Static CT analysis and reconstruction method and system based on arc detector and arc ray source

Abstract

According to the analysis and reconstruction method and system of the static CT based on the arc-shaped detector and the arc-shaped ray source, the analysis and reconstruction method of the static CT based on the arc-shaped detector and the arc-shaped ray source is carried out through the following five steps, and finally a final CT image is obtained. The method has the beneficial effects that in a filtering back projection algorithm, a variable optimization method of geometric parameter transformation and traditional equiangular fan beam reconstruction is introduced, an accurate arc-shaped geometric scanning model is established, and an analysis reconstruction algorithm of linear multi-source static CT is referred to; meanwhile, the influence of the geometric structure characteristics of the arc ray source-arc detector and the projection data completeness on the reconstruction effect is considered, so that stripe artifacts and motion artifacts can be effectively reduced, and the CT image quality is improved. Meanwhile, the method keeps a frame of filtering back projection, and is low in calculation complexity and rapid in reconstruction.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of medical computed tomography image reconstruction, in particular to a static CT analytical reconstruction method and system based on an arc-shaped detector and an arc-shaped ray source. BACKGROUND

[0002] Traditional CT systems adopt a rotating scanning architecture with a slip ring, which has problems of high mechanical complexity, limited scanning speed, and large device volume. In scanning scenarios such as cardiac angiography and brain perfusion, slight movement of the patient can cause image blurring. A static CT system uses a carbon nanotube (CNT) array and a detector to achieve instantaneous scanning, reducing image motion artifacts and improving the quality of reconstructed images.

[0003] Currently, commercial traditional CT systems mainly use a reconstruction algorithm based on the Filtered Back-Projection (FBP) framework. This algorithm is a reconstruction algorithm that filters projection data along parallel beams and then performs back-projection. It can be extended from circular scanning trajectory parallel beam reconstruction to circular scanning trajectory two-dimensional fan beam reconstruction, and can reconstruct high-quality images in a relatively short time. However, the existing filtered back-projection reconstruction algorithm is not optimized for non-circular trajectory arc-shaped multi-source geometry static CT, resulting in low reconstruction efficiency and poor reconstruction image quality. Directly using existing linear multi-source static CT reconstruction algorithms can cause reconstruction failure and algorithm inadaptation.

[0004] Linear multi-source static CT ignores the curvature characteristics of arc-shaped geometry, resulting in geometric distortion, edge distortion of the reconstructed image, and visual problems such as discontinuity of small structures. Due to the non-optimized integral path, star-shaped artifacts appear in the center of the image, which seriously affects the quality of the reconstructed image and hinders clinical diagnosis and analysis tasks. Currently, static CT reconstruction mainly relies on two algorithms: (1) iterative reconstruction algorithms (such as Algebraic Reconstruction Technique (ART), Simultaneous Iterative Reconstruction Technique (SIRT), etc.), which have large computational complexity and long reconstruction time, making it difficult to meet the needs of real-time imaging in cardiac angiography and brain perfusion. Deep learning reconstruction algorithms rely on a large amount of training data, have poor generalization, and have black box characteristics that do not meet the application requirements of medical equipment. Moreover, existing reconstruction algorithms do not establish an accurate arc-shaped coordinate mapping model and design an anti-projection path that adapts to non-uniform sampling, resulting in geometric distortion, stripe artifacts, and other problems in the reconstructed image. Furthermore, existing iterative reconstruction algorithms have large computational complexity and long reconstruction time, which cannot meet the needs of real-time imaging.

[0005] Therefore, in view of the deficiencies in the prior art, it is particularly necessary to provide an analytical reconstruction method and system for static CT based on an arc-shaped detector and an arc-shaped ray source to solve the deficiencies in the prior art. SUMMARY

[0006] The first object of the present application is to provide an analytical reconstruction method for static CT based on an arc-shaped detector and an arc-shaped ray source to solve the deficiencies in the prior art. The analytical reconstruction method for static CT based on an arc-shaped detector and an arc-shaped ray source is based on filtered back-projection reconstruction theory and a non-slip ring multi-source arc-shaped geometry static CT structure, thereby reducing image reconstruction time and improving the quality of the reconstructed image.

[0007] The above object of the present application is achieved by the following technical measures:

[0008] The present application provides an analytical reconstruction method for static CT based on an arc-shaped detector and an arc-shaped ray source, which is performed in the following steps:

[0009] S1, obtaining original projection data g(γ, α) collected from an arc-shaped ray source and an arc-shaped detector of a static CT system, wherein γ is the included angle between each X-ray emitted by the light source point and the central X-ray, and α represents the angle of the X-ray source relative to the origin of the Cartesian coordinate system of the arc-shaped ray source array;

[0010] S2, adding a plurality of geometric weight factors to the original projection data g(γ, α) obtained in S1 to obtain weighted projection data g weighted (γ, α);

[0011] S3, filtering the weighted projection data g weighted (γ, α) obtained in S2 to obtain filtered projection data g filtered (γ, α);

[0012] S4, adding a geometric weight factor to the filtered projection data g filtered (γ, α) obtained in S3 and reconstructing along the ray path to each pixel point in the image space to obtain a two-dimensional CT image f(x, y) of the object linear attenuation coefficient;

[0013] S5, post-processing the two-dimensional CT image f(x, y) obtained in S4 to obtain a final CT image.

[0014] In the S2, the geometric weight factor includes an arc-shaped geometry weight and an angle-dependent weight.

[0015] In the S4, the geometric weight factor is a distance reciprocal weight.

[0016] In the S2, the weighted projection data g weighted(γ, α) is represented by formula (1):

[0017]

[0018] wherein, is an arc geometry weight, is an angle dependent weight, R s is a curvature radius of the arc-shaped ray source array, B is a vertical distance from the center of the arc-shaped ray source array to the x-axis, u is a distance from a light source point to the origin of the Cartesian coordinate system, and γ' is a detector angle of a ray passing through the reconstructed x object point.

[0019] In the S3, the filtered projection data g filtered (γ, α) is represented by formula (2):

[0020] g filtered (γ, α) = g weighted (γ, α) * h(γ) …… formula (2);

[0021] wherein, h is a filter kernel function, and * is a convolution operation.

[0022] Preferably, the filter of the filter kernel function is Ram-Lak, Shepp-Logan or Hamming.

[0023] In the S4, the back projection is specifically to back project the filtered projection data to an image space, to reconstruct a linear attenuation coefficient of each pixel point, and the light source point angle α is from -α m to +α m Integration covers all light source angles, and the detector angle γ is from -γ m to +γ m Integration covers all detector angles, wherein +α m is an upper limit of light source angle integration; -α m is a lower limit of light source angle integration; +γ m is an upper limit of detector angle integration; and -γ m is a lower limit of detector angle integration.

[0024] Preferably, the S4 includes the following steps:

[0025] S4.1, initializing a two-dimensional image matrix, and setting all pixel values to zero;

[0026] S4.2, calculating a geometric parameter corresponding to the current image point (x, y) in each light source angle α and each detector angle γ; then obtaining a corresponding data value from the filtered projection data g filtered (γ, α) through interpolation; and finally multiplying the data value by a geometric weight factor and accumulating to a pixel of the image matrix;

[0027] S4.3, when the light source point angle a is from -a m to +a m integrate over all light source angles and detector angle g from -g m to +g m integrate over all detector angles, the two-dimensional CT image f(x, y) is obtained.

[0028] Preferably, the reconstruction formula of the two-dimensional CT image f(x, y) is represented by formula (3):

[0029]

[0030] wherein, is the distance reciprocal weight, and L is the distance from the light source point to the reconstructed object point.

[0031] The second object of the present application is to provide an analytical reconstruction system of static CT based on an arc-shaped detector and an arc-shaped ray source to avoid the shortcomings of the prior art. The analytical reconstruction system of static CT based on the arc-shaped detector and the arc-shaped ray source is based on the filtered back-projection reconstruction theory and the non-slip ring multi-source arc-shaped geometry static CT structure, thereby reducing the image reconstruction time and improving the quality of the reconstructed image.

[0032] The above object of the present application is achieved by the following technical measures:

[0033] The present application provides an analytical reconstruction system of static CT based on an arc-shaped detector and an arc-shaped ray source, which is provided with:

[0034] an arc-shaped ray source array for emitting X-rays, which is composed of a plurality of independent X-ray sources and arranged in a circular arc shape with a radius of curvature R s ;

[0035] an arc-shaped detector array concentrically arranged with the arc-shaped ray source array, for receiving the X-ray signal after penetrating the scanned object and obtaining the original projection data g(g, a);

[0036] a data processing unit for performing the analytical reconstruction method of static CT based on the arc-shaped detector and the arc-shaped ray source as described above;

[0037] an image output unit for displaying the final CT image.

[0038] Preferably, the data processing unit is provided with:

[0039] a weighting module for adding a geometric weight factor to the original projection data g(g, a) to generate weighted projection data g weighted (g, a);

[0040] a filtering module for filtering the weighted projection data g weighted(γ, α) is filtered to generate filtered projection data g. filtered (γ, α);

[0041] Back projection module – used to project filtered data g filtered (γ, α) are back-projected into the image space to reconstruct a two-dimensional CT image f(x, y) of the linear attenuation coefficient of the object.

[0042] This invention discloses an analytical reconstruction method and system for static CT based on an arc detector and an arc X-ray source. The analytical reconstruction method for static CT based on an arc detector and an arc X-ray source comprises the following steps: S1, acquiring raw projection data g(γ, α) from the arc X-ray source and arc detector of the static CT system, where γ is the angle between each X-ray emitted from the source point and the central X-ray, and α represents the angle of the X-ray source array relative to the origin of the Cartesian coordinate system; S2, adding multiple geometric weighting factors to the raw projection data g(γ, α) obtained in S1 to obtain weighted projection data g. weighted (γ, α); S3, weighted projection data g obtained from S2 weighted (γ, α) is filtered to obtain filtered projection data g. filtered (γ, α); S4, the filtered projection data g obtained from S3 filtered (γ, α) Add geometric weight factors and backproject along the ray path to each pixel in the image space for reconstruction, obtaining a 2D CT image f(x, y) with linear attenuation coefficient of the object; S5, Postprocess the 2D CT image f(x, y) obtained in S4 to obtain the final CT image. The beneficial effects of this invention are: In the filtered backprojection algorithm, a variable optimization method combining geometric parameter transformation and traditional isoangular fan-beam reconstruction is introduced to establish an accurate arc-shaped geometric scanning model. Referring to the analytical reconstruction algorithm of linear multi-source static CT, and considering the influence of the geometric structure characteristics of the arc-shaped ray source-arc detector and the completeness of projection data on the reconstruction effect, it can effectively reduce stripe artifacts and motion artifacts and improve the quality of CT images. At the same time, this invention maintains the framework of filtered backprojection, has low computational complexity, and fast reconstruction. Attached Figure Description

[0043] The invention will be further described with reference to the accompanying drawings, but the contents of the drawings do not constitute any limitation on the invention.

[0044] Figure 1 This is a flowchart illustrating an analytical reconstruction method for static CT based on an arc detector and an arc X-ray source.

[0045] Figure 2 This is a schematic diagram of the static CT scanning structure of the arc-shaped X-ray source and arc-shaped detector of the present invention.

[0046] Figure 3 The static CT reconstruction geometry of the arc-shaped ray source and the arc-shaped detector of the present application.

[0047] Figure 4 The reconstruction result diagram of the analytical reconstruction algorithm of the present application in the arc-shaped geometry system. DETAILED DESCRIPTION

[0048] The technical solutions of the present application are further illustrated in combination with the following examples.

[0049] Example 1

[0050] An analytical reconstruction method of a static CT based on an arc-shaped detector and an arc-shaped ray source, as shown in Figure 1 , is performed in the following steps:

[0051] S1, obtaining the original projection data g(γ,α) collected from the arc-shaped ray source and the arc-shaped detector of the static CT system, wherein γ is the included angle between each X-ray emitted from the light source point and the central X-ray, and α represents the angle of the X-ray source relative to the origin of the Cartesian coordinate system of the arc-shaped ray source array;

[0052] S2, adding a plurality of geometric weight factors to the original projection data g(γ,α) obtained in S1 to obtain weighted projection data g weighted (γ,α);

[0053] S3, performing filtering processing on the weighted projection data g filtered (γ,α) obtained in S2 to obtain filtered projection data g filtered (γ,α);

[0054] S4, adding a geometric weight factor to the filtered projection data g filtered (γ,α) obtained in S3 to reconstruct each pixel point in the image space along the ray path, and reconstructing to obtain a two-dimensional CT image f(x,y) of the linear attenuation coefficient of the object, wherein (x,y) is the horizontal and vertical coordinates of the pixel in the Cartesian coordinate system.

[0055] S5, performing post-processing on the two-dimensional CT image f(x,y) obtained in S4 to obtain a final CT image.

[0056] In S2, the geometric weight factor is an arc-shaped geometry weight and an angle-dependent weight; and in S4, the geometric weight factor is a distance reciprocal weight.

[0057] It should be noted that the static CT scanning structure of the arc-shaped ray source and the arc-shaped detector of the present application is shown in Figure 2 , and the static CT scanning structure is as follows: Figure 2It can be seen that the arc-shaped ray source and the arc-shaped detector of the present application are arranged in an arc structure with the center of the object as the center of the circle. The static CT reconstruction geometry diagram of the arc-shaped ray source and the arc-shaped detector of the present application is shown in Figure 3 The arc-shaped geometry weight of the present application is used to accurately match the arc-shaped layout of the light source and the detector, and to ensure that the projection data is consistent with the physical geometry model. The angle-dependent weight is used to correct the geometric effect of the fan-shaped beam, and to prevent the distortion of the image edge. The distance reciprocal weight is used to correct the attenuation of the X-ray intensity with the increase of the distance between the light source and the reconstruction point. Through the three geometric weight factors of the arc-shaped geometry weight, the angle-dependent weight and the distance reciprocal weight, the distortion and the non-uniform sampling problem caused by the arc-shaped scanning geometry structure are compensated. The geometric parameter transformation and the variable optimization are realized by introducing the geometric weight factor. Specifically, by transforming the geometric parameters and referring to the variable optimization method in the equiangular fan-shaped beam reconstruction of the circular scanning, and by referring to the analytical reconstruction algorithm of the multi-source linear translation scanning static CT and adapting it to the static CT system of the arc-shaped ray source and the arc-shaped detector, the analytical reconstruction algorithm suitable for the static CT scanning system is derived. The filtering in S3 of the present application is used to eliminate the blur, suppress the noise and reduce the artifacts.

[0058] In S2, the weighted projection data g weighted (γ,α) is represented by formula (1):

[0059]

[0060] wherein, is the arc-shaped geometry weight, is the angle-dependent weight, R s is the curvature radius of the arc-shaped ray source array, B is the vertical distance from the center of the arc-shaped ray source array to the x-axis, u is the distance from the light source point to the origin of the Cartesian coordinate system, and γ' is the detector angle of the ray passing through the reconstructed x object point.

[0061] In S3, the filtered projection data g filtered (γ,α) is represented by formula (2):

[0062] g filtered (γ,α) = g weighted (γ,α) * h(γ) …… formula (2);

[0063] wherein, h is the filter kernel function, and * is the convolution operation. The filter of the filter kernel function is Ram-Lak, Shepp-Logan or Hamming.

[0064] It should be noted that the filtering step is represented in the reconstruction formula by a filter kernel function h(γ'-γ), where h is a selected filter function, and the filtering operation is applied to the weighted projection data to remove blurring, noise and artifacts. Commonly used filters are Ram-Lak, Shepp-Logan or Hamming filter. In the formula, h(γ'-γ) is convolved with the weighted projection data g(γ,α) to achieve filtering in the frequency domain or spatial domain. The Ram-Lak filter is an ideal high-pass filter, and the filter kernel function is which can preserve high-frequency details but may amplify noise. The Shepp-Logan filter is a smoothed version of Ram-Lak, and the filter kernel function is multiplied by a window function (such as a sinc function), which reduces noise amplification and improves image smoothness. The Hamming filter uses a Hamming window function, which further suppresses the ringing effect and provides a more balanced frequency response. In the algorithm, the filtering step filters the weighted projection data g weighted (γ,α). Specifically, for each fixed angle α, along the detector angle γ direction, the convolution of g weighted (γ,α) and the filter kernel function h is calculated.

[0065] In S4, back projection specifically refers to back projecting the filtered projection data to the image space, reconstructing the linear attenuation coefficient of each pixel point, and the light source point angle α is integrated from -α m to +α m , covering all light source angles, and the detector angle γ is integrated from -γ m to +γ m , covering all detector angles, where +α m is the upper limit of the light source angle integration, i.e. the half opening angle of the arc-shaped ray source array; -α m is the lower limit of the light source angle integration; +γ m is the upper limit of the detector angle integration, i.e. the half opening angle of the arc-shaped detector array; -γ m is the lower limit of the detector angle integration, which is symmetrically covered with +γ m . S4 includes the following steps:

[0066] S4.1, initialize a two-dimensional image matrix, set all pixel values to zero;

[0067] S4.2, calculate the geometric parameters corresponding to the current image point (x, y) in each light source angle α and each detector angle γ; then obtain the corresponding data value from the filtered projection data g filtered (γ,α) by interpolation; finally, multiply the data value by the geometric weight factor and accumulate it to the image matrix pixel;

[0068] S4.3, when the light source angle α is integrated from -α m to +α mThe integration covers all light source angles and detector angles γ from -γ m to +γ m After all the detector angles are traversed, the two-dimensional CT image f(x, y) is obtained.

[0069] It should be noted that the S4 back projection step is implemented by double integration, i.e., integration of α and γ. The integration range covers all light source angles (α from -α m to +α m ) and all detector angles (γ from -γ m to +γ m ), ensuring data completeness. The inner integration (for γ) integrates the filtered data at all detector angles for each light source point angle α. The outer integration (for α) covers all light source points and completes the full-angle back projection within the specified range. In the algorithm implementation, the back projection step maps the filtered data g filtered (γ, α) to the image grid (x, y).

[0070] For each image point (x, y), its corresponding geometric parameters (such as L, u, γ ′ ) are calculated, and then integration and summation are performed for all α and γ.

[0071] The reconstruction formula of the two-dimensional CT image f(x, y) is represented by equation (3):

[0072]

[0073] wherein, is the distance reciprocal weight, and L is the distance from the light source point to the reconstructed object point.

[0074] In S5, the post-processing is at least one of contrast adjustment or window width and window level setting. It should be noted that the two-dimensional CT image f(x, y) obtained by the present application is subjected to necessary post-processing, and then displayed through a computer display or a medical image workstation. Thus, the final CT image for clinical diagnosis by a doctor is output.

[0075] The analytical reconstruction method of the static CT based on the arc-shaped detector and the arc-shaped ray source introduces geometric parameter transformation and variable optimization method of the traditional equal-angle fan beam reconstruction in the filtered back projection algorithm, establishes an accurate arc-shaped geometric scanning model, references the analytical reconstruction algorithm of the straight-line-shaped multi-source static CT, simultaneously considers the influence of the geometric structure characteristics of the arc-shaped ray source-arc-shaped detector and the projection data completeness on the reconstruction effect, can effectively reduce the stripe artifacts and motion artifacts, and improves the CT image quality. Meanwhile, the present application maintains the framework of the filtered back projection, has low calculation complexity, and is fast in reconstruction.

[0076] Example 2

[0077] An application of analytical reconstruction method of static CT based on arc-shaped detector and arc-shaped ray source, as shown in Figure 4 This embodiment describes the implementation process on three sets of different source data in detail. Among them Figure 4 The first is the Shepp-Logan head model example, the second is the hospital collected craniocerebral DICOM example, and the third is the hospital collected chest DICOM example. The overall process of the three examples is consistent, mainly including data acquisition and preprocessing, system geometric parameter determination, ray-driven forward projection, frequency domain filtering, two-section analytical reconstruction, and image domain two-section synthesis and display verification. Now the main operations and parameters used in each step are described step by step.

[0078] First, data acquisition and preprocessing are performed. In the embodiment, the simulated Shepp-Logan head model image can be used as the first set of data, with an image size of 512x512 pixels; the second and third sets of data are hospital collected craniocerebral and chest DICOM images, with original size and pixel spacing determined according to the DICOM file header information. When reading the DICOM data, linear scaling processing is performed on the original pixel value according to the RescaleSlope and RescaleIntercept in the DICOM tag, and the scaled pixel value is mapped to the range corresponding to the linear attenuation coefficient of water according to the needs, and in this embodiment, the linear attenuation coefficient of water is taken as 0.0192 per millimeter; to ensure numerical stability, the minimum intensity of the image is limited to 0.001; when needed, the DICOM image is resampled to 512x512 pixels using bilinear interpolation to match the field of view and resolution of subsequent reconstruction.

[0079] Determine the system geometric parameters to establish the spatial relationship between forward projection and back projection. In this embodiment, the X-ray source and the arc-shaped detector are arranged in an arc shape, and the specific parameters are as follows: the detector arc radius is 468.95 millimeters, the X-ray source arc radius is 468.95 millimeters, the chord length of the detector arc is 837 millimeters, and the detector unit size is set to 0.3 millimeters, so the number of detector units is about 2790; the number of light sources for each scan is set to 31, and the light sources are distributed along the arc at equal intervals; the detector angle coverage range is 165 degrees, and the light source angle coverage range is 130 degrees; the geometric rotation angle of the second scan relative to the first scan is set to 45 degrees; the field of view radius of the reconstructed image is set to 80 millimeters, and the reconstructed image size is 512x512 pixels. The above parameters are used to determine the coordinates of each light source and each detector unit in the two-dimensional plane, so as to simulate the ray geometry in the image domain.

[0080] The ray driving method is used for the forward projection simulation. The ray path is calculated for each light source position and each detector unit position, and the entering point and the exiting point of the ray in the image domain are determined; the sampling step length of the ray in the image domain is set to 0.15 mm (equivalent to half of the size of the detector unit), and the entering point and the exiting point are equidistantly sampled according to the step length; the bilinear interpolation is used for reading the image intensity value at the sampling point position, and the numerical integral is performed on the sampling value to obtain the projection value of the ray. The first section and the second section independently complete the forward projection calculation, wherein the source and the detector position of the second section are rotated by 45 degrees to obtain the second section, so as to simulate the acquisition at different angles without angle interpolation of the image.

[0081] The forward projection data is filtered in the frequency domain to meet the requirement of the filtered back projection. The embodiment constructs the filter response in the one-dimensional frequency domain, the filter type adopts the Hamming window, the alpha parameter in the Hamming window is 0.54, and the cutoff frequency of the filter is set to 1.0. The projection sequence of each detector channel is first zero-padded to an appropriate length, and then the fast Fourier transform is performed, and after the multiplication with the filter response in the frequency domain, the inverse transform is performed and the effective part is intercepted to obtain the filtered projection data. The filter type and the cutoff frequency can be appropriately adjusted according to the image noise characteristics to balance the detail retention and the noise suppression.

[0082] The filtered back projection reconstruction of the first section is performed. The ray driving back projection is used for the filtered projection data of the first section: for each filtered ray, the corresponding pixel index is found in the image domain according to the sampling point, and the projection value is accumulated, and the number of times of accumulation of each pixel is recorded as the weight count; after the reconstruction, the pixel value is normalized according to the weight to eliminate the deviation caused by the uneven sampling; in order to match the reconstructed value with the physical order of magnitude, an empirical scale correction factor can be multiplied, and the empirical correction factor used in the embodiment is 200.

[0083] The filtered back projection reconstruction of the second section is performed and the image rotation interpolation is avoided. The geometric parameters of the second section are the same as those of the first section, but the overall coordinates are rotated by 45 degrees around the image center to construct the second group of light source and detector positions; by rotating the geometric coordinates instead of the image, the blur and the numerical error introduced by the angle interpolation based on the image can be avoided. Then, the aforementioned frequency domain filtering and ray driving back projection steps are repeated for the projection data of the second section to obtain the reconstructed image of the second section.

[0084] The two pieces of reconstruction results are synthesized in image domain to obtain the final image. In this embodiment, simple addition superposition is used as the synthesis method, that is, the reconstruction images of the first piece and the second piece are added point by point at the pixel level to obtain the final reconstruction result; when needed, weighted superposition strategy can also be used according to the angular coverage or noise level to further optimize the imaging quality. Image domain synthesis can improve the overall angular coverage and redundant information, thereby compensating for the blind area of single-piece reconstruction in the spatial spectrum, improving the structure connectivity and suppressing the strip artifacts.

[0085] For intuitive comparison of results, the original image, the first piece of reconstruction image, the second piece of reconstruction image and the two-piece synthesis image are displayed in the same window. Figure 4 The three rows in the table correspond to the simulated Shepp-Logan data, the hospital brain DICOM data and the hospital chest DICOM data respectively; in each group of examples, it can be observed from the visual comparison that the two-piece synthesis result is obviously better than any single-piece reconstruction result in terms of artifact suppression and structure continuity.

[0086] In engineering implementation, several key points need to be paid attention to in order to ensure the implementation effect. First, the sampling step of forward projection and back projection should match the size of the detector unit, and the sampling step of 0.15 mm is used in this embodiment to balance the precision and calculation amount; second, the filter type and cutoff frequency have a great influence on noise amplification, and the Hamming or Shepp-Logan window can be selected for real clinical data and the cutoff frequency can be appropriately reduced to suppress high-frequency noise; third, the physical scale alignment and necessary resampling of the original pixel value from DICOM are the premise to ensure geometric consistency; finally, the scale correction factor in the back projection accumulation process can be adjusted according to the device calibration or experimental measurement.

[0087] In order to improve the calculation efficiency, the forward projection and back projection algorithms of this embodiment can be implemented by vectorization or parallelization, and multi-threading or GPU acceleration is recommended in engineering deployment to meet the time requirements of the actual system. In addition, the filtering process uses FFT to significantly speed up the frequency domain operation, and the zero padding length is selected as the power of 2 to improve the performance of FFT.

[0088] In Figure 4The three groups of examples of the application not only verify the correctness of the numerical implementation on the simulation data, but also demonstrate the universality and robustness of the method of the application on real DICOM data of the brain and the chest. Through the geometric complementarity of the first segment and the second segment, the application can compensate for the lack of single-segment projection information in the image domain, thereby achieving relatively stable imaging effects under different anatomical sites and imaging noise conditions. Compared with the iterative reconstruction method, the reconstruction method of the application has significant engineering advantages and image quality advantages, which are specifically manifested as follows: the application retains the high-efficiency calculation characteristics of analytical reconstruction while reducing the strip artifacts caused by insufficient angles through geometric double-segment coverage, so that the reconstructed image has fewer artifacts and better structural connectivity; the reconstructed value obtained by the application is closer to the real distribution of the original data in spatial distribution, and has higher reconstruction accuracy and better stability. Compared with the iterative reconstruction, the application does not require complex iterative parameter adjustment and expensive calculation cost, and can achieve similar or even better visual effect and numerical accuracy on actual data as the iterative method.

[0089] Embodiment 3

[0090] An analytical reconstruction system of static CT based on an arc-shaped detector and an arc-shaped ray source is provided with:

[0091] An arc-shaped ray source array composed of a plurality of independent X-ray sources arranged in a circular arc shape with a radius of curvature R s ;

[0092] An arc-shaped detector array concentrically arranged with the arc-shaped ray source array, used for receiving X-ray signals after penetrating a scanned object to obtain original projection data g(γ,α);

[0093] A data processing unit for performing the analytical reconstruction method of static CT based on the arc-shaped detector and the arc-shaped ray source of embodiment 1;

[0094] An image output unit for displaying a final CT image.

[0095] The data processing unit is provided with:

[0096] A weighting module for adding a geometric weight factor to the original projection data g(γ,α) to generate weighted projection data g weighted (γ,α);

[0097] A filtering module for filtering the weighted projection data g weighted (γ,α) to generate filtered projection data g filtered (γ,α);

[0098] A back projection module for back projecting the filtered projection data g filteredThe (gamma, alpha) back-projection is projected to the image space, and a two-dimensional CT image f(x, y) of the object linear attenuation coefficient is reconstructed.

[0099] The analytical reconstruction system of the static CT based on the arc-shaped detector and the arc-shaped ray source introduces the geometric parameter transformation and the variable optimization method of the traditional equal-angle fan beam reconstruction in the filtered back-projection algorithm, establishes an accurate arc-shaped geometric scanning model, references the analytical reconstruction algorithm of the straight-line-shaped multi-source static CT, simultaneously considers the influence of the geometric structure characteristics of the arc-shaped ray source-arc-shaped detector and the completeness of the projection data on the reconstruction effect, can effectively reduce the stripe artifacts and the motion artifacts, and improves the CT image quality. Meanwhile, the invention maintains the framework of the filtered back-projection, has low calculation complexity, and is fast in reconstruction.

[0100] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, and are not intended to limit the scope of protection of the present application. Although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present application can be modified or replaced by equivalents without departing from the essence and scope of the technical solutions of the present application.

Claims

1. An analytical reconstruction method for static CT based on an arc-shaped detector and an arc-shaped X-ray source, characterized in that, Follow these steps: S1. Obtain the raw projection data g(γ, α) collected from the arc-shaped X-ray source and arc-shaped detector of the static CT system, where γ is the angle between each X-ray emitted from the source point and the central X-ray, and α represents the angle of the X-ray source relative to the origin of the Cartesian coordinate system in the arc-shaped X-ray source array. S2. Add multiple geometric weighting factors to the original projection data g(γ, α) obtained in S1 to obtain the weighted projection data g. weighted (γ, α); S3, the weighted projection data g obtained from S2 weighted (γ, α) is filtered to obtain filtered projection data g. filtered (γ, α); S4. The filtered projection data g obtained from S3 filtered (γ, α) Add geometric weight factors and backproject along the ray path to each pixel in the image space for reconstruction, and obtain a two-dimensional CT image f(x, y) with linear attenuation coefficient of the object. S5. Post-process the two-dimensional CT image f(x, y) obtained in S4 to obtain the final CT image.

2. The analytical reconstruction method for static CT based on an arc-shaped detector and an arc-shaped X-ray source according to claim 1, characterized in that: In S2, the geometric weighting factor is an arc geometric weight and an angle-related weight; In S4, the geometric weight factor is the inverse distance weight.

3. The analytical reconstruction method for static CT based on an arc-shaped detector and an arc-shaped X-ray source according to claim 2, characterized in that: In S2, the weighted projection data g weighted (γ, α) is represented by equation (1): in, For arc-shaped geometric weights, For angle-related weights, R s Let be the radius of curvature of the arc-shaped ray source array, B be the vertical distance from the center of the arc-shaped ray source array to the x-axis, u be the distance from the source point to the origin of the Cartesian coordinate system, and γ′ be the detector angle of the ray that reconstructs the x-object point.

4. The analytical reconstruction method for static CT based on an arc-shaped detector and an arc-shaped X-ray source according to claim 3, characterized in that: In S3, the filtered projection data g filtered (γ, α) is represented by equation (2): g filtered (γ,α)=g weighted (γ,α)*h(γ)……Expression (2); Where h is the filtering kernel function, and * is the convolution operation.

5. The analytical reconstruction method for static CT based on an arc-shaped detector and an arc-shaped X-ray source according to claim 4, characterized in that, In step S4, backprojection specifically involves backprojecting the filtered projection data onto the image space to reconstruct the linear attenuation coefficient of each pixel, with the light source angle α ranging from -α. m to +α m The integral covers all light source angles, with the detector angle γ ranging from -γ. m to +γ m The integral covers all detector angles, where +α m -α is the upper limit of the integral of the light source angle; m The lower limit of the integral of the light source angle; +γ m -γ is the upper limit of the detector's angular integral; m This is the lower limit of the detector's angular integral.

6. The analytical reconstruction method for static CT based on an arc-shaped detector and an arc-shaped X-ray source according to claim 5, characterized in that, S4 includes the following steps: S4.1 Initialize a two-dimensional image matrix by setting all pixel values ​​to zero; S4.2 Calculate the geometric parameters corresponding to the current image point (x,y) in each light source angle α and each detector angle γ; then calculate the parameters from the filtered projection data g. filtered (γ,α) is obtained by interpolation; finally, the data value is multiplied by the geometric weight factor and accumulated to the image matrix pixels; S4.3 When the angle α of the light source point changes from -α m to +α m The integral covers all light source angles and detector angles γ from -γ m to +γ m After the integral coverage of all detector angles has been traversed, the two-dimensional CT image f(x, y) is obtained.

7. The analytical reconstruction method for static CT based on an arc-shaped detector and an arc-shaped X-ray source according to any one of claims 1 to 6, characterized in that: The reconstruction formula for the two-dimensional CT image f(x, y) is expressed by equation (3): in, The distance weight is the inverse of the distance, where L is the distance from the light source point to the reconstructed object point.

8. The analytical reconstruction method for static CT based on an arc-shaped detector and an arc-shaped X-ray source according to claim 4, characterized in that: The filter kernel function is either Ram-Lak, Shepp-Logan, or Hamming. In S5, the post-processing is at least one of contrast adjustment or window width and window level settings.

9. A static CT analytical reconstruction system based on an arc-shaped detector and an arc-shaped X-ray source, characterized in that: The settings are as follows: Arc-shaped X-ray source array – emits X-rays, composed of multiple independent X-ray sources arranged in an arc shape with a radius of curvature R. s ; Arc-shaped detector array—arranged concentrically with the arc-shaped X-ray source array, used to receive X-ray signals after penetrating the scanned object and obtain raw projection data g(γ, α); Data processing unit—executes the analytical reconstruction method for static CT based on an arc detector and an arc X-ray source as described in any one of claims 1 to 8; Image output unit – displays the final CT image.

10. The static CT analytical reconstruction system based on an arc-shaped detector and an arc-shaped X-ray source according to claim 9, characterized in that, The data processing unit is equipped with: Weighting module – Adds geometric weighting factors to the original projection data g(γ, α) to generate weighted projection data g. weighted (γ, α); Filtering module – used for weighted projection data g weighted (γ, α) is filtered to generate filtered projection data g. filtered (γ, α); Back projection module – used to project filtered data g filtered (γ, α) are back-projected into the image space to reconstruct a two-dimensional CT image f(x, y) of the linear attenuation coefficient of the object.

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