040] Figure 9A illustrates a raw FBP reconstruction of the third airport bag; [0041] Figure 9B illustrates an improved FBP reconstruction of the third airport bag based on minimizing a sum of squares of values of pixels that have negative values described herein;

[0042] Figure 10A illustrates a raw FBP reconstruction of the fourth airport bag;

[0043] Figure 10B illustrates an improved FBP reconstruction of the fourth airport bag based on minimizing a sum of squares of values of pixels that have negative values described herein;

[0044] Figure 11 A illustrates a raw FBP reconstruction of the fifth airport bag;

[0045] Figure 11B illustrates an improved FBP reconstruction of the fifth airport bag based on minimizing a sum of squares of values of pixels that have negative values described herein;

[0046] Figure 12A illustrates a raw FBP reconstruction image of the first airport bag; [0047] Figure 12B illustrates an improved reconstruction image of the first airport bag using TV norm minimization;

[0048] Figure 12C illustrates an improved reconstruction image of the first airport bag using negative pixel energy minimization;

[0049] Figure 12D illustrates an improved reconstruction image of the first airport bag using a combination of TV norm minimization and negative pixel energy minimization; [0050] Figure 13A illustrates a raw FBP reconstruction image of the second airport bag; [0051] Figure 13B illustrates an improved reconstruction image of the second airport bag using TV norm minimization;

[0052] Figure 13C illustrates an improved reconstruction image of the second airport bag using negative pixel energy minimization;

[0053] Figure 13D illustrates an improved reconstruction image of the second airport bag using a combination of TV norm minimization and negative pixel energy minimization;

[0054] Figure 14A illustrates a raw FBP reconstruction image of the third airport bag; [0055] Figure 14B illustrates an improved reconstruction image of the third airport bag using TV norm minimization; [0056] Figure 14C illustrates an improved reconstruction image of the third airport bag using negative pixel energy minimization;

[0057] Figure 14D illustrates an improved reconstruction image of the third airport bag using a combination of TV norm minimization and negative pixel energy minimization;

[0058] Figure 15 A illustrates a raw FBP reconstruction image of the fourth airport bag; [0059] Figure 15B illustrates an improved reconstruction image of the fourth airport bag using TV norm minimization;

[0060] Figure 15C illustrates an improved reconstruction image of the fourth airport bag using negative pixel energy minimization;

[0061] Figure 15D illustrates an improved reconstruction image of the fourth airport bag using a combination of TV norm minimization and negative pixel energy minimization;

[0062] Figure 16A illustrates a raw FBP reconstruction image of the fifth airport bag; [0063] Figure 16B illustrates an improved reconstruction image of the fifth airport bag using TV norm minimization;

[0064] Figure 16C illustrates an improved reconstruction image of the fifth airport bag using negative pixel energy minimization;

[0065] Figure 16D illustrates an improved reconstruction image of the fifth airport bag using a combination of TV norm minimization and negative pixel energy minimization; [0066] Figure 17A illustrates a raw FBP reconstruction image of the fifth airport bag; [0067] Figure 17B illustrates an improved reconstruction image of the fifth airport bag using TV norm minimization with a different metal segmentation threshold;

[0068] Figure 17C illustrates an improved reconstruction image of the fifth airport bag using negative pixel energy minimization with a different metal segmentation threshold; [0069] Figure 17D illustrates an improved reconstruction image of the fifth airport bag using a combination of TV norm minimization and negative pixel energy minimization with a different metal segmentation threshold;

[0070] Figure 18A illustrates a metal map of the fifth airport bag based on segmentation threshold of 1/3 of the maximum pixel value;

[0071] Figure 18B illustrates a metal map of the fifth airport bag based on segmentation threshold of 1/10 of the maximum pixel value;

[0072] Figure 19A illustrates a sinogram processed with a method described herein;

[0073] Figure 19B illustrates a raw sinogram generated by a CT scan; [0074] Figure 19C illustrates a difference between the processed sinogram of Figure 19A and the raw sinogram of Figure 19B;

[0075] Figure 20 illustrates a flowchart of an example method for reducing metal artifacts in CT images;

[0076] Figure 21 illustrates a flowchart of an example method for using a machine learning network to identify one or more features associated with a particular type of artifact in CT images and removing the artifacts caused by the particular type of artifacts in a given CT image; and

[0077] Figure 22 illustrates a schematic of a computer system for reduction of artifacts in computerized tomography.

DETAILED DESCRIPTION

[0078] Computed tomography (CT) refers to a computerized x-ray imaging procedure in which a narrow beam of x-rays is aimed at a body of an object and quickly rotated around the body of the object, producing signals that are processed by the machine’s computer to generate a matrix of measurements (also referred to as a projection or a sinogram) in a projection domain. The measurements in the projection domain are machine-readable, but hard to understand by human users. A human-readable CT image in an image domain can be reconstructed from the projection. Different algorithms, such as (but not limited to) filtered back projection (FBP), may be used to reconstruct images from projections. On the other hand, the reconstructed images can also be converted back to projections via a forward projection (FP) operation.

[0079] In CT images, metal artifacts are caused by beam hardening effects, which are nonlinearly dependent on the metallic materials. These nonlinear effects introduce errors to the line-integral model of the measurements. The line-integral amplitudes are distorted when the integration lines pass through metals. Usually, the distorted line-integral value is smaller than the true value. The distortion is nonlinear and difficult to estimate, because the metallic materials in the objects are unknown. For example, for a collection of random metallic and non-metallic objects, it is almost impossible to establish a beam hardening model to convert the broad-spectrum measurements into pseudo mono-energy measurements so that the metal artifacts can be removed.

[0080] The embodiments disclosed herein solve the above-described problem by identifying one or more metal segments in a raw CT image, forward projecting the one or more metal segments to generate one or more shadows in a projection domain, iteratively adjusting measurements in the one or more shadows in the projection domain to reduce metal artifacts in the raw CT image, and reconstructing an improved CT image based on the adjusted measurements in the one or more shadows (and measurements not in the one or more shadows) in the projection domain.

[0081] In some embodiments, the iterative adjusting of the measurements in the one or more shadows in the projection domain to reduce the artifacts in the one or more metal segments includes iteratively adjusting the measurements in the one or more shadows to reduce a total variation norm of the matrix of non-metal pixels in the image domain (hereinafter also referred to as “total variation norm minimization”). In some embodiments, an optimization method, such as (but not limited to) a gradient descent method, is used to minimize the total variation norm of the matrix of non-metal pixels in the image domain.

[0082] In some embodiments, the iterative adjusting of the measurements in the one or more shadows in the projection domain to reduce the artifacts in the one or more metal segments includes identifying pixels in the image domain that have negative values and iteratively adjusting the measurements in the one or more shadows to reduce a sum of squares of values of the pixels in the image domain that have negative values (herein after also referred to as “negative pixel energy minimization”). In some embodiments, an optimization method, such as (but not limited to) a gradient descent method, is used to minimize the sum of squares of values of the pixels in the image domain that have negative values.

[0083] In some embodiments, the iterative adjusting of the measurements in the one or more shadows in the projection domain to reduce the artifacts in the one or more metal segments includes iteratively adjusting the measurements in the one or more shadows to reduce a combination of (1) a sum of squares of values of the pixels in the image domain that have negative values, and (2) a total variation norm of the matrix of non-metal pixels in the image domain. In some embodiments, the combination of (1) the sum of squares of values of the pixels in the image domain that have negative values, and (2) the total variation norm of the matrix of non-metal pixels in the image domain is a weighted combination, in which the sum of squares of values of the pixels in the image domain that have negative values is given a first weight, and the total variation norm of the matrix of non-metal pixels in the image domain is given a second weight. In some embodiments, an optimization method, such as (but not limited to) a gradient descent method, is used to minimize the weighted combination.

[0084] Notably, the total variation norm and the sum of squares of values of pixels that have negative values are merely two artifact features that are associated with the metal artifacts. There may be additional artifact features that are also associated with the metal artifacts or any other artifacts caused by other materials or circumstances. A similar process may be implemented to minimize the metal artifacts based on other artifact features or minimize other artifacts based on the same or other artifact features.

[0085] In some embodiments, a machine learning network, such as (but not limited to) a neural network, a convolutional neural network, is used to identify one or more artifact features based on training data. The training data includes a plurality of CT images, each of which is labeled as good or bad. The images that are labeled good do not have metal artifacts. The images that are labeled bad have metal artifacts. In some embodiments, the measurements in the one or more shadows in the projection domain are iteratively adjusted to minimize effect of at least one of the one or more artifact features . In some embodiments, a gradient descent method is used to minimize the effect of the at least one of the one or more artifact features.

[0086] Objective Function Associated with Total Variation (TV) Norm Minimization [0087] As briefly discussed above, in some embodiments, the interactive adjusting of the measurements is to reduce or minimize a total variation norm of the matrix of non- metal pixels of an image in the image domain.

[0088] Let /be an image reconstructed via FBP. The image /is represented in a two- dimensional (2D) array, and f_j is pixel values of the image at the ith row and jth column. A total variation (TV) norm of /is defined as:

[0089] Equation (1)

[0090] In some embodiments, T in Equation (1) is used as an objective function for optimizing the image. When the quality under the square root in Equation (1) is positive, the partial derivative of T with respect to pixel (i, j) is calculated as:

f ^j f —^ij Equation (2) (f i-l,j-fi-l,j+l)² +(f i-lj-fij)²

[0092] When the quantity under the square root is zero, the quantity reaches its minimum and a penalty function is no longer needed. In this situation, it is safe to set the derivative to zero. In some embodiments, a very small positive constant e (e.g., e = 10⁸) may be implemented to the Equation (2) to generate the following equation: _ flj-fl-lj _ Equation (3)

Jif i-l,j-fi-l,j+l)² +(f i-l,j^~fi,j)^{2 +e}

[0094] In some embodiments, an iterative gradient descent algorithm is implemented to minimize the objective function T defined in Equation (1). The iterative gradient descent algorithm may be defined as:

[0095] f ^w = f°_j ^ld - Ui_j Equation (4)

[0096] In some embodiments, the Randon transform is applied to both sides of

Equation (4) to generate the following equation:

[0097]

Equation (5)

[0098] Where l is a relaxation parameter. For example, in some embodiments, the relaxation parameter may be chosen to be 0.01. 5R is the Radon transform operator, and p_t, ø= 5R{/} with (t, Q) being the measurement space coordinates.

[0099] Further, a mask function mask_metai is multiplied on both sides of Equation (5) to generate the following equation:

[00100] v el_metcd) = Vt^l£(metai) ^~ * ^{x mask}metai x 9l{U_tJ} Equation (6)

[00101] In order to find this mask function, the FBP algorithm is used to reconstruct an initial image, which may contain lots of metal artifacts. A threshold value is selected (for example, 1/3 of the maximum pixel value) and used to segment the FBP reconstruction to create a metal object image f metal. The mask, denoted as maskmetai, is a function in the projection-domain and is based on the Radon transform of f metal. The mask function maskmetai is 1 at the location that the Radon transform of fmetai is positive and is 0 at the location that the Radon transform of fmetai is 0. The mask function restricts Equation (5) only on the region when maskmetai is 1. As such, Equation (6) updates the line-integral measurements that the projection rays pt, e(metal) touch the metal objects.

[00102] However, Equation (6) may smooth out some or all metallic objects while minimizing the TV norm in Equation (1). In order to keep the metallic objects in the image, the image-domain masking function fmetai can be used to hide the metals in TV gradient image. In some embodiments, Ui_j is replaced with Ui_j x ( 1 - fmetai) in Equation (6) to generate the following equation:

Equation (7)

[00104] Equation (7) can then be implemented in the following steps: [00105] (i) obtain a raw FBP reconstruction (i.e., a raw image reconstructed via FBP);

[00106] (ii) use a threshold to segment a metal image f_metai from the raw FBP reconstruction;

[00107] (iii) set the raw measurements as the initial values and perform iterative updates for the unreliable measurement P_t,e_{(metai )} iⁿ the shadows according to Equation (7). [00108] (iv) obtain a final FBP reconstruction with measurements, where the unreliable portions of the final FBP reconstruction have been revised by step (iii).

[00109] We now turn to experimental results that were obtained through implementation of the above-described software application. The experimental data was acquired with an Imatron C300 clinical CT scanner, which was a fifth generation CT scanner based on a scanning electron beam X-ray source. The number of views was 180 over 180°. The number of channels (i.e., the detection bin at each view) was 597. The projections used the parallel-beam imaging geometry. The reconstructed image size was 420 x 420.

[00110] Figures 1 A- ID, 2A-2D, 3A-3D, 4A-4D, 5A-5D, and 6A-6E depict five airport- bag examples that illustrate the effectiveness of the method described herein. Within the described figures, Figures 1A, 2A, 3A, 4A, and 5A depict the raw FBP reconstruction of the x-ray of each respective bag. Figures IB, 2B, 3B, 4B, and 5B illustrate the segmented metal image f_metai of the x-ray of each respective bag. Figures 1C, 2C, 3C, 4C, and 5C illustrate the final FBP reconstruction using the restored projections of the x-ray of each respective bag in accordance with embodiments of the present invention. Additionally, Figures ID, 2D, 3D, 4D, and 5D illustrate the reconstructed image using the image-domain TV iterative algorithm. The relaxation parameter for the data fidelity term was 0.001, and the relaxation parameter for the TV constraint term was 0.005. The number of iterations was 400 for both the projection-domain iteration algorithm described herein and for the image-domain iterative TV algorithm. The reconstructions are displayed from the minimum pixel value to 0.3 times the maximum pixel value. The results from these five examples are shown in Figures 1A-1D, 2A-2D, 3A-3D, 4A-4D, and 5A-5D, respectively.

[00111] Figures 6A-6E show the projection masks for the measurements of bags 1 to 5, respectively. These are binary images with values 0 (black) and 1 (white). The white regions indicate the projection values that are adjusted by the algorithm described herein. The black regions indicate the projection values that are kept unchanged. [00112] In this section, three methods are compared in terms of their performance on correcting metal-induced errors. These three methods are: (1) the conventional FBP algorithm, (2) the TV-minimization algorithm with image-domain update, and (3) the algorithm described herein (i.e., TV-minimization algorithm with projection-domain update). For the five airport bags, the reconstructed images using these three methods are shown in Figures 1A-1D, 2A-2D, 3A-3D, 4A-4D, and 5A-5D, respectively.

[00113] The metal obj ect-induced artifacts appear as dark undershoots around the bright metal objects. Visual assessments indicate that the conventional FBP algorithm (shown in Figures 1 A, 2A, 3A, 4A, and 5A) gives the most severe artifacts, the image-domain-update TV algorithm (shown in Figures ID, 2D, 3D, 4D, and 5D) somewhat reduces the artifacts with worsened spatial resolution, and the algorithm described herein (shown in Figures 1C, 2C, 3C, 4C, and 5C) is most effective in metal artifact reduction.

[00114] Numerical evaluation of the metal artifact reduction is performed by measuring the minimum image pixel value in a dark undershoot region. Firstly, an undershoot region- of-interest (ROI) is identified visually. The ROI is a 40 ^c 40 square region. Secondly, the minimum value in this ROI is searched. This minimum value serves as the figure-of-merit. A smaller minimum value indicates a more severe artifact. A smaller value is a value closer to the negative infinite. The numerical results are summarized in Table 1, from which the method described herein performs the best among the three methods.

Table 1

[00115] These numerical results also imply that the metal streaking artifacts can be reflected by the image TV norm. In view of these results, the method described herein minimizes the image-domain TV norm of the FBP reconstruction. This algorithm does not use any models for unreliable projections. Accordingly, this algorithm can also be applied to many applications other than removing beam-hardening artifacts. [00116] Objective Function Associated with Negative Pixel Energy Minimization [00117] Additionally, in at least one embodiment, the metal artifacts have regions with negative pixel values in the FBP reconstruction. The principles described herein also include using an objective function associated with the negative pixel values. [00118] Let A be the operator of the FBP algorithm, P be proj ection measurements, and

X be the FBP reconstruction. Both P and X are expressed in the vector form, and A is expressed in the matrix form. The FBP reconstruction X is AP. The elements in X are xi. Let Y be the column vector containing the entries:

[00119] ; = min (0, xi) Equation (8) [00120] Thus, the vector Y is the same as the FBP reconstruction X, except that all positive pixels of X are set to zero.

[00121] In some embodiments, an objective function is a squared L2-norm of Y, defined as the following equation:

[00122]

Equation (9) [00123] The objective function defined by Equation (9) is then minimized to optimize the FBP reconstruction image. The variables for this objective function are metal affected projections PM. In some embodiments, the entries in PM are determined by the following steps:

[00124] (i) use the FBP algorithm to generate a raw image X_mw using projection measurements P. The raw image may contain severe metal artifacts.

[00125] (ii) segment the raw image to obtain a metal-only image, using a threshold value, for example, as the 1/3 of the maximum pixel value of A,-,,,,· where all pixel values that are smaller than this threshold value are set to zero; and [00126] (iii) forward project the metal-only image to obtain the indices of PM. [00127] In some embodiments, a gradient descent algorithm is used to minimize the objective function defined by Equation (9) by updating the variables in PM. Let pj be an entry in Pm. To find the gradient of dF/dp_j is not straightforward, because the min function in Equation (8) makes Equation (8) undifferentiable. In embodiments, subdifferential concept is used to find the gradient of dF/dp_j as the following: [00128] VF=2A^T min{0, APj = 2A^T Y Equation (10)

[00129] Where A^T is the adjoint operator of the FBP algorithm and min (0, APj sets each positive entry of AP to zero. Here, AP is the FBP image reconstruction using projections P, and A¹ is the forward projection followed by the ramp filtration with the one-directional (ID) convolution kernel, which is defined as: [00131] The gradient descent iterative algorithm is given as

[00132]

Equation (12)

[00133] Where the superscript (k) is the iteration index. The proj ection vector P consists of two parts: (1) the metal affected part P_M and the metal not affected part P_notM. The metal not affected part P_notM does not get updated from iteration to iteration. The operator D in Equation (12) is a dimension reduction operator that discards the entries in P_notM. The parameter b in Equation (12) controls the step size of the gradient descent algorithm. [00134] We now turn to experimental results that were obtained through the implementation of the above-described software application. Equation (12) was applied to several sets of CT data of airport bags. The step size b was chosen to be 1, and the number of iterations was 500. The number of views for the scaled-down version was 180 over 180. The number of channels (i.e., the detection bin at each view) for the scaled-down version was 597. The reconstructed image size was 420 x 420. [00135] Figures 7A-7B, 8A-8B, 9A-9B, 10A-10B, and 1 lA-1 IB illustrate five different airport bags. Figures 7A, 8A, 9A, 10A, and 11 A illustrate raw FBP reconstruction images, and Figures 7B, 8B, 9B, 10B, and 11B illustrate the improved images processed by the method described herein. The negative values are shown as the darkest color, and the metals are shown as the brightest color. The display window is set to [-0.1a, 0.5a], where a is the maximum pixel value. The display window for the raw image and the display window for the final image are the same. The negative image pixel values only appear in the closed neighborhood of the metals in the raw FBP reconstruction images. After applying the method described herein, the negative image pixels are significantly removed, and dark streaking artifacts are also reduced. Such improvement cannot be achieved by merely setting the negative image pixel values to zero in the raw FBP reconstructions. Further, as illustrated, the method described herein also reduces angularly aliasing artifacts (due to insufficient view angles).

[00136] Note, the sum of all the values of all the negative pixels is only one particular way of defining an objective function for minimizing the metal artifacts in CT images. Any other norm can also be applied to the negative pixels to achieve same or similar results of reducing or minimizing the metal artifacts in CT images. [00137] Objective Function Associated with a Combination of Total Variation (TV) Norm Minimization and Negative Pixel Energy Minimization

[00138] In some embodiments, an objective function associated with both TV and pixels having negative values may be implemented. For example, such an objective function may be defined as:

[00139] p_!*T + p₂*F Equation (13)

[00140] Where T is defined by Equation (1), and F is defined by Equation (9), and [h and fh are two parameters whose values may be selected based on the conditions of the images. In some embodiments, the FBP reconstruction images are optimized by minimizing the objective function defined by Equation (13).

[00141] We now turn to experimental results that were obtained through the implementation of the above-described software application. Figures 12A-12D, 13A-13D, 14A-14D, 15A-15D, and 16A-16D show the reconstruction results of five different unknown airport bags. For each airport bag, four images are shown. Figures 12A, 13 A, 14A, 15A, and 16A are original raw FBP reconstruction images of the five airport bags. Figures 12B, 13B, 14B, 15B, and 16B are improved reconstruction images of the five airport bags using TV norm minimization only (with bi = 0.004 and b 2 = 0). Figures 13C, 14C, 15C, 16C, and 17C illustrate improved reconstruction images of the five airport bags using negative pixel energy minimization only (with b 1 = 0 and b 2 = 5) Figures 12D, 13D, 14D, 15D, and 16D illustrate improved reconstruction images of the five airport bags using a combination of TV norm minimization and negative pixel energy minimization (with b 1 = 0.004 and b 2 = 5).

[00142] All images in Figures 12A-12D, 13A-13D, 14A-14D, 15A-15D, and 16A-16D have the same display window. Black color represents negative values, and white color represents large positive values. In order to visualize the metal artifacts, the display window is determined by the raw FBP reconstruction using the originally measured sinogram (i.e., projection). The display window is airport bag-specific. The 1/3 of the maximum raw FBP pixel value is mapped to the gray level 255 (white). Any value larger than 255 is set to 255. The metal pixels are much brighter than other pixels in the image. If the very bright metal pixels are not clipped, the other structures are hard to see in the image. The minimum raw FBP value (which may be negative) is mapped to the gray level 0 (black). The mapping is linear in the range below 1/3 of the maximum value. All four images for a same airport bag use the same gray-scale mapping. Therefore, black pixels are the “negative pixels.” The number of iterations for all experiments was 1000 in the gradient descent algorithm. The image array size was 420 x 420, and the pixel size was 0.92 mm.

[00143] In particular, Figure 12A illustrates a raw FBP reconstruction image of the first airport bag (also referred to as “Bag 1”), Figure 12B illustrates an improved reconstruction image of Bag 1 using TV norm minimization, Figure 12C illustrates an improved reconstruction Bag 1 using negative pixel energy minimization, and Figure 12D illustrates an improved reconstruction image of Bag 1 using a combination of TV norm minimization and negative pixel energy minimization. Table 2 below illustrates the minimum and maximum values in the different reconstruction images shown in Figures 12A-12D.

Table 2

[00144] Figure 13A illustrates a raw FBP reconstruction image of the second airport bag (also referred to as “Bag 2”), Figure 13B illustrates an improved reconstruction image of Bag 2 using TV norm minimization, Figure 13C illustrates an improved reconstruction Bag 2 using negative pixel energy minimization, and Figure 13D illustrates an improved reconstruction image of Bag 2 using a combination of TV norm minimization and negative pixel energy minimization. Table 3 below illustrates the minimum and maximum values in the different reconstruction images shown in Figures 13A-13D.

Table 3

[00145] Figure 14A illustrates a raw FBP reconstruction image of the third airport bag (also referred to as “Bag 3”), Figure 14B illustrates an improved reconstruction image of Bag 3 using TV norm minimization, Figure 14C illustrates an improved reconstruction Bag 3 using negative pixel energy minimization, and Figure 14D illustrates an improved reconstruction image of Bag 3 using a combination of TV norm minimization and negative pixel energy minimization. Table 4 below illustrates the minimum and maximum values in the different reconstruction images shown in Figures 14A-14D.

Table 4

[00146] Figure 15 A illustrates a raw FBP reconstruction image of the fourth airport bag (also referred to as “Bag 4”), Figure 15B illustrates an improved reconstruction image of Bag 4 using TV norm minimization, Figure 15C illustrates an improved reconstruction Bag 4 using negative pixel energy minimization, and Figure 15D illustrates an improved reconstruction image of Bag 4 using a combination of TV norm minimization and negative pixel energy minimization. Table 5 below illustrates the minimum and maximum values in the different reconstruction images shown in Figures 15A-15D.

Table 5

[00147] Figure 16A illustrates a raw FBP reconstruction image of the fifth airport bag (also referred to as “Bag 5”), Figure 16B illustrates an improved reconstruction image of Bag 5 using TV norm minimization, Figure 16C illustrates an improved reconstruction Bag 5 using negative pixel energy minimization, and Figure 16D illustrates an improved reconstruction image of Bag 5 using a combination of TV norm minimization and negative pixel energy minimization. Table 6 below illustrates the minimum and maximum values in the different reconstruction images shown in Figures 16A-16D.

Table 6 [00148] It can be seen that all raw FBP images shown in Figures 12A, 13 A, 14A, 15 A, and 16A, contain severe black streaking artifacts, indicating streaks of negative values. When the objective function only has the TV norm term (i.e., fh = 0), most black streaks are removed shown in Figures 12B, 13B, 14B, 15B, and 16B. Similarly, when the objective function only has the negative pixel energy minimization (i.e., bi = 0), the black streaking artifacts are also effectively removed, shown in Figures 12C, 13C, 14C, 15C, and 16C. Finally, when both the TV norm minimization and the negative pixel energy minimization are used in the objective function (i.e., bi = 0.004 and /¾ = 5), the resultant images shown in Figures 12D, 13D, 14D, 15D, and 16D are further improved compared to the resultant images shown in Figures 12B-12C, 13B-13C, 14B-14C, 15B-15C, and 16B-15C. For example, the resultant images shown in Figures 12D, 13D, 14D, 15D, and 16D not only provide additional low-contrast structures compared to the resultant images shown in Figures 12B, 13B, 14B, 15B, and 16B, but also reduce noises compared to the resultant images shown in Figures 12C, 13C, 14C, 15C, and 16C. [00149] Further, depending on the images and the circumstances, the threshold value for segmenting the metal images and/or the values of the parameters bi and /¾ can also be adjusted to further improve the results. Figures 17A-17D illustrate another set of images of bag 5 (same as that in Figures 16A-16D). However, the images in Figures 17A-17D are generated using a different threshold value 1/10 (instead of 1/3) to segment the metal image and a different bi = 0.0002 (instead of 0.004). Figure 17A illustrates a raw FBP reconstruction image, Figure 17B illustrates a resultant image when the objective function uses only the TV norm minimization (i.e., bi = 0.0002, /¾ = 0), Figure 17C illustrates a resultant image when the objective function only uses the negative pixel energy minimization (i.e., bi = 0 , /¾ = 5), and Figure 17D illustrates a resultant image when the objective function using both the TV norm minimization and the negative pixel energy minimization (i.e., bi = 0.0002, /¾ = 5). Table 7 below illustrates the minimum and maximum values in the different reconstruction images shown in Figures 17A-17D

Table 7 [00150] Compared to the reconstruction images shown in Figures 16B-16D, the reconstruction images shown in Figures 17B-17D removed more dark streaking artifacts. The different results in the two sets of images in Figures 16B-16D and 17B-17D are mainly due to the different configurations in metal image segmentation. As briefly discussed above, the FBP images shown in Figures 16A-16D are segmented into the metal image if the pixel values are greater than 1/3 of the maximum pixel value. In Figures 17A-17D, the FBP image pixels are segmented into the metal image if the pixel values are greater than 1/10 of the maximum pixel value. The change of the segmentation threshold results in different metal images. [00151] Figures 18A-18B illustrate as illustrated two different metal maps of Bag 5 with different thresholds. Figure 18A illustrates a metal map of Bag 5based on a segmentation threshold of 1/3 of the maximum pixel value, and Figure 18B illustrates a metal map of Bag 5based on a segmentation threshold of 1/10 maximum pixel value. [00152] When the segmentation threshold is set as 1/10 maximum pixel value, it is advantageous to change the value of bi from 0.004 to 0.0002 to prevent the resulting image from being too smooth or losing too many details.

[00153] Figures 19A-19C illustrate different sinograms (i.e., projections) processed with different parameters fii and/or /C Figure 19A illustrates a sinogram processed with bi = 0.004 and /¾= 5, Figure 19B shows the raw sinogram, and Figure 19C illustrates a difference between the raw sinogram (shown in Figure 19B) and the processed sinogram (shown in Figure 19 A).

[00154] Using Machine Learning to Select Features

[00155] Notably, the TV norm and negative pixels energy are two features that are associated with metal artifacts. There may be additional features that are also associated with metal artifacts and/or any other artifacts caused by different materials and/or circumstances. In some embodiments, a machine learning network, e.g., (but not limited to) a neural network, a convolutional neural network, is implemented to identify one or more features that are associated with a particular type of artifacts. In some embodiments, supervised learning is used to identify the one or more features. During the supervised learning, a plurality of labeled images, each of which is labeled as having the particular type of artifacts (bad images) or not having the particular type of artifacts (good images), are used as training data. In response to identifying the one or more features, an objective function associated with the one or more features is defined to minimize the particular type of artifacts. [00156] The following discussion now refers to a number of methods and method acts that may be performed. Although the method acts may be discussed in a certain order or illustrated in a flow chart as occurring in a particular order, no particular ordering is required unless specifically stated, or required because an act is dependent on another act being completed prior to the act being performed.

[00157] Figure 20 illustrates a flowchart of an example method 2000 for reducing metal artifacts in computerized tomography (CT) images. The method 2000 includes reconstructing a raw CT image in an image domain from a CT projection domain (act 2010). The CT projection includes a matrix of measurements in the projection domain obtained via a CT scan, and the raw CT image includes a matrix of pixels in an image domain that are reconstructed from the matrix of measurements in the projection domain. The method 2000 also includes identifying one or more metal segments in the raw CT image (act 2020) and forward projects the one or more metal segments to generate one or more shadows in the projection domain (act 2030). Measurements in the one or more shadows in the projection domain are then iteratively adjusted to reduce metal artifacts in the raw CT image (act 2040). The adjusted measurements in the one or more shadows in the projection domain are then used to reconstruct an improved CT image (act 2050). In some embodiments, the reconstructing of the raw CT image and/or reconstructing the improved CT image are performed via a filtered back projection (FBP) method.

[00158] In some embodiments, the iterative adjusting of the measurements in the one or more shadows in the projection domain is to iteratively reduce a total variation norm of the matrix of non-metal pixels in the image domain. In some embodiments, a gradient descent method is used to minimize the total variation norm of the matrix of non-metal pixels in the image domain.

[00159] In some embodiments, the iterative adjusting of the measurements in the one or more shadows in the projection domain is to iteratively reduce a sum of squares of values of pixels that have negative values. In some embodiments, a gradient descent method is used to minimize the sum of squares of values of the pixels that have negative values.

[00160] In some embodiments, the iterative adjusting the measurements in the one or more shadows in the projection domain is to iteratively reduce a combination of (1) a sum of squares of values of pixels that have negative values and (2) a total variation norm of the matrix of pixels in the image domain. In some embodiments, the combination is a weighted combination, in which the sum of squares of values of pixels that have negative values is given a first weight, and the total variation norm of the matrix of pixels in the image domain is given a second weight. In some embodiments, the gradient descent method is used to minimize the weighted combination.

[00161] Figure 21 illustrates a flowchart of an example method 2100 for using machine learning to identify one or more features associated with artifacts in CT images and reconstructing an improved CT image to reduce the artifacts. The method 2100 includes providing a plurality of labeled CT images as training data (act 2110). The labeled CT images are labeled as having a particular type of artifact or not having the particular type of artifact. The method further includes providing a machine learning network (act 2120), such as (but not limited to) a neural network, or a convolutional neural network. The method 2100 further includes identifying one or more features associated with the particular type of artifact using the machine learning network and the plurality of labeled CT images (act 2130).

[00162] In some embodiments, the method 2100 further includes receiving a CT projection in a projection domain (act 2140) and reconstructing a raw CT image in an image domain from the CT projection in the projection domain (act 2150). The CT projection includes a matrix of measurements in a projection domain obtained via a CT scan, and the raw CT image includes a matrix of pixels in an image domain reconstructed from the matrix of measurements in the projection domain. The method 2100 further includes identifying one or more artifact segments in the raw CT image (act 2160), and forward projecting the one or more artifact segments to generate one or more shadows in the projection domain (act 2170). Measurements in the one or more shadows in the projection domain are iteratively adjusted to reduce the particular type of artifact in the raw CT image (act 2180). The adjusted measurements in the one or more shadows in the projection domain are then used to reconstruct an improved CT image in the image domain (act 2190).

[00163] Figure 22 illustrates a schematic of a computer system 2200 for reducing artifacts in computerized tomography. As depicted, the computer system 2200 includes one or more processors 2230 and computer memory 2240 that are both accessible through a software application 2220. The computer system 2200 is in communication in a beam wave device 2210. The beam wave device may comprise an x-ray machine or any other image device. The computer system 2200 is configured to reduce artifacts in computerized tomography.

[00164] The methods described above may be practiced by a computer system (e.g., the computer system 2200 of Figure 22), including one or more processors (e.g., 2230 of Figure 22) and computer-readable media such as computer memory (e.g., computer memory 2240 of Figure 22). In particular, the computer memory may store computer- executable instructions that, when executed by one or more processors, cause various functions to be performed, such as the acts recited in the embodiments.

[00165] Computing system functionality can be enhanced by a computing systems’ ability to be interconnected to other computing systems via network connections. Network connections may include, but are not limited to, connections via wired or wireless Ethernet, cellular connections, or even computer to computer connections through serial, parallel, USB, or other connections. The connections allow a computing system to access services at other computing systems and to quickly and efficiently receive application data from other computing systems.

[00166] Interconnection of computing systems has facilitated distributed computing systems, such as so-called “cloud” computing systems. In this description, “cloud computing” may be systems or resources for enabling ubiquitous, convenient, on-demand network access to a shared pool of configurable computing resources (e.g., networks, servers, storage, applications, services, etc.) that can be provisioned and released with reduced management effort or service provider interaction. A cloud model can be composed of various characteristics (e.g., on-demand self-service, broad network access, resource pooling, rapid elasticity, measured service, etc.), service models (e.g., Software as a Service (“SaaS”), Platform as a Service (“PaaS”), Infrastructure as a Service (“IaaS”), and deployment models (e.g., private cloud, community cloud, public cloud, hybrid cloud, etc.).

[00167] Cloud and remote-based service applications are prevalent. Such applications are hosted on public and private remote systems such as clouds and usually offer a set of web-based services for communicating back and forth with clients.

[00168] Many computers are intended to be used by direct user interaction with the computer. As such, computers have input hardware and software user interfaces to facilitate user interaction. For example, a modem general-purpose computer may include a keyboard, mouse, touchpad, camera, etc., for allowing a user to input data into the computer. In addition, various software user interfaces may be available.

[00169] Examples of software user interfaces include graphical user interfaces, text command line based user interface, function key or hot key user interfaces, and the like. [00170] Disclosed embodiments may comprise or utilize a special purpose or general- purpose computer, including computer hardware, as discussed in greater detail below. Disclosed embodiments also include physical and other computer-readable media for carrying or storing computer-executable instructions and/or data structures. Such computer-readable media can be any available media that can be accessed by a general- purpose or special-purpose computer system. Computer-readable media that store computer-executable instructions are physical storage media. Computer-readable media that carry computer-executable instructions are transmission media. Thus, by way of example, and not limitation, embodiments of the invention can comprise at least two distinctly different kinds of computer-readable media: physical computer-readable storage media and transmission computer-readable media.

[00171] Physical computer-readable storage media includes RAM, ROM, EEPROM, CD-ROM or other optical disk storage (such as CDs, DVDs, etc.), magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store desired program code means in the form of computer-executable instructions or data structures and which can be accessed by a general-purpose or special purpose computer.

[00172] A “network” is defined as one or more data links that enable the transport of electronic data between computer systems and/or modules and/or other electronic devices. When information is transferred or provided over a network or another communications connection (either hardwired, wireless, or a combination of hardwired or wireless) to a computer, the computer properly views the connection as a transmission medium. Transmissions media can include a network and/or data links which can be used to carry program code in the form of computer-executable instructions or data structures and which can be accessed by a general-purpose or special purpose computer. Combinations of the above are also included within the scope of computer-readable media.

[00173] Further, upon reaching various computer system components, program code means in the form of computer-executable instructions or data structures can be transferred automatically from transmission computer-readable media to physical computer-readable storage media (or vice versa). For example, computer-executable instructions or data structures received over a network or data link can be buffered in RAM within a network interface module (e.g., a “NIC”), and then eventually transferred to computer system RAM and/or to less volatile computer-readable physical storage media at a computer system. Thus, computer-readable physical storage media can be included in computer system components that also (or even primarily) utilize transmission media.

[00174] Computer-executable instructions comprise, for example, instructions and data which cause a general-purpose computer, special purpose computer, or special purpose processing device to perform a certain function or group of functions. The computer- executable instructions may be, for example, binaries, intermediate format instructions such as assembly language, or even source code. Although the subject matter has been described in language specific to structural features and/or methodological acts, it is to be understood that the subject matter defined in the appended claims is not necessarily limited to the described features or acts described above. Rather, the described features and acts are disclosed as example forms of implementing the claims.

[00175] Those skilled in the art will appreciate that the invention may be practiced in network computing environments with many types of computer system configurations, including, personal computers, desktop computers, laptop computers, message processors, hand-held devices, multi-processor systems, microprocessor-based or programmable consumer electronics, network PCs, minicomputers, mainframe computers, mobile telephones, PDAs, pagers, routers, switches, and the like. The invention may also be practiced in distributed system environments where local and remote computer systems, which are linked (either by hardwired data links, wireless data links, or by a combination of hardwired and wireless data links) through a network, both perform tasks. In a distributed system environment, program modules may be located in both local and remote memory storage devices.

[00176] Alternatively, or in addition, the functionality described herein can be performed, at least in part, by one or more hardware logic components. For example, and without limitation, illustrative types of hardware logic components that can be used include Field-programmable Gate Arrays (FPGAs), Program-specific Integrated Circuits (ASICs), Program-specific Standard Products (ASSPs), System-on-a-chip systems (SOCs), Complex Programmable Logic Devices (CPLDs), etc.

[00177] The present invention may be embodied in other specific forms without departing from its spirit or characteristics. The described embodiments are to be considered in all respects only as illustrative and not restrictive. The scope of the invention is, therefore, indicated by the appended claims rather than by the foregoing description. All changes which come within the meaning and range of equivalency of the claims are to be embraced within their scope.

Claims

CLAIMS What is claimed is:

1. A computer system for reducing metal artifacts in computed tomography (CT) images, comprising: one or more processors; and one or more computer-readable storage devices having stored thereon executable instructions that when executed by the one or more processors configure the computer system to perform at least: reconstruct a raw computed tomography (CT) image from a CT projection, wherein the CT projection includes a matrix of measurements obtained via a CT scan in a projection domain, and the raw CT image includes a matrix of pixels in an image domain that are reconstructed from the matrix of measurements in the projection domain; identify one or more metal segments in the raw CT image; forward project the one or more metal segments to generate one or more shadows in the projection domain; iteratively adjust measurements in the one or more shadows in the projection domain to reduce metal artifacts in the raw CT image; and reconstruct an improved CT image in the image domain based on the adjusted measurements in the one or more shadows and measurements not in the one or more shadows and measurements not in the one or more shadows in the projection domain.

2. The computer system of claim 1 , wherein reconstructing the raw CT image or reconstructing the improved CT image is performed via a filtered back projection (FBP) method.

3. The computer system of claim 1, wherein iteratively adjusting the measurements in the one or more shadows in the projection domain to reduce metal artifacts in the raw CT image includes iteratively adjusting the measurements in the one or more shadows to reduce a total variation norm of the matrix of non-metal pixels in the image domain.

4. The computer system of claim 3, wherein iteratively adjusting the measurements in the one or more shadows to reduce a total variation of the matrix of pixels in the image domain includes using a gradient descent method to minimize the total variation norm of the matrix of non-metal pixels in the image domain.

5. The computer system of claim 1, wherein iterative adjusting the measurements in the one or more shadows in the projection domain to reduce metal artifacts of the one or more metal segments includes: identifying pixels in the image domain that have negative values; and iteratively adjusting the measurements in the one or more shadows in the projection domain to reduce a sum of squares of values of the pixels in the image domain that have negative values.

6. The computer system of claim 5 wherein iteratively adjusting the measurements in the one or more shadows in the projection domain to reduce a sum of squares of values of the pixels in the image domain that have negative values includes using an optimization method to minimize the sum of squares of values of the pixels in the image domain that have negative values.

7. The computer system of claim 6, wherein the optimization method comprises a gradient descent method.

8. The computer system of claim 1, wherein iterative adjusting the measurements in the one or more shadows in the projection domain to reduce metal artifacts of the one or more metal segments includes: identify pixels in the image domain that have negative values; and iteratively adjusting the measurements in the one or more shadows in the projection domain to reduce a combination of (1) a sum of squares of values of the pixels in the image domain that have negative values and (2) a total variation norm of the matrix of non-metal pixels in the image domain.

9. The computer system of claim 8, wherein the combination of (1) the sum of squares of values of the pixels in the image domain that have negative values and (2) the total variation norm of the matrix of non-metal pixels in the image domain is a weighted combination, in which the sum of squares of values of the pixels in the image domain that have negative values is given a first weight, and the total variation norm of the matrix of non-metal pixels in the image domain is given a second weight.

10. The computer system of claim 9, wherein iterative adjusting the measurements in the one or more shadows in the projection domain to reduce the weighted combination of (1) the sum of squares of values of the pixels in the image domain that have negative values and (2) the total variation norm of the matrix of non-metal pixels in the image domain includes using a gradient descent method to minimize the weighted combination.

11. A method implemented at a computer system for reducing metal artifacts in computed tomography (CT) images, comprising: reconstructing a raw CT image from a CT projection, wherein the CT projection includes a matrix of measurements in a projection domain obtained via a CT scan, and the raw CT image includes a matrix of pixels in an image domain that are reconstructed from the matrix of measurements in the projection domain; identifying one or more metal segments in the raw CT image; forward projecting the one or more metal segments to generate one or more shadows in the projection domain; iteratively adjusting measurements in the one or more shadows in the projection domain to reduce metal artifacts in the raw CT image; and reconstructing an improved CT image based on the adjusted measurements in the one or more shadows and measurements not in the one or more shadows in the projection domain.

12. The method of claim 11, wherein reconstructing the raw CT image or reconstructing the improved CT image is performed via a filtered back projection (FBP) method.

13. The method of claim 11, wherein iteratively adjusting the measurements in the one or more shadows in the projection domain to reduce metal artifacts of the one or more metal segments includes iteratively adjusting the measurements in the one or more shadows to reduce a total variation norm of the matrix of non-metal pixels in the image domain.

14. The method of claim 13, wherein iteratively adjusting the measurements in the one or more shadows to reduce a total variation of the matrix of pixels in the image domain includes using a gradient descent method to minimize the total variation norm of the matrix of non-metal pixels in the image domain.

15. The method of claim 11, wherein iterative adjusting the measurements in the one or more shadows in the projection domain to reduce metal artifacts of the one or more metal segments includes: identify pixels in the image domain that have negative values; and iteratively adjusting the measurements in the one or more shadows in the projection domain to reduce a sum of squares of values of the pixels in the image domain that have negative values.

16. The method of claim 15, wherein iteratively adjusting the measurements in the one or more shadows in the projection domain to reduce a sum of squares of values of the pixels in the image domain that have negative values includes using an optimization method to minimize the sum of squares of values of the pixels in the image domain that have negative values.

17. The method of claim 16, wherein the optimization method comprises a gradient descent method.

18. The method of claim 11, wherein iterative adjusting the measurements in the one or more shadows in the projection domain to reduce the metal artifacts in the one or more metal segments includes: identify pixels in the image domain that have negative values; and iteratively adjusting the measurements in the one or more shadows in the projection domain to reduce a combination of (1) a sum of squares of values of the pixels in the image domain that have negative values and (2) a total variation norm of the matrix of non-metal pixels in the image domain.

19. A computer system for reducing metal artifacts in computed tomography (CT) images, comprising: one or more processors; and one or more computer-readable storage devices having stored thereon executable instructions that when executed by the one or more processors configure the computer system to perform at least: access a plurality of labeled CT images as training data, each of the plurality of labeled CT images being labeled as having a particular type of artifact or not having the particular type of artifact; access a machine learning network; identify one or more artifact features that are associated with the particular type of artifact using the machine learning network and the plurality of labeled CT images; receive a CT projection in a projection domain, wherein the CT projection includes a matrix of measurements obtained via a CT scan in a projection domain; reconstruct a raw CT image in an image domain from the CT projection in the projection domain, wherein the raw CT image includes a matrix of pixels in an image domain that are reconstructed from the matrix of measurements in the projection domain; identify one or more artifact segments in the raw CT image; forward project the one or more artifact segments to generate one or more shadows in the projection domain; iteratively adjust measurements in the one or more shadows in the projection domain to minimize effect of at least one of the one or more artifact features ; and reconstruct an improved CT image based on the adjusted measurements in the one or more shadows and measurements not in the one or more shadows in the projection domain.

20. The computer system of claim 19, wherein the machine learning network is a machine learning neural network.