Multi-center scanning CT imaging geometric structure and projection partial differential equation under circular trajectory

Abstract

The present application relates to the technical field of CT imaging, and in particular to a multi-center scanning CT imaging geometric structure and a projection partial differential equation under a circular trajectory. The CT imaging geometric structure is a CT imaging structure under a circular trajectory composed of N groups of scanning geometric structures, wherein each group of scanning geometric structures comprises one rotation center and M light source positions at different angles; each light source position corresponds to D detector units; and the CT imaging structure comprises N rotation centers, and the N rotation centers are distributed in a certain pattern. Under multi-center scanning geometry, a partial differential equation is used to perform interpolation extension on a projection. By means of the multi-center scanning CT imaging geometric structure provided in the present application, streak artifacts of images under sparse angle sampling conditions are reduced on the basis of a projection interpolation scheme of the structure and a projection partial differential equation under a circular trajectory, thereby improving image quality. The present application is used for decreasing the number of projection angles in CT scanning, reducing a radiation dose, reducing system costs and improving a scanning speed.

Description

CT imaging geometry of multi-center scanning and projected partial differential equations under circular trajectories Technical Field

[0001] The embodiments of the present application relate to the field of CT imaging technology, and in particular to a CT imaging geometric structure of multi-center scanning and a projection partial differential equation under a circular trajectory. Background Art

[0002] CT imaging technology is widely used in fields such as nondestructive testing and medical security inspections. While X-rays can provide nondestructive inspections, their misuse can lead to health problems. Current solutions employ sparse sampling to reduce radiation dose during diagnosis. This also improves temporal resolution and reduces system costs. However, due to the limited number of measurements, reconstructed images often suffer from sparse angle reconstruction artifacts, making them difficult to meet application quality requirements.

[0003] Summary of the Invention

[0004] An embodiment of the present application provides a CT imaging geometry structure for multi-center scanning and a projection partial differential equation under a circular trajectory. By using a projection interpolation scheme based on the CT imaging geometry structure and the projection partial differential equation under a circular trajectory, the stripe artifacts of the image under sparse angular sampling conditions are reduced and the image quality is improved.

[0005] To solve the above technical problems, in the first aspect, an embodiment of the present application provides a multi-center scanning CT imaging geometry structure, including: the CT imaging geometry structure is a CT imaging structure under a circular trajectory composed of N groups (N≥2) of scanning geometric structures; wherein each group of the scanning geometric structures includes a rotation center and M light source positions at different angles; each light source position corresponds to D detector units; the CT imaging structure includes N rotation centers, and the N rotation centers are distributed in a certain regular pattern; in the CT imaging structure, there are M acquisition angles in the group, and by sampling at equal intervals within a range of 360°, a multi-circular distributed point source scheme is formed; or, by sampling at equal intervals within an angle range of 360° / N, a multi-arc distributed point source scheme is formed; or, a specific sampling angle is set according to the scanning geometry.

[0006] In some exemplary embodiments, the scanning trajectory of the scanning geometric structure includes sparse angle, limited angle and full angle scanning; under sparse angle and full angle scanning, a closed scanning structure can be formed through N groups of scanning geometric structures, thereby completely covering the object.

[0007] In some exemplary embodiments, the CT imaging structure includes a fan-beam scanning geometry and a cone-beam scanning geometry; when the detector is an arc-shaped or linear detector, the CT imaging structure is a fan-beam scanning geometry; when the detector is a arc-shaped or flat detector, the CT imaging structure is a cone-beam scanning geometry.

[0008] In some exemplary embodiments, when an array ray source is used as the source, a multi-center CT imaging geometric structure is formed by multiple arc or plane array sources; by combining with different types of detectors, a CT imaging structure with a stationary ray source and a rotating detector can be formed.

[0009] In some exemplary embodiments, under the CT imaging structure, by optimizing the multi-center structural parameters, it is possible to achieve the characteristics of uniform projection angle and detector distribution compared with a single rotation center under the same scanning angle, and the angle between the intersecting rays is small and the number of intersecting rays is large, thereby obtaining better reconstructed image quality.

[0010] In some exemplary embodiments, when sampling is performed at equal intervals within a 360° range to form a multi-ring distributed point source scheme, the coefficient of variation is used to optimize the multi-center structural parameters; the optimization process includes: taking the traditional rotation center as a reference, the rotation center includes a position offset and an angle offset; converting the projection index into a parallel beam index and drawing a scatter plot; calculating the coefficient of variation of the scatter plot; using an optimization function to optimize the angle offset and the position offset; when the coefficient of variation is selected as the optimization formula, the coefficient of variation of the scatter plot is calculated using formula (1):

[0011] In formula (1), is the average number of projections in the block area; S is the variance of the number of projections in the block area; the smaller the CV value, the more uniform the projection distribution;

[0012] When sampling at equal intervals within a 360° / N angle range to form a multi-arc distributed point source solution, the coefficient of variation and arc circumference constraints are used to optimize the multi-center structural parameters. The optimization process includes: taking the traditional rotation center as the reference, the arc includes an arc length variable π and a radius variable R, and an overlap angle variable δ between the arcs;

[0013] Under sparse angle and full angle scanning, the N groups of arcs have the following constraint relationship: N(π-δ)=2π (2)

[0014] The projection indices of N groups of arcs are converted into parallel beam indices and a scatter plot is drawn; the coefficient of variation of the scatter plot is calculated; and an optimization function is used to optimize the arc length variable π, the radius variable R, and the overlap angle variable δ between the arcs.

[0015] In some exemplary embodiments, under N sets of scanning geometries, boundary value conditions that satisfy specific partial differential equations are constructed to supplement missing projection information in sparse angular scanning situations and perform image reconstruction.

[0016] In a second aspect, the embodiment of the present application further provides a partial differential equation for projection of a circular trajectory of a multi-center scanning CT imaging geometric structure, including first-order and higher-order partial differential equations:

[0017] in, is the partial differential value of the current ray at different rotation centers, S is the distance between the two rotation centers, is the differential of adjacent parallel beam rays; if The rotation center of is defined as the ray source point, then becomes the differential between adjacent detectors;

[0018] Second-order and higher-order partial differential equations are as follows:

[0019] In some exemplary embodiments, the CT imaging structure adopts partial differential projection completion; when calculating the partial differential projection completion, the following process is used for iterative interpolation to obtain a higher density expanded projection; the iterative interpolation process includes: initializing N rotation centers, obtaining M angle projections under each rotation center, and the total number of projections is K=N*M*D projection values; converting the current fan beam projection into a parallel beam projection index coordinate (t,θ), where t is the detector index and θ is the angle between the ray normal and the horizontal axis; setting the number of interpolation iterations Z; setting variables z and k; z and k represent the kth ray under z iterations; performing interpolation iterations, finding rays that intersect with the kth ray, screening the intersection angles, calculating the projection differentials for interpolation, and obtaining adjacent interpolation projection indexes (t±1,θ); judging whether all rays have been traversed, if not, continuing the traversal; if k=K, judging whether the iteration is complete, if not, setting K=3K for the next round of iterative traversal, and ending the interpolation if z=Z.

[0020] In some exemplary embodiments, reconstructing the interpolated and expanded projections includes the following steps: constructing an imaging model based on a Lagrangian optimization objective function according to the projection data as a mathematical model to be solved iteratively:

[0021] In formula (6), F(R) = Af represents the sampling function; b is the projection after interpolation; is the sampling matrix; Z is the number of pixels in the image; P(R) is a specific constraint term, and β is the regularization parameter.

[0022] In some exemplary embodiments, the CT imaging structure is completed using partial differential projections; the projection data is interpolated and expanded using partial differential equations; and the interpolation is performed using first-order or a combination of first-order and higher-order forms.

[0023] In some exemplary embodiments, the CT imaging structure uses the following process for iterative interpolation during partial differential projection completion calculation to obtain a higher density expanded projection; the iterative interpolation process includes: initializing N rotation centers, obtaining M angle projections under each rotation center, and the total number of projections is K=N*M*D projection values; converting the current fan beam projection into a parallel beam projection index coordinate (t,θ), where t is the detector index and θ is the angle between the ray normal and the horizontal axis; setting the number of interpolation iterations Z; setting variables z and k; z and k represent the kth ray under z iterations; performing interpolation iterations, finding rays that intersect with the kth ray, screening the intersection angles, calculating the projection differentials for interpolation, and obtaining adjacent interpolation projection indexes (t±1,θ); judging whether all rays have been traversed, and if not, continuing the traversal; if k=K, judging whether the iteration is complete, and if not, setting K=3K for the next round of iterative traversal, and ending the interpolation if z=Z.

[0024] In some exemplary embodiments, reconstructing the interpolated and expanded projections includes the following steps: constructing an imaging model based on a Lagrangian optimization objective function according to the projection data as a mathematical model to be solved iteratively:

[0025] In formula (7), F(R) = Af represents the sampling function; b is the projection after interpolation; is the sampling matrix; Z is the number of pixels in the image; P(R) is a specific constraint term, and β is the regularization parameter.

[0026] The technical solution provided by the embodiments of the present application has at least the following advantages:

[0027] An embodiment of the present application provides a multi-center scanning CT imaging geometry and a projection partial differential equation under a circular trajectory. The CT imaging geometry is a CT imaging structure under a circular trajectory composed of N groups (N≥2) of scanning geometries; each group of scanning geometries includes a rotation center and M light source positions at different angles; each light source position corresponds to D detector units; the CT imaging structure includes N rotation centers, and the N rotation centers are distributed in a certain pattern; in the CT imaging structure, there are M acquisition angles in the group, and by sampling at equal intervals within a 360° range, a multi-circular distributed point source scheme is formed; or, by sampling at equal intervals within a 360° / N angle range, a multi-arc distributed point source scheme is formed; or, a specific sampling angle is set according to the scanning geometry.

[0028] This embodiment of the present application also provides a partial differential equation for the projection of a multi-center scanning CT imaging geometry on a circular trajectory, including first-order and higher-order differential equations for describing the relationship between projection angle and detector on a circular trajectory. In the multi-center scanning geometry on a circular trajectory, the partial differential equation is used to interpolate and expand the projection, and reconstruction is performed based on this interpolation.

[0029] The embodiment of the present application provides a multi-center scanning CT imaging geometry and a projection partial differential equation under a circular trajectory. When the ray source scanning trajectory is a circle, under a given number of rotation angles (M*N), different rotation angles are divided into N groups according to a certain rule; each group contains M rotation angles, each rotation angle contains D detector units, and the same group shares a rotation center, that is, the scanning geometry contains N rotation centers, and all groups cover the imaging object (ROI); the N rotation centers can be arbitrarily distributed. In the above case, by designing the multi-center structural parameters, the projection distribution is made to have the following rules: (1) the projection angle and the detector distribution are more uniform; (2) more small angles are formed between the intersecting projection rays, and there are more non-overlapping intersections, which meet the specific partial differential equation boundary conditions and can be used to supplement the missing projection information in the case of sparse angle scanning. On this basis, the CT imaging geometry of multiple rotation centers is used to reconstruct the ROI, thereby reducing the stripe artifacts of the image under sparse angle sampling and improving the image quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] One or more embodiments are exemplarily described by the pictures in the corresponding drawings. These exemplifications do not constitute limitations on the embodiments. Unless otherwise stated, the pictures in the drawings do not constitute proportional limitations.

[0031] Figure 1 is a scanning illustration of a group of arc distributed point sources according to 360° / N sampling provided by an embodiment of the present application. The group consists of an array light source + corresponding detector distributed on a surface or curve, and its rotation center is point 1.

[0032] Figure 2 illustrates a multi-center scanning geometry using different sets of geometric centers based on 360° / N sampling, according to one embodiment of the present application. The figure shows two rotation centers, points 1 and 2, corresponding to two sets of 360° / N sampling CT scanning structures.

[0033] FIG3 is a scanning illustration of a set of 360° sparse angle sampling cases provided by an embodiment of the present application.

[0034] FIG4 is an illustration of a multi-center scanning geometry constructed using different groups of geometric centers in a 360° sparse angle sampling case provided by an embodiment of the present application.

[0035] FIG5 shows a CT scanning structure based on a multi-center CT imaging geometry of N=8, M=7 in the case of a linear detector, with a stationary source and a rotating detector, provided by an embodiment of the present application.

[0036] FIG6 shows a CT scanning structure based on a multi-center CT imaging geometry of N=8, M=7 in the case of an arc-shaped detector, in which the source is stationary and the detector rotates, provided by an embodiment of the present application.

[0037] FIG7 is a schematic diagram illustrating an offset relationship provided in an embodiment of the present application.

[0038] FIG8 is a flowchart of interpolation iteration provided in an embodiment of the present application.

[0039] FIG9 is a scatter plot of parallel beam indices based on 8 centers and a single center provided in an embodiment of the present application. Obviously, in the multi-center CT structure, the sinusoidal diagram of the CT projection is denser and the sampling error is smaller, so the reconstruction quality is theoretically better.

[0040] FIG10 is a visualization diagram based on 8-center and single-center rays provided in an embodiment of the present application. The diagram also shows that the projection rays cover the imaging object more evenly, so the reconstruction quality is theoretically better.

[0041] FIG11 is a ray visualization diagram of the intersection of a single ray based on 8-center and single-center rays, provided in an embodiment of the present application. The diagram shows that in a multi-center CT structure, the angle of ray intersection is smaller, which is conducive to simplifying the aforementioned partial differential equation solution process and improving the solution accuracy.

[0042] FIG12 is a schematic diagram of an imaging phantom provided in an embodiment of the present application.

[0043] FIG13 is a schematic diagram showing a comparison of reconstruction results provided in an embodiment of the present application. DETAILED DESCRIPTION

[0044] As we can see from the background, existing technologies have designed sparse sampling to reduce radiation dose during diagnosis. Sparse sampling can also be used to improve temporal resolution and reduce system costs. However, in practice, the small number of samples can lead to streaking artifacts in the reconstructed image, thus reducing the quality of the reconstructed image.

[0045] Several technical solutions have been proposed to address these shortcomings. Currently, some solutions only improve the quality of reconstructed images with sparse angular sampling using traditional scanning methods, specifically single-center scanning geometry, by designing different reconstruction algorithms. However, this improvement in image quality is limited, as the upper limit of image quality is determined by the sampling geometry. In single-center scanning geometry, for example, the distribution of projection angles and detectors is uneven, as shown in Figures 8 and 9. This demonstrates the uneven sampling under this sampling geometry.

[0046] This application proposes to use multi-center scanning instead of single-center scanning geometry. Compared with single-center, the projection angle and detector distribution are more uniform, and the differential relationship in the projection can be satisfied in the multi-center case, and the missing projection information can be supplemented, thereby improving the quality of the reconstructed image.

[0047] Based on this, the present application provides a CT imaging geometry for multi-center scanning, which includes but is not limited to: using N groups (N≥2) of scanning geometries to form a CT imaging structure under a circular trajectory; wherein each group of scanning geometries includes a rotation center, M acquisition angles, and D detector units under each acquisition angle; the CT imaging structure includes N rotation centers, and the N rotation centers are distributed in a certain pattern; in the CT imaging structure, there are M acquisition angles in the group, which can be sampled at equal intervals within a 360° range to form a multi-circular distributed point source scheme, or can be sampled at equal intervals within a 360° / N angle range to form a multi-arc distributed point source scheme, or a specific sampling angle can be set according to the scanning geometry.

[0048] This application provides a multi-center scanning CT imaging geometry structure to illustrate how to reduce image stripe artifacts in sparse angular sampling conditions and improve the quality of reconstructed images.

[0049] The present invention will be further described below with reference to the accompanying drawings. The advantages and features of the present invention will become clearer according to the following description. It should be noted that the drawings are in a very simplified form and are not in precise proportions, which are only used to conveniently and clearly assist in explaining the purpose of the embodiments of the present invention. In order to make the purposes, features and advantages of the present invention more obvious and easy to understand, please refer to the accompanying drawings. It should be noted that the structures, proportions, sizes, etc. illustrated in the drawings of this specification are only used to match the contents disclosed in the specification for people familiar with this technology to understand and read, and are not used to limit the conditions for the implementation of the present invention. Any modification of the structure, change in the proportional relationship or adjustment of the size, as long as it is the same or similar to the effect that the present invention can produce and the purpose that can be achieved, should still fall within the scope of the technical content disclosed in the present invention. The specific design features of the present invention disclosed herein, including, for example, specific dimensions, directions, positions and shapes, will be determined in part by the specific environment to be applied and used.

[0050] The embodiment of the present application provides a multi-center scanning CT imaging geometry structure, which is a CT imaging structure under a circular trajectory using N groups (N≥2) of scanning geometries; wherein each group of scanning geometries includes a rotation center, M acquisition angles, and D detector units under each acquisition angle; the CT imaging structure includes N rotation centers, and the N rotation centers are distributed in a certain regular pattern; in the CT imaging structure, there are M acquisition angles in the group, which can be sampled at equal intervals within a 360° range, or at equal intervals within a 360° / N angle range, or a specific sampling angle can be set according to the scanning geometry. As shown in Figure 1, a scanning geometry description of M=5 is given under a group of rotation centers within a 360° / N angle range. Among them, 1 represents the current rotation center, 102 is the circular trajectory under the current rotation center, 101 is the actual scanning trajectory under the current rotation geometry, and 1011~1015 are different angle sampling points (M=5). As shown in Figure 3, a scanning geometry description of M=8 is given under a group of rotation centers with 360° uniform sampling. Wherein, 1 represents the current rotation center, 101 represents the circular trajectory under the current rotation center, and 1011 to 1018 represent different angle sampling points (M=8).

[0051] For example, N may be 2, 3, 4, 5, 6, 7, ..., that is, the scanning geometry may include 2, 3, 4, 5, 6 or 7 rotation centers, or another number of rotation centers.

[0052] By combining multiple sets of rotation centers, a multi-center scanning CT imaging geometry can be constructed. Figure 2 shows a multi-center scanning structure with N = 7 and M = 5. 00 represents a closed circular trajectory scan formed by multiple sets of rotation centers. 1 and 2 represent the relative positions of two different sets of rotation centers; 102 and 202 represent the corresponding circular trajectory scans; 101 and 201 represent two sets of scanning trajectories in the combined multi-center CT imaging geometry; 1011 to 1015 and 2011 to 2025 represent different sampling angles.

[0053] By combining multiple sets of rotation centers, a multi-center scanning CT imaging geometry can be constructed. As shown in Figure 4, a scanning structure with N = 3 and M = 8 is constructed. 101, 201, and 301 represent closed circular trajectory scans formed by multiple sets of rotation centers. 1, 2, and 3 denote the relative positions of three different sets of rotation centers, respectively. 1011 to 1018, 2011 to 2028, and 3011 to 3018 represent different sampling angles.

[0054] In some embodiments, a circular scanning trajectory of the ray source is obtained by scanning trajectories at different sampling angles; the sampling angles include sparse angle sampling, limited angle sampling, and full sampling.

[0055] In some embodiments, when the source is an array cold cathode ray source, a multi-center CT structure can be formed using multiple arcs or planar array sources. By combining with different types of detectors (e.g., linear or planar detectors), a CT structure in which the ray source is stationary and the detector rotates can be formed. As shown in Figures 5 and 6, a CT structure in which the source is stationary and the detector rotates, based on N = 8 centers and M = 7 arc and flat-panel detectors, is shown. 1 to 8 are the multi-center indices for N = 8, where the N rotation centers form a circle with a radius of 8; 101 to 801 are the arc ray source indices, and n011 to n018 (n = 1, ..., 8) are the projected sampling points corresponding to center number n; and 9 is the flat-panel or arc detector.

[0056] In some embodiments, when the scanning trajectory is a plurality of finite angle samples with different radii, the circular scanning trajectory of the ray source is a plurality of arc segments or arc surface scanning trajectories.

[0057] In some embodiments, the CT imaging geometry of multi-center scanning includes fan beam scanning geometry and cone beam scanning geometry; when the detector is an arc-shaped or linear detector, the CT imaging geometry of multi-center scanning is fan beam scanning geometry; when the detector is a arc-shaped or flat detector, the CT imaging geometry of multi-center scanning is cone beam scanning geometry.

[0058] Specifically, taking the fan beam CT imaging geometry of multi-center scanning as an example, the multi-center offset can be obtained by (x1 n ,x2 n ,θ n ), where i represents the center index and θ is the rotation angle offset. The offset relationship is shown in Figure 7.

[0059] Taking the fan-beam CT imaging geometry of multi-center scanning as an example, when N = 8 rotation centers, the optimization function design process is briefly introduced. It is worth noting that the design of the optimization function and the optimization process are not unique.

[0060] In some embodiments, the rotation center is optimized using an optimization function to improve the uniformity of the projection angle and detector distribution; the optimization function is optimized through the coefficient of variation, and the optimization process includes: taking the traditional rotation center as a reference, the rotation center includes a position offset and an angle offset; converting the projection index into a parallel beam index and drawing a scatter plot; calculating the coefficient of variation of the scatter plot; and using an optimization algorithm to optimize the angle offset and position offset.

[0061] In some embodiments, the rotation center is optimized using an optimization function to improve the uniformity of the projection angle and the detector distribution; the optimization function is optimized through the coefficient of variation and arc circumference constraints, and the optimization process includes: taking the traditional rotation center as a reference, the arc includes the arc length variable Π and the radius variable R, and the overlapping angle variable δ between the arcs; N groups of projection indexes are converted into parallel beam indices, and a scatter plot is drawn; the coefficient of variation of the scatter plot is calculated; and the arc length variable Π and the radius variable R, and the overlapping angle variable δ between the arcs are optimized using the optimization function.

[0062] The formula used is incorrect! The reference source was not found. Calculate the coefficient of variation of the scatter plot:

[0063] In formula (1), is the average number of projections in the block area; S is the variance of the number of projections in the block area; the smaller the CV value, the more uniform the projection distribution.

[0064] When sampling at equal intervals within a 360° / N angle range to form a multi-arc distributed point source solution, the coefficient of variation and arc circumference constraints are used to optimize the multi-center structural parameters. The optimization process includes: taking the traditional rotation center as the reference, the arc includes an arc length variable π and a radius variable R, and an overlap angle variable δ between the arcs;

[0065] Under sparse angle and full angle scanning, the N groups of arcs have the following constraint relationship: N(π-δ)=2π (2)

[0066] The projection indices of N groups of arcs are converted into parallel beam indices and a scatter plot is drawn; the coefficient of variation of the scatter plot is calculated; and an optimization function is used to optimize the arc length variable π, the radius variable R, and the overlap angle variable δ between the arcs.

[0067] In some embodiments, under N sets of scanning geometries, boundary value conditions that satisfy specific partial differential equations are constructed to supplement missing projection information in sparse angular scanning situations and perform image reconstruction.

[0068] In some embodiments, the coefficient of variation is used to quantify the sparseness of the projection distribution, and a particle swarm algorithm is used for optimization. The specific process is divided into the following steps:

[0069] Step (1): transform the projection index of the fan beam into a parallel beam.

[0070] Step (2): Draw a scatter plot of all data points.

[0071] Step (3): Divide the scatter plot into blocks and count the number of projections in each block.

[0072] Step (4), calculate the coefficient of variation of the scatter plot, in is the average number of projections in the block area, S is the variance of the number of projections in the block area, and the smaller the CV value, the more uniform the projection distribution.

[0073] In step (5), the particle swarm algorithm can be used to optimize the angle offset and the polygon side length.

[0074] The present application also provides a projection partial differential equation for the circular trajectory of a multi-center scanning CT imaging geometry, including first-order and higher-order partial differential equations. By constructing boundary value conditions that satisfy specific partial differential equations, it is used to supplement the missing projection information in the case of sparse angular scanning and perform image reconstruction. The partial differential equation used is:

[0075] in, is the partial differential value of the current ray at different rotation centers, S is the distance between the two rotation centers, is the differential of adjacent parallel beam rays. The rotation center of can be defined as the ray source point, then becomes the differential between adjacent detectors.

[0076] In some embodiments, to further improve interpolation accuracy, second-order and higher-order partial differential equations may be used for interpolation:

[0077] In some embodiments, the interpolated extended projection is reconstructed, and the interpolation extension process is shown in FIG8 ; wherein the iterative mathematical model includes the following steps: constructing an imaging model that minimizes the 2-norm based on the projection data:

[0078] Wherein, F(R)=Af represents the sampling function; is the sampling matrix; Z is the number of pixels in the image; P(R) is a specific constraint term, and β is the regularization parameter.

[0079] In some embodiments, P2(R) may employ TV constraints.

[0080] Take the fan-beam CT imaging geometry of multi-center scanning with N=8 and M=5 as an example. Under the condition of 1 / 15 sparse sampling, the image reconstruction quality under single-rotation center and multi-rotation center scanning is compared. The number of projections for single-center and multi-center is the same, both 80. The detector D is 800, the full scan angle is 1200, and the half-fan angle is 26°. By visualizing the projection sampling points, the parallel beam projection index as shown in Figure 9 can be obtained. Compared with a single rotation center, the projection distribution of multiple rotation centers is more uniform. The ray beams are visualized, and the results are shown in Figures 10 and 11. It can be seen from the above figures that the multi-center ray intersection points are more and the angle of the intersecting rays is smaller, which is more conducive to solving the partial differential equation interpolation.

[0081] The imaging phantom shown in Figure 12 was used to scan and obtain projection data, where the object voxel size was 1mm×1mm and the dimensions were 512×512. After 1 / 15 sparse sampling, the projection was interpolated and expanded using partial differential equations in the multi-center projection data, and a TV-based iterative reconstruction framework was used to generate single-center and 8-center reconstructed images, respectively. The reconstruction results are shown in Figure 13. From the reconstruction results, it can be seen that under the condition of sparse sampling, the PSNR (Peak signal to noise ratio) of the single-center and 8-center reconstructed images was calculated respectively. Compared with the single-center, the 8-center can improve by nearly 6dB, and there are no obvious artifacts in the reconstructed image. This experimental result shows that multiple rotation centers can further improve image quality.

[0082] Based on the above technical solution, the embodiment of the present application provides a multi-center scanning CT imaging geometry structure and a projection partial differential equation under a circular trajectory. The CT imaging geometry structure is a CT imaging structure under a circular trajectory composed of N groups (N≥2) of scanning geometries; each group of scanning geometry structures includes a rotation center and M light source positions at different angles; each light source position corresponds to D detector units; the CT imaging structure includes N rotation centers, and the N rotation centers are distributed in a certain pattern; in the CT imaging structure, there are M acquisition angles in the group, and by sampling at equal intervals within the 360° range, a multi-circular distributed point source scheme is formed; or, by sampling at equal intervals within the 360° / N angle range, a multi-arc distributed point source scheme is formed; or, a specific sampling angle is set according to the scanning geometry.

[0083] This embodiment of the present application also provides a partial differential equation for the projection of a multi-center scanning CT imaging geometry on a circular trajectory, including first-order and higher-order differential equations for describing the relationship between projection angle and detector on a circular trajectory. In the multi-center scanning geometry on a circular trajectory, the partial differential equation is used to interpolate and expand the projection, and reconstruction is performed based on this interpolation.

[0084] The embodiment of the present application provides a multi-center scanning CT imaging geometry and a projection partial differential equation under a circular trajectory. When the ray source scanning trajectory is a circle, under a given number of rotation angles (M*N), different rotation angles are divided into N groups according to a certain rule; each group contains M rotation angles, each rotation angle contains D detector units, and the same group shares a rotation center, that is, the scanning geometry contains N rotation centers, and all groups cover the imaging object (ROI); the N rotation centers can be arbitrarily distributed. In the above case, by designing the multi-center structural parameters, the projection distribution is made to have the following rules: (1) the projection angle and the detector distribution are more uniform; (2) more small angles are formed between the intersecting projection rays, and there are more non-overlapping intersections, which meet the specific partial differential equation boundary conditions and can be used to supplement the missing projection information in the case of sparse angle scanning. On this basis, the CT imaging geometry of multiple rotation centers is used to reconstruct the ROI, thereby reducing the stripe artifacts of the image under sparse angle sampling and improving the image quality.

[0085] Those skilled in the art will appreciate that the above-described embodiments are specific examples for implementing the present application, and that in actual applications, various changes in form and detail may be made thereto without departing from the spirit and scope of the present application. Any person skilled in the art may make changes and modifications without departing from the spirit and scope of the present application. Therefore, the scope of protection of the present application shall be subject to the scope defined in the claims.

Claims

1. A CT imaging geometry for multi-center scanning, characterized in that: The CT imaging geometric structure is a CT imaging structure under a circular trajectory composed of N groups of scanning geometric structures; wherein N ≥ 2; Each group of the scanning geometric structures includes a rotation center and M light source positions at different angles; each of the light source positions corresponds to D detector units; The CT imaging structure includes N rotation centers, and the N rotation centers are distributed in a certain regular pattern; In the CT imaging structure, there are M acquisition angles in the group, and a multi-circular distributed point source scheme is formed by sampling at equal intervals within a range of 360°; or, a multi-arc distributed point source scheme is formed by sampling at equal intervals within a range of 360° / N angles; or, a specific sampling angle is set according to the scanning geometry.

2. The CT imaging geometry of multi-center scanning according to claim 1, characterized in that: The scanning trajectory of the scanning geometry includes sparse angle, limited angle and full angle scanning; Under sparse angle and full-angle scanning, a closed scanning structure can be formed through N groups of scanning geometric structures, thereby completely covering the object.

3. The CT imaging geometry of multi-center scanning according to claim 1, characterized in that: The CT imaging structure includes a fan beam scanning geometry and a cone beam scanning geometry; When the detector is an arc-shaped or linear detector, the CT imaging structure is a fan beam scanning geometry structure; When the detector is a curved or flat detector, the CT imaging structure is a cone beam scanning geometric structure.

4. The CT imaging geometry of multi-center scanning according to claim 1, characterized in that: When an array ray source is used as the source, a multi-center CT imaging geometric structure is formed by multiple arc or plane array sources; by combining with different types of detectors, a CT imaging structure in which the ray source is stationary and the detector is rotating can be formed.

5. The CT imaging geometry of multi-center scanning according to claim 1, characterized in that: Under the CT imaging structure, by optimizing the multi-center structural parameters, it is possible to achieve the characteristics of uniform projection angle and detector distribution compared with a single rotation center under the same scanning angle, and a small angle between intersecting rays and a large number of intersecting rays, thereby obtaining better reconstructed image quality.

6. The CT imaging geometry of multi-center scanning according to any one of claims 1 to 5, characterized in that: When sampling is performed at equal intervals within 360° to form a multi-ring distributed point source scheme, the coefficient of variation is used to optimize the multi-center structural parameters; The optimization process includes: Taking the traditional rotation center as a reference, the rotation center includes a position offset and an angle offset; Convert the projection index to a parallel beam index and draw a scatter plot; Calculating the coefficient of variation of the scatter plot; An optimization function is used to optimize the angle offset and position offset; When the coefficient of variation is selected as the optimization formula, the coefficient of variation of the scatter plot is calculated using formula (1): In formula (1), is the average number of projections in the block area; S is the variance of the number of projections in the block area; the smaller the CV value, the more uniform the projection distribution; When sampling is performed at equal intervals within the 360° / N angle range to form a multi-arc distributed point source scheme, the coefficient of variation and arc perimeter constraints are used to optimize the multi-center structural parameters; The optimization process includes: Taking the traditional rotation center as the reference, the arc includes arc length variable Π and radius variable R, and overlapping angle variable δ between arcs; Under sparse angle and full angle scanning, N groups of arcs have the following constraint relationships: N(π-δ)=2π (2) Convert N groups of arc projection indices into parallel beam indices and draw a scatter plot; Calculating the coefficient of variation of the scatter plot; The optimization function is used to optimize the arc length variable Π, the radius variable R, and the overlapping angle variable δ between arcs.

7. The CT imaging geometry of multi-center scanning according to claim 1, characterized in that: In the case of N sets of scanning geometries, boundary value conditions satisfying specific partial differential equations are constructed to supplement the missing projection information in the case of sparse angular scanning and perform image reconstruction.

8. A partial differential equation for projection of a circular trajectory of a multi-center scanning CT imaging geometry, characterized in that: This equation is used to describe the relationship between the angle and the detector under the circular scanning trajectory; wherein the partial differential equation is: in, is the partial differential value of the current ray at different rotation centers, S is the distance between the two rotation centers, is the differential of adjacent parallel beam rays; if The rotation center of is defined as the ray source point, then becomes the differential between adjacent detectors; Second-order and higher-order partial differential equations are as follows:

9. The partial differential equation of circular trajectory projection of multi-center scanning CT imaging geometry according to claim 8, characterized in that: The CT imaging structure adopts partial differential projection completion; when calculating the partial differential projection completion, the following process is adopted to perform iterative interpolation to obtain a higher density expanded projection; The iterative interpolation process includes: Initialize N rotation centers, obtain M angle projections under each rotation center, and the total number of projections is K = N*M*D projection values; convert the current fan beam projection to the parallel beam projection index coordinate (t, θ), where t is the detector index and θ is the angle between the ray normal and the horizontal axis; Set the number of interpolation iterations Z; Set variables z and k; z and k represent the kth ray in the zth iteration; Perform interpolation iterations to find the ray that intersects with the kth ray, screen the intersection angles, calculate the projection differential for interpolation, and obtain the adjacent interpolation projection index (t±1,θ); Determine whether all rays have been traversed. If not, continue traversing. If k=K, determine whether the iteration is complete. If not, set K=3K for the next round of iterative traversal. If z=Z, end interpolation.

10. The partial differential equation projected under a circular trajectory of the CT imaging geometric structure of multi-center scanning according to claim 9, characterized in that: Reconstructing the projection after interpolation and expansion includes the following steps: According to the projection data, an imaging model based on the Lagrangian optimization objective function is constructed as a mathematical model for iterative solution: In formula (6), F(R) = Af represents the sampling function; b is the projection after interpolation; is the sampling matrix; Z is the number of pixels in the image; P(R) is a specific constraint term, and β is the regularization parameter.

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