Weighted source straight line scan CT analytical reconstruction method

Abstract

The present application relates to a kind of based on weighted source straight line scanning CT analytic reconstruction method, belong to micro focus computer tomography reconstruction technical field.The method includes: S1: the layout of F-mSTCT scanning mode is built;S2: in F-mSTCT scanning mode, design the weighting function for correcting redundant projection and truncated projection;S3: according to the weighting function constructed in step S2, construct W-FBP reconstruction algorithm suitable for F-mSTCT.The present application can solve the problem of truncation in STCT imaging, and overcome the shortcomings of poor imaging resolution of V-FBP algorithm under low projection number, realize the reconstruction of high-resolution image under lower ray source sampling rate, while reducing the number of projections.

Description

Technical Field

[0001] This invention belongs to the field of microfocus computed tomography reconstruction technology, and relates to a weighted source linear scanning CT analytical reconstruction method. Background Technology

[0002] Micro-focus computed tomography (Micro-CT) non-destructively acquires information about the internal structure of an object by detecting the intensity attenuation of X-rays as they pass through the sample, and has been widely used in industrial inspection, materials science, mineralogy analysis, and medical research. However, its limited field of view (FOV) restricts its further widespread application. To expand the FOV of Micro-CT, researchers have developed various imaging geometries, including detector offset, continuous translational rotation scanning, rotational translational multi-scan mode (RTT), rotational translational multi-scan mode (RT), elliptical trajectory, complementary circular scanning, and rotating detector. Recently, a research group developed a multi-source linear scanning CT (mSTCT) to expand the FOV. mSTCT is characterized by adjusting the FOV by changing the length of the translational trajectory of the X-ray source parallel to the flat panel detector (FPD).

[0003] However, almost all imaging geometries used to extend the field of view face the problem of projection truncation, which poses a challenge to reconstructing artifact-free images using analytical algorithms. The truncated projection data, after filtering, exhibits the Gibbs phenomenon at the truncation point because most filtering operations require a complete, untruncated projection. In truncated projection, discontinuities across the illumination boundary are amplified by the filtering step, resulting in amplified numerical fluctuations at the truncation boundary. These amplified values ​​are incorrectly propagated to pixels near the boundary, causing pixel values ​​in the reconstructed image to rise. This leads to a burst of pixel values ​​near the illumination boundary after backprojection, producing bright stripe artifacts.

[0004] Reconstruction algorithms for projection truncation problems in imaging geometry with extended field of view can be mainly divided into three categories. The first category is reconstruction algorithms based on backprojection-filtering (BPF). The main idea of ​​BPF is to obtain a differential backprojection (DBP) image by backprojecting the derivative of the truncated projection, and then recover the CT image from the DBP image using the inverse formula of the finite Hilbert transform. Since the differential is a local operator and the Hilbert transform is implemented in the image domain, BPF can mitigate the impact of projection truncation on the entire reconstructed image. In detector offset scanning, Leng applied BPF to the fan-beam case, Li applied this idea to cone-beam scanning, and Schafer developed two novel BPF algorithms for circumferential CT with an off-center detector. Chen proposed a BPF-based reconstruction algorithm in RT scanning mode.

[0005] The second type is based on virtual geometry. This involves assuming a set of virtual X-ray source focal points whose rays projected onto the detector (or virtual detector) completely cover the object, thus converting the real truncated projection into a virtual non-truncated projection. Based on this concept, Muller developed reconstruction algorithms suitable for both RTT and RT scanning modes. Previously, we developed a virtual geometry-based filtered back projection (V-FBP) algorithm for mSTCT reconstruction. In V-FBP, the virtual projection is a set of X-rays converged to the same detector unit. When the X-ray source sampling is dense, V-FBP achieves high-resolution, high-quality reconstruction; however, if the X-ray source sampling is coarse, it affects the high-frequency information in the reconstructed image.

[0006] The third category is weighted schemes, which utilize data redundancy in complementary projections to suppress artifacts caused by sine wave truncation by appropriately weighting the projections. This method has been widely used in detector offset scanning. For example, Cho effectively suppresses truncation artifacts by processing the overlapping projection regions before or after the filtering step in the FDK algorithm using a weighting function similar to Parker weights. Subsequently, Wang proposed a weighted FDK algorithm. More recently, Sanctorum incorporated redundant weighting into synchronous iterative reconstruction techniques, which significantly improves image quality even with large detector offsets.

[0007] However, the BPF algorithm requires image rotation and interpolation when applied to STCT scans, which introduces errors. The V-FBP algorithm, developed using virtual projection geometry, struggles to reconstruct high-resolution images with a limited number of projections. Furthermore, existing mSTCT scan modes suffer from complex redundancy, making it difficult to design suitable weighting functions to eliminate truncation artifacts. Therefore, a new CT analytical reconstruction method is urgently needed to address the truncation problem in STCT imaging and overcome the poor imaging resolution of the V-FBP algorithm with a low number of projections. Summary of the Invention

[0008] In view of this, the purpose of this invention is to provide a weighted source line scanning CT analytical reconstruction method to solve the truncation problem in STCT imaging and overcome the shortcomings of the V-FBP algorithm in poor imaging resolution with low number of projections, so as to realize the reconstruction of high-resolution images with a lower X-ray source sampling rate and at the same time reduce the number of projections.

[0009] To achieve the above objectives, the present invention provides the following technical solution:

[0010] A weighted source linear scan CT analytical reconstruction method specifically includes the following steps:

[0011] S1: Construct a full-scan mSTCT (F-mSTCT) mode layout; where mSTCT is a multi-source linear scanning CT.

[0012] S2: In F-mSTCT scanning mode, a weighting function designed to correct redundant and truncated projections;

[0013] S3: Based on the weighting function constructed in step S2, construct a W-FBP (weighted filter back projection algorithm) reconstruction algorithm suitable for F-mSTCT.

[0014] Furthermore, in step S1, the layout of the F-mSTCT scanning pattern is constructed, specifically including: F-mSTCT is a two-dimensional imaging geometric model composed of multiple STCT scans; the number of STCT scans T in F-mSTCT... f for:

[0015]

[0016] The ceil() function returns the nearest integer rounded up; Δθ is the projection coverage angle that a segment of STCT scan can obtain, expressed as Δθ = 2arctan(d / h), where d is half the width of the detector and h is the distance from the object to the detector;

[0017] The rotation angle Δθ between two adjacent STCT segments f for:

[0018] Furthermore, in step S2, the designed weighting function is:

[0019]

[0020] in, Let be the weight of the i-th segment of STCT, (λ) i+1 |λ i ,u i >,u i+1 |λ i ,u i >) is a ray (λ) i ,u i In the (i+1)th segment of STCT, s represents half the distance the X-ray source moves, and d represents half the width of the detector; u r =min(u i |λ i ,d i+1 >,u i |-s i+1 ,λ i >), u i |λ i ,d i+1> is related to the i-th segment detector and the straight line (λ) i ,d i+1 The local coordinates of the intersection point of the two points on the i-th segment of the detector; u i |-s i+1 ,λ i There are similar definitions;

[0021] To ensure that there is only one equivalent ray, the weight of the (i+1)th segment of STCT is:

[0022]

[0023] Furthermore, in step S2,

[0024] Furthermore, in step S3, the W-FBP reconstruction algorithm formula for F-mSTCT is:

[0025]

[0026]

[0027] Where l is the distance from the radiation source to the object, and T is the number of STCT scans. q(u) represents the projection data acquired by the i-th segment of the STCT scan. i ′-u i ) represents the convolution kernel of the ramp filter; u i ′ indicates that during the i-th segment of STCT, the X-ray source is at λ. i The local coordinates of the ray emitted from point (x, y) and projected onto the detector are expressed as:

[0028]

[0029] The beneficial effects of this invention are as follows: This invention is a CT imaging strategy composed of F-mSTCT scanning and the W-FBP algorithm, which not only solves the truncation problem in STCT imaging but also overcomes the shortcomings of the V-FBP algorithm in terms of poor imaging resolution with a low number of projections. This invention's strategy can effectively reduce the number of projections required for high-resolution imaging, improving reconstruction efficiency. With the help of a weighting function, the W-FBP algorithm designed in this invention can directly reconstruct high-quality images without artifacts without additional processing of the projections, greatly improving the efficiency of data acquisition and reconstruction.

[0030] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0031] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0032] Figure 1 This is a schematic diagram of mSTCT imaging mode; where (a) is a three-dimensional imaging model, (b) is a two-dimensional geometry, and (c) is the two-dimensional geometry of a single-segment STCT.

[0033] Figure 2 Here is a redundancy diagram of mSTCT; where (a) is the sine curve of the mSTCT projection; (b) and (c) are the redundancy distributions of the original mSTCT and the mSTCT after the translation angle is reduced, respectively, where redundancy appears in the black area;

[0034] Figure 3 The diagram shows the imaging mode and projection of F-mSTCT; (a) is the two-dimensional geometry; (b) is a segment of the STCT projection sine curve, which is truncated within the dashed box; (c) is the sine curve of F-mSTCT projection; and (d) is the redundancy distribution of F-mSTCT, with the black area representing the region where redundancy occurs.

[0035] Figure 4 Here is a schematic diagram of the weighting function design; where (a) represents the redundant data of adjacent STCT scans; (b) represents the weights of the i-th and (i+1)-1-th STCT projections; and (c) represents the projections processed by the weighting function.

[0036] Figure 5 The results are W-FBP and FBP; where (a) shows the STCT reconstruction results of each step by FBP; (b) shows the STCT reconstruction results of each step by W-FBP; (c) and (d) show the complete results of FBP and W-FBP for F-mSTCT, respectively; and (e) shows... Figure 5 (c) Figure 5 (d) and the central cross section of the phantom;

[0037] Figure 6The images show the reconstruction results of V-FBP and W-FBP. (a)-(d) are the V-FBP (mSTCT) results predicted from 1800 (600×3), 3600 (1200×3), 7200 (2400×3), and 14400 (4800×3), respectively. (e)-(h) are the corresponding magnified images of the bounded portion of the first row of images. (i)-(l) are the W-FBP (F-mSTCT) prediction results from 1800 (300×6), 3600 (600×6), 7200 (1200×6), and 14400 (2400×6), respectively. (m)-(p) are the magnified images corresponding to the bounded portion of the third row of images, with the display window being [0,3].

[0038] Figure 7 250 rows of horizontal contours of 320–459 pixels were reconstructed for W-FBP (F-mSTCT) and V-FBP (mSTCT); where (a) the number of predicted digits was 1800; (b) the number of projected digits was 3600; (c) the number of predicted digits was 7200; and (d) the number of predicted digits was 14400.

[0039] Figure 8 MTF curves of W-FBP and V-FBP under different projection numbers;

[0040] Figure 9 The images show the reconstruction results of V-FBP and W-FBP. (a)-(c) are the V-FBP (mSTCT) results predicted from 1800 (600×3), 3600 (1200×3), and 7200 (2400×3), respectively; (d)-(f) are the corresponding magnified images of the bounded portion of the first row of images; (g)-(i) are the W-FBP (F-mSTCT) prediction results from 1800 (300×6), 3600 (600×6), and 7200 (1200×6), respectively; and (j)-(l) are the magnified images of the bounded portion of the third row of images.

[0041] Figure 10 Let be the distribution and sampling geometry of the projection in Fourier space; where (a) is the distribution of the STCT projection in Fourier space; (b) is the sampling geometry of W-FBP; and (c) is the sampling geometry of V-FBP. Detailed Implementation

[0042] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0043] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0044] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0045] Please see Figures 1-10 This invention provides a weighted FBP algorithm (W-FBP) for processing projection truncation in mSTCT. Since this method requires the projection redundancy data region to include the projection truncation region, we modify the mSTCT configuration to full-scan mSTCT (F-mSTCT). The W-FBP algorithm can reconstruct high-resolution images even with coarse sampling of the X-ray source, and can serve as an important supplement to V-FBP.

[0046] 1. Characteristics of mSTCT

[0047] Figure 1 (a) shows the mSTCT 3D imaging geometry composed of multiple STCT scans. In each STCT scan, the object is moved closer to the X-ray source and further away from the stationary FPD (detector). The X-ray source is translated along a straight line parallel to the FPD to obtain projections at different angles. A Cartesian coordinate system with the origin fixed at the center of the object is established. Figure 1 (c) The trajectory of the ray source can be represented as:

[0048]

[0049] in

[0050]

[0051] Where l is the distance from the ray source to the object, s is half the distance the ray source moves, and θ i This represents the rotation angle, and T is the number of STCT scans. In mSTCT, the rotation angle between two STCT scans is...

[0052] Δθ=θ i+1 -θ i =2arctan(d / h) (3)

[0053] The number of STCT scans is

[0054]

[0055] Where d is half the detector width, h is the distance from the object to the detector, and α represents a geometric angle. The ceil() function returns a rounded-up nearest integer. Using this configuration, mSTCT can provide at least 180 degrees of projected coverage area radius for each point.

[0056]

[0057] 2. Establish the F-mSTCT scanning mode and the W-FBP algorithm suitable for F-mSTCT.

[0058] 1) Main idea of ​​the method

[0059] Because the X-ray source can only illuminate a portion of the object at each location, mSTCT scanning results in projection truncation, leading to anomalous high-frequency components in Fourier space, one source of reconstruction artifacts. In this invention, we address truncation artifacts by introducing an overlapping region into the scanning geometry. This is because a weighting function can be used in the overlapping region to smooth the projection data near the truncation boundary. This smoothing makes the edge gradient continuous, thereby eliminating the high-frequency components in Fourier space caused by truncation. Furthermore, the weighting function used to handle projection truncation is the same as the weighting function used to handle data redundancy in the overlapping region. In other words, we can use the same weighting function to correct both redundant and truncation projections simultaneously.

[0060] In this approach, the projected overlap region should include truncated edges, which presents two challenges for implementing a weighted scheme in the mSTCT layout.

[0061] Challenge 1: Figure 2(b) shows the redundancy distribution of mSTCT, where redundancy only occurs between the first and last STCT segments. There is no redundancy between the remaining segments, so weighting is not possible.

[0062] Challenge 2: Even with a reduced rotation angle θ i This causes redundancy in each STCT segment, such as Figure 2 As shown in (c), two types of redundancy also occur in mSTCT, making it very difficult to design a suitable weighting function to eliminate redundancy and smooth truncation at the same time.

[0063] 2) F-mSTCT

[0064] Figure 3 (b) is the STCT projection sine curve, whose cutoff is symmetrical along u and λ. To ensure that redundancy also possesses the same symmetry and covers the cutoff portion, this invention proposes a novel multiple STCT scanning configuration, called F-mSTCT, because all points within a radius R1 region have 360° projection coverage. Figure 3 As shown in (a), the number of segments in the STCT scan in F-mSTCT is:

[0065]

[0066] The rotation angle between two adjacent STCT segments is:

[0067]

[0068] from Figure 3 (c) and Figure 3 As can be seen from the F-mSTCT projection and redundancy distribution in (d), its redundancy completely covers the truncated portion. Furthermore, there is only one simple and regular type of data redundancy in the F-mSTCT, making it feasible to design a weighting function to handle both redundancy and truncation simultaneously.

[0069] 3) Weighting function

[0070] The design of the weighting function is as follows: Figure 4 As shown, the main steps include identifying redundant data and constructing a weighting function. Because each STCT segment has the same redundancy in the F-mSTCT scan, this invention first analyzes two adjacent STCT segments (the i-th segment and the (i+1)-th segment). First, to identify redundant data, this invention uses the coordinates (λ...) of the x-rays in the i-th STCT segment... i ,u i ) parameterize, and give the following definition.

[0071] Definition 1: (λ) i+1 |λ i ,u i >,u i+1 |λi ,u i >) is a ray (λ) i ,u i The representation of ) in the (i+1)th segment STCT.

[0072] This means that the same X-ray is (λ) in the i-th segment of STCT. i ,u i ) indicates that, at the same time, in the (i+1)th segment of STCT, it is (λ i+1 |λ i ,u i >,u i+1 |λ i ,u i > indicates. Therefore, there is

[0073]

[0074] Considering the lengths of the detector and the ray source trajectories, if λ i+i |λ i ,u i >∈[-s,s] and u i+i |λ i ,u i If ?∈[-d,d] are satisfied simultaneously, then and This will be a pair of redundant data.

[0075] Secondly, the construction of the weighting function should satisfy the following conditions.

[0076] For redundancy: (1) Only one equivalent ray passes through every point of the object; (2) The weighting function is continuous.

[0077] For truncation: (1) The weight is 1 outside the redundant region and within the detector range, and 0 outside the detector range; (2) Within the redundant region, the function should provide a smooth transition from 1 to 0 along the truncation direction u.

[0078] Therefore, the redundancy weighting function designed in this invention is:

[0079]

[0080] in,

[0081]

[0082] u r =min(u i |λ i ,d i+1 >,u i |-s i+1 ,λ i >), ui |λ i ,d i+1 > is related to the i-th segment detector and the straight line (λ) i ,d i+1 The local coordinates of the intersection point of the two points on the i-th segment of the detector; u i |-s i+1 ,λ i There is a similar definition. To ensure there is only one equivalent ray, the weight of the (i+1)th segment of the STCT is:

[0083]

[0084] Table 1 shows the pseudocode for calculating the weights. Figure 4 (b) The calculated weights can be used for each STCT segment. Figure 4 (c) shows the STCT projection, the truncated portion of which is smoothly transitioned to 0 along the u direction by weights.

[0085] Table 1. Pseudocode for calculating weights

[0086]

[0087] 4) W-FBP algorithm

[0088] This section first derives the FBP algorithm for STCT scanning. Based on the parallel-beam FBP algorithm and... Figure 1 (c) The initial form of the STCT geometry and the FBP algorithm for STCT scanning can be expressed as:

[0089]

[0090] in, It is the angle measured counterclockwise from the y-axis to the x-ray, and r is the distance from the origin to the x-ray. It is a function of (λ, u);

[0091]

[0092] Substituting equation (13) into equation (12), performing projection filtering along the detector direction, and simplifying, we obtain:

[0093]

[0094] in,

[0095]

[0096] Where u′ represents the local coordinates of the ray emitted from the X-ray source at λ, passing through the point (x,y) and projected onto the detector. Considering projection truncation and data redundancy, the W-FBP reconstruction formula for F-mSTCT is:

[0097]

[0098] 4. Experimental Setup

[0099] To verify the effectiveness of the strategy proposed in this invention, the W-FBP (F-mSTCT) of this invention was compared with the existing V-FBP (mSTCT). Considering the differences between F-mSTCT and mSTCT in the scanning segments, the experimental design is as follows.

[0100] 1) Simulation Experiment

[0101] This experiment used a 512×512 pixel Forbild phantom to evaluate the proposed strategy through numerical simulation. The geometric parameters of the simulation experiment are as follows: distance between the X-ray source and the object 13.75 mm, distance between the detector and the object 106.5 mm, detector size 1024×1024 pixels, detector pixel size 0.127 mm, and X-ray source translation distance 35 mm. The field of view radius R1 of the simulated STCT scan is 6.6 mm. mSTCT consists of 3 STCT scans with an interval angle of 62.8°; F-mSTCT consists of 6 STCT scans with an interval angle of 60°. The V-FBP and W-FBP algorithms were used to reconstruct images in mSTCT and F-mSTCT, respectively.

[0102] To obtain the performance of V-FBP (mSTCT) and W-FBP (F-mSTCT) with different numbers of projections, the number of projections per STCT segment was set to 300, 600, 1200, 2400, and 4800, respectively. Since the beam width (BW) is approximately 15 μm, the X-ray source sampling interval in V-FBP (mSTCT) should be less than 7.5 μm to satisfy the Nyquist criterion, meaning the number of projections per STCT segment should be greater than 4667. Therefore, the maximum number of projections per STCT segment was set to 4800.

[0103] This experiment uses quantitative analysis metrics, including root mean square error (RMSE), peak signal-to-noise ratio (PSNR), and structural similarity index (SSIM), to evaluate image quality. RMSE measures the overall error between the reconstructed image and the reference image, PSNR measures the noise level in the image, and SSIM measures the similarity between the two images. Generally, the lower the RMSE and the higher the PSNR and SSIM, the better the image quality.

[0104] 2) Actual Experiment

[0105] This experiment established a cone-beam microfocus STCT experimental system to verify the performance of the proposed method on real-world data. The experimental platform is as follows: Figure 5As shown, the system consists of a microfocus cone-beam X-ray source (L10321, Hamamatsu, Japan), a rotating platform (RGV100BL, Newport, USA), an FPD (PaxScan1313DX, Varian, USA), and a translation platform (M-ILS250PP, Newport, USA). The X-ray source is mounted on the translation platform to achieve source translation. The object to be detected is located on the rotating platform to achieve multi-segment STCT scanning. The geometric parameters of the actual experiment are consistent with those of the simulation experiment. Furthermore, the X-ray source operates at a tube voltage of 40 kV and a tube current of 60 μA. A reconstruction program was written in MATLAB 2019b using the GPU-accelerated ASTRA toolbox and tested on a computer with an Intel(R) Core(TM) i5-9400 CPU @ 2.90 GHz.

[0106] 5. Results

[0107] 1) Simulation Experiment Results

[0108] (1) Weighted

[0109] Figure 5 The reconstruction results are shown for W-FBP and FBP. Due to truncated and finite-angle projection data, aliasing and stripe artifacts appear in each segment of the STCT image reconstructed by FBP. Figure 5 (a)). After weighting, the aliasing artifacts in each STCT image reconstructed by W-FBP completely disappeared. Figure 5 (b)). For example Figure 5 As shown in (c), after summing the six STCT segments reconstructed by FBP, aliasing and stripe artifacts still exist in the image due to data truncation and redundancy. However, the image obtained by summing the six STCT segments reconstructed by W-FBP... Figure 5 In (d), these artifacts disappeared. Figure 5 (e) drew Figure 5 (c) and Figure 5 (d) and the horizontal center grayscale curve in the Forbild phantom image. It can be seen that the W-FBP results agree well with the phantom, proving the effectiveness of the proposed method.

[0110] (2) Image quality

[0111] Figure 6 Reconstructed images of V-FBP (mSTCT) and W-FBP (F-mSTCT) with different projection numbers are shown. Figure 6 (a)-(d) show the reconstruction results of V-FBP(mSTCT) under 1800 (600×3), 3600 (1200×3), 7200 (2400×3) and 14400 (4800×3) projections, respectively. Figure 6 (e)-(h) show the corresponding magnified local images. As the number of projections decreases, the image becomes blurry, especially when mSTCT collects only 1800 projections. This is because the V-FBP algorithm filters the projections along the ray source direction, resulting in more loss of high-frequency components as the number of projections per STCT segment decreases. Figure 6 (i)-(l) show the reconstruction results of W-FBP (F-mSTCT) under 1800 (300×6), 3600 (600×6), 7200 (1200×6) and 14400 (2400×6) projections. Figure 6 (m)-(p) show the corresponding magnified images. Their quality remains similar as the number of projections is changed. Even when F-mSTCT collects only 1800 projections, the reconstructed images from W-FBP remain sharp. However, as the number of projections decreases, the uniformity of the image gradually deteriorates.

[0112] Figure 7 The horizontal grayscale curve is used to reconstruct the image. For the reconstructed image, the high-frequency components of the curve represent the edges and details of the image, while the smoothness of the curve reflects the uniformity of the image. From Figure 7 (a) and Figure 7 (b) It can be seen that when acquiring 1800 and 3600 projections, the W-FBP curve contains more high-frequency details, but its smoothness is not as good as that of V-FBP. With the increase in the number of projections, the smoothness of the W-FBP curve improves, while the high-frequency components in the V-FBP curve increase. This is consistent with... Figure 6 The trend of change in the images is consistent.

[0113] Table 2 lists the quantitative evaluation metrics. The metrics for both W-FBP and V-FBP decrease with decreasing projection count, with V-FBP showing a greater impact. When acquiring 7200 and 14400 projections, V-FBP outperforms W-FBP. However, when the number of projections decreases to 3600 and 1800, W-FBP's RMSE and PSNR are significantly better than V-FBP, indicating that W-FBP has higher reconstruction accuracy and signal-to-noise ratio compared to V-FBP when the number of projections is lower. As the number of projections decreases from 7200 to 3600, W-FBP maintains high resolution, and the loss in image quality is acceptable compared to V-FBP, while V-FBP experiences significant resolution degradation. Furthermore, with the same number of projections, W-FBP (F-mSTCT) reconstructs faster than V-FBP (mSTCT) because F-mSTCT has simpler redundancy weights. In summary, W-FBP (F-mSTCT) outperforms V-FBP (mSTCT) in both performance and reconstruction speed when the number of projections is relatively small, while V-FBP requires as many as 7,200 or even 14,400 projections to achieve high-quality reconstruction.

[0114] Table 2 Figure 6 Quantitative evaluation of reconstruction

[0115]

[0116] (3) MTF

[0117] We quantitatively investigated the spatial resolution performance of V-FBP (mSTCT) and W-FBP (F-mSTCT) using the modulation transfer function (MTF). MTF is the Fourier transform of the line spread function (LSF), which is the derivative of the edge response function (ERF), representing the system's response to the smallest details in the image. Ignoring focus size, we reconstructed 512×512 pixel cylinders (within the same pixel size) using different algorithms. Figure 8 (d) Therefore, ERF is the average of all contour lines through the center of the cylinder.

[0118] Figure 8 In (a), the MTF curve performance of W-FBP(mSTCT) is comparable under different projection numbers, indicating that the projection number does not affect the reconstruction resolution of W-FBP. Conversely, V-FBP(mSTCT) ( Figure 8 (b) The MTF curve degenerates as the projection decreases. Figure 8 (c) The two algorithms were compared, and Table 3 lists the quantitative results for 10% MTF. V-FBP with 14,400 projections has a higher final resolution, but when the number of projections is reduced to 7,200, its resolution is only slightly higher than W-FBP (only 1,800 projections) by 0.24 lp / mm. As the number of projections decreases further, the disadvantage of V-FBP in terms of reconstruction resolution gradually widens. W-FBP (F-mSTCT) requires only about 1 / 4 of the projections to achieve a reconstruction resolution comparable to W-FBP (F-mSTCT), demonstrating the resolution advantage of W-FBP with a low number of projections.

[0119] 2) Actual experimental results

[0120] To further evaluate the performance of our method on real-world data, we scanned a flower bud using the aforementioned CT system. Figure 9 (a)-(c) show V-FBP (mSTCT) images reconstructed from 1800 (600×3), 3600 (1200×3), and 7200 (2400×3) projections. In V-FBP (mSTCT) reconstruction, we still observe a decrease in image quality and spatial resolution as the number of projections decreases. Figure 9As shown in the magnified views of (d) and (e), the V-FBP images are blurred and have missing microstructures when the projection number is 1800 and 3600. Figure 9 (g)-(i) are W-FBP (F-mSTCT) images reconstructed from 1800 (300×6), 3600 (600×6) and 7200 (1200×6) projections. Figure 9 (j)-(l) show the corresponding magnified images. These images show only minor differences in spatial resolution and microstructure, and noise decreases with increasing projection. More importantly, despite the noise, the image obtained using W-FBP (F-mSTCT) with 3600 projections is still close in quality to the image obtained using V-FBP (mSTCT) with 7200 projections. With an integration time of 1000 ms, scanning flower buds and acquiring 7200 projections takes approximately 6 hours, while acquiring 3600 projections takes only about 3 hours. Even when resolution is the primary consideration, W-FBP (F-mSTCT) only needs about 1.5 hours to acquire 1800 projections to achieve performance comparable to V-FBP (mSTCT acquiring 7200 projections).

[0121] 6. Discussion

[0122] In the above experiments, compared to V-FBP (mSTCT), W-FBP (F-mSTCT) exhibits better reconstruction resolution with a smaller number of projections and faster reconstruction speed with the same amount of data. The advantage of W-FBP in reconstruction speed stems from the simpler weighting function in F-mSTCT. This is because F-mSTCT has only one type of data redundancy, while mSTCT has two.

[0123] The difference in reconstruction resolution between W-FBP and V-FBP is mainly due to their different filtering directions. Comparing the W-FBP formula (16) and the V-FBP formula...

[0124]

[0125] The W-FBP algorithm filters along the detector direction, while the V-FBP algorithm filters along the X-ray source direction. Figure 10 (a) shows the distribution of STCT projection data in Fourier space. In the frequency domain, the ray spacing Δδ determines the coverage of the sampling frequency ξ.

[0126]

[0127] Among them, the high-frequency components of ξ correspond to the edges and details of the reconstructed image. Losing high-frequency components will lead to image blurring, which means lower resolution. As can be seen from Equation (18), reducing Δδ will increase the high-frequency components in ξ, thereby improving the resolution of the image.

[0128] Figure 10 (b) shows the sampling geometry of the W-FBP, where the ray spacing Δδ is related to the detector element spacing Δu.

[0129] Δδ=Δu·l / (l+h) (19)

[0130] A fully fabricated Micro-CT detector has a fixed Δu, typically only 0.1-0.2 mm. Therefore, W-FBP can reconstruct high-resolution images with minimal projection. For Figure 10 (c) shows the V-FBP sampling geometry, where the X-rays converged to the same detector unit cover the entire object. This solves the truncation problem, but also causes the sampling interval Δλ to affect the ray interval Δδ.

[0131] Δδ=Δλ·h / (l+h) (20)

[0132] Δλ is directly related to the number of projections N in each STCT segment.

[0133] Δλ=2s / (N-1) (21)

[0134] Since decreasing N increases Δδ, improving the reconstruction resolution of V-FBP requires more projections. However, in mSTCT scans, if the number of projections per STCT segment increases by ΔN, the total number of projections increases by T·ΔN, which means a surge in data and a decrease in acquisition and reconstruction efficiency. Furthermore, since the projections do not contain elements smaller than B... w / 2(B w For details regarding the equivalent beam width, the increase of N is limited. Therefore, when Δδ = B w At a ratio of 2 / 2, further reducing the ray spacing has little effect on increasing the reconstructed information. Equations (19), (20), and experimental parameters show that V-FBP requires 2136 projections per STCT segment to achieve the same resolution as W-FBP, while W-FBP only requires 300 projections per STCT segment (N cannot be too low to avoid sparse artifacts). In this case, the total number of projections for mSTCT is 6048, while the total number of projections for F-mSTCT is only 1800.

[0135] However, the uniformity of W-FBP reconstructed images decreases as the number of projections decreases. Image uniformity is related to the number of projection views. At the same projection angle, more projection views are equivalent to finer sampling in RCT scans, resulting in smoother grayscale curves and images with better uniformity. In W-FBP, X-rays from the same focal point constitute a projection view, and the number of views equals N. In V-FBP, X-rays converging to the same detector element form a projection view, and the number of views is equal to the number of detector elements. Therefore, as N decreases, the number of projection views in V-FBP remains unaffected, while the imaging uniformity of W-FBP deteriorates due to the reduction in the number of projection views.

[0136] 7. Conclusion

[0137] This invention provides a CT imaging strategy consisting of F-mSTCT scanning and the W-FBP algorithm, which not only solves the truncation problem in STCT imaging but also overcomes the poor imaging resolution of the V-FBP algorithm with low projection counts. With the help of a weighting function, the derived W-FBP algorithm can directly reconstruct high-quality images without artifacts, without additional processing of the projections. Numerical simulations and practical experiments demonstrate that this strategy can effectively reduce the number of projections required for high-resolution imaging and improve reconstruction efficiency. While V-FBP can achieve higher performance limits through dense sampling, W-FBP maintains high reconstruction resolution regardless of the projection count. Considering both imaging quality and resolution, W-FBP (F-mSTCT acquiring 3600 projections) requires only about half the projection count to achieve a resolution comparable to VFBP (mSTCT acquiring 7200 projections), with acceptable image quality loss. When resolution is prioritized, W-FBP requires only about 1 / 4 of the projection count compared to V-FBP. Therefore, F-mSTCT (W-FBP) greatly improves the efficiency of data acquisition and reconstruction and will be an important supplement to mSTCT (V-FBP).

[0138] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A weighted source linear scanning CT analytical reconstruction method, characterized in that, The method specifically includes the following steps: S1: Establish the F-mSTCT scanning pattern layout, specifically including: F-mSTCT is a two-dimensional imaging geometric model composed of multiple STCT scans; the number of STCT scan segments in F-mSTCT. for: Among them, F-mSTCT is full-scan mSTCT, and mSTCT is multi-source linear scanning CT. ceil The () function returns the nearest integer rounded up; Let be the projection coverage angle obtainable from a segment of STCT scan, expressed as: , d Half the width of the detector. h This represents the distance from the object to the detector. Rotation angle between two adjacent STCT segments for: ; S2: In F-mSTCT scanning mode, a weighting function designed to correct redundant and truncated projections; S3: Based on the weighting function constructed in step S2, construct the W-FBP reconstruction algorithm suitable for F-mSTCT, the formula of which is: Among them, W-FBP is a weighted filtering back projection algorithm. l The distance from the ray source to the object is denoted as . T The number of STCT scans. s Half the distance the radiation source moved. d Half the width of the detector. For the first i The weight of segment STCT, Indicates the first i Projection data acquired by segmental STCT scan, This represents the convolution kernel of the ramp filter; Indicates the first i During STCT, the radiation source is It was sent from the point, passing through the point The local coordinates of the ray projected onto the detector are expressed as: .

2. The weighted source linear scanning CT analytical reconstruction method according to claim 1, characterized in that, In step S2, the weighting function is designed as follows: in, For the first i The weight of segment STCT, For rays In the ( i +1) The representation in segment STCT, s Half the distance the radiation source moved. d It is half the width of the detector; , Is with the first i Segment detector and straight line The intersection point is at the 1st i Local coordinates on the segment detector; There are similar definitions; To ensure that there is only one equivalent ray, the ( ) i The weight of segment STCT +1 is: 。 3. The weighted source linear scanning CT analytical reconstruction method according to claim 2, characterized in that, In step S2, .

Images