A X-ray image reconstruction method based on direction-aware tensor modeling

Abstract

The present invention relates to the field of X-ray image processing, and discloses an X-ray image reconstruction method based on direction-aware tensor modeling. The method obtains multiple X-ray projection images with different incident angles, establishes a projection direction mapping matrix in combination with tissue direction distribution; constructs a high-order direction-aware tensor field based on the mapping matrix and structural prior information to describe the dominant structural direction and anisotropic response characteristics of each image position; generates a direction enhancement response map through tensor-guided gradient calculation to achieve dynamic enhancement of local edges; then extracts the structural response intensity to construct a structural sensitivity function map as a weighting factor in image reconstruction; constructs an image reconstruction objective function containing a direction consistency constraint based on the weighted map and the tensor field, performs joint optimization, and dynamically updates the regularization term to achieve high-fidelity reconstruction of the image under low-dose conditions. The method improves the image detail preservation and noise suppression capabilities, and has strong adaptability and robustness.

Description

Technical Field

[0001] The present invention relates to the technical field of medical image processing, and in particular to an X-ray image reconstruction method based on direction-aware tensor modeling. Background Art

[0002] X-ray image reconstruction methods are currently widely used in medical imaging fields such as computed tomography (CT) and digital subtraction angiography (DSA). To improve the quality of reconstructed images, researchers have proposed a variety of iterative reconstruction algorithms based on variational optimization, such as total variation (TV) regularization, structural tensor modeling, and anisotropic constraints that incorporate limited-angle or low-dose projection information. Some of these methods also incorporate projection direction priors or image structure priors to enhance edge preservation and noise suppression.

[0003] However, existing methods still have certain limitations in practical applications. On the one hand, traditional anisotropic regularization often only models in a limited number of fixed directions, making it difficult to accurately adapt to the directional changes of complex tissue structures, which can easily lead to blurred edges or loss of details. On the other hand, some methods that fuse projection direction information fail to establish a high-order tensor representation with direction consistency in the image domain, resulting in insufficient utilization of directional information during the reconstruction process. In addition, the regularization weight design of most algorithms lacks the ability to dynamically perceive structural salience, which limits further improvement of image quality.

[0004] In view of this, there is an urgent need to develop a technical solution that can fully utilize the correspondence between tissue structure directionality and projection direction during image reconstruction. Summary of the Invention

[0005] The present application provides an X-ray image reconstruction method based on direction-aware tensor modeling to improve the detail preservation and noise suppression capabilities of X-ray image reconstruction.

[0006] The present application provides an X-ray image reconstruction method based on direction-aware tensor modeling, comprising:

[0007] Acquire multiple X-ray projection images at different incident angles, establish an initial direction correspondence relationship with the tissue direction distribution within the reconstruction area based on preset angle parameters, and generate a projection direction mapping matrix;

[0008] Based on the projection direction mapping matrix and structural prior information of the reconstruction area, a high-order direction-aware tensor field coupling the main direction of the tissue and the propagation direction of the ray is constructed;

[0009] performing a tensor-guided local gradient calculation operation on each of the plurality of X-ray projection images to generate a direction-enhanced response map;

[0010] Constructing a structure sensitivity function map based on the local structure response intensity extracted from the direction enhancement response map, wherein the structure sensitivity function map is used to characterize the anisotropic response degree of each image position;

[0011] The structure-sensitive function map is used as a weighting factor to guide the construction of a tensor regularization term, and the image reconstruction objective function is constructed in combination with the direction-aware tensor field, wherein the objective function takes minimizing the projection error and the direction consistency loss as an optimization goal;

[0012] A joint optimization operation is performed on the image reconstruction objective function, and the directional consistency constraint in the tensor regularization term is dynamically updated using the directional response distribution of the current reconstructed image. The process is iterated until the reconstructed image converges to a solution that optimizes directional detail preservation and noise suppression, thereby obtaining the final reconstructed image.

[0013] The beneficial effects of the technical solution provided by this application include:

[0014] (1) By constructing a high-order direction-aware tensor field that couples the main direction of the tissue structure with the direction of ray propagation, it is possible to fully capture the dominant direction information of each position in the image, achieve accurate modeling of complex anatomical structures, and significantly improve the structural fidelity of the reconstructed image. (2) The introduction of tensor-guided local gradient calculation and direction enhancement response map can dynamically enhance the true edge area and suppress non-structural noise, thereby improving edge clarity and detail resolution, and meeting the imaging requirements under low-dose projection conditions. (3) By constructing a structure-sensitive function map and introducing it as a regularization weighting factor, adaptive modeling of the degree of image anisotropy response is achieved, so that the image reconstruction process can be differentiated according to local structural features, thereby improving the overall image quality. (4) The constructed image reconstruction objective function combines the direction-aware tensor and the structure-sensitive function, and dynamically updates the direction consistency constraint during iterative optimization, effectively improving the regularization term's ability to maintain the true direction features, and achieving the optimal balance between noise suppression and detail preservation. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 This is a flowchart of an X-ray image reconstruction method based on direction-aware tensor modeling provided in the first embodiment of the present application. DETAILED DESCRIPTION

[0016] The following description sets forth many specific details to facilitate a thorough understanding of the present application. However, the present application can be implemented in many other ways than those described herein, and those skilled in the art can make similar generalizations without violating the scope of the present application. Therefore, the present application is not limited to the specific implementations disclosed below.

[0017] The first embodiment of the present application provides an X-ray image reconstruction method based on direction-aware tensor modeling. Figure 1 , which is a schematic diagram of the first embodiment of this application. Figure 1 The first embodiment of the present application provides an X-ray image reconstruction method based on direction-aware tensor modeling, which is described in detail.

[0018] Step S101: Acquire multiple X-ray projection images at different incident angles, establish an initial direction correspondence relationship with the tissue direction distribution in the reconstruction area according to preset angle parameters, and generate a projection direction mapping matrix.

[0019] The core purpose of step S101 is to obtain multiple X-ray projection images at different incident angles, establish an initial direction correspondence based on this, and then generate a projection direction mapping matrix. First, an X-ray imaging system with multi-angle imaging capabilities is required. A typical system may include a rotating CT scanning platform, a detector array with motion control functions, or a multi-source arrangement to obtain projection images at different incident angles. In specific implementation, the object to be scanned can be fixed at the center of the platform, and a robotic arm or electric slide is used to rotate the X-ray source relative to the scanned object around a central axis. The scan is usually performed in steps at an angle interval of θ (e.g., 1 to 5 degrees). A two-dimensional projection image is acquired at each angle, ultimately obtaining a projection image sequence consisting of multiple different incident angles.

[0020] For each X-ray projection image, record its corresponding incident angle information, which can be expressed as a relative rotation angle with reference to the scanning axis. , An angle number, typically expressed in degrees (°) or radians (rad). This angle information should correspond one-to-one with the image index and be stored in the angle parameter set for subsequent use in constructing the directional mapping relationship. It is important to note that to ensure effective directional perception, the captured projection angles should cover a sector of at least 180 degrees, preferably 360 degrees, to improve the completeness and accuracy of the reconstruction.

[0021] After completing the image acquisition and establishing the angle parameter set, it is necessary to establish an initial direction correspondence based on the tissue direction distribution in the reconstruction area and the projection angle information. The way to obtain the tissue direction distribution can use different structural priors according to the tissue type. For example, in brain or lung imaging, the main direction information of the tissue provided by MRI, ultrasound or historical anatomical data can be used. When there is no additional prior data, methods based on image gradient statistics, structural tensor analysis or local symmetry assumptions can also be used to extract tissue direction distribution from preliminary reconstructed images or low-resolution prior images. The representation of direction information can be done using two-dimensional unit vectors. or angle value , which represents the direction of the local dominant structure.

[0022] Based on the aforementioned projection angle information and tissue orientation information, a mathematical mapping relationship is established to associate each projection angle with the principal structural direction of each pixel in the reconstructed area. This mapping relationship determines how a pixel in the image should respond to the projection information along the principal direction at a specific projection angle, thereby forming a projection direction mapping matrix composed of both angular and spatial coordinate dimensions.

[0023] Each element of the matrix can be expressed as a triple (x, y, θ), where (x, y) is the image pixel position (x is the horizontal coordinate, y is the vertical coordinate), and θ is the angle between the incident direction of the point at the current projection angle and the main direction of the structure. In addition, the degree of consistency of the unit vector direction can also be calculated by the inner product. For example, the mapping matrix can be defined as ,in Indicates the The incident angle of the projected image, Indicates the main structure direction angle of the point.

[0024] Each element in the mapping matrix is ​​defined as a triplet (x, y, θ). Here x and y are the coordinates of a pixel point in the image plane, representing the position index of the pixel in the horizontal and vertical directions respectively. The unit is usually pixels or millimeters (depending on the image sampling pitch). The entire image is composed of several such pixels, forming a two-dimensional pixel grid, and each position Corresponds to a certain spatial position of the actual scanned object. The third component in the triplet , is an angle value used to represent the angle between the incident direction of the X-ray and the main structural direction of the pixel at the current projection angle. The existence of this angle reflects the relative orientation between the X-ray penetration path at that position and the direction of the local structure. If the X-ray is incident exactly along the structural direction, the angle is 0 degrees; if it is incident vertically, it is 90 degrees. This angular relationship has a key impact on subsequent directional weighting, gradient response enhancement, and regularization constraints, because the higher the directional consistency, the easier it is for structural information to be correctly identified and retained.

[0025] The following expression is a way to quantify this directional relationship, using the cosine function to measure the degree of consistency between the two directions. Specifically, for a certain pixel point , in In the projection image, the corresponding projection incident angle is recorded as This angle is known because the rotation angle of the X-ray source is controllable and recorded when each X-ray projection image is acquired. It refers to the angle value of the X-ray projection direction relative to the horizontal axis of the image plane (or other uniform reference direction), and the unit can be degrees or radians. Similarly, for this pixel point The dominant structural direction can be determined by structural tensor analysis, principal direction estimation algorithm or anatomical prior information. The angle of this direction is recorded as This value describes the main direction of the tissue or edge at that point in space, and is also the deflection angle relative to the horizontal axis.

[0026] The "main structure direction angle" refers to the dominant extension direction of the local tissue structure corresponding to each pixel point in the image reconstruction area in space, and an angle value is used to represent the deflection angle of this direction relative to the reference coordinate system (usually the horizontal direction).

[0027] Specifically, in a two-dimensional image, each pixel is usually located at the edge of a tissue, texture, or structure. This structure often presents a certain direction in space, such as blood vessels extending diagonally and bone boundaries distributed horizontally. The most significant direction in the neighborhood of this pixel can be estimated through image gradients, structural tensors, or prior models. The angle value of this direction is the "main structural direction angle", which is recorded as This angle is used to express the relationship between the pixel structure orientation and the X-ray projection direction, thereby guiding direction-aware calculations. It is one of the basic parameters in directional tensor modeling and reflects the structural geometric characteristics of the image.

[0028] This projection direction mapping matrix serves as a core intermediate variable and is subsequently used to construct the direction-aware tensor field. It then continuously participates in direction guidance, regularization constraints, and direction consistency assessment throughout the reconstruction process. Therefore, step S101 not only requires completing the image's angle annotation and acquisition, but also establishes a point-by-point direction mapping relationship in image space and outputs a structured mapping matrix data structure to support subsequent direction modeling and optimization.

[0029] In summary, the specific implementation of step S101 should include: acquiring projection images using a multi-angle X-ray acquisition method; recording the incident angle parameters corresponding to each image; acquiring or estimating the tissue direction distribution information within the reconstruction area; constructing a mapping relationship between the incident angle and the structural direction based on pixel-level direction calculation; and forming a projection direction mapping matrix with image coordinates and projection angles as dimensions.

[0030] Furthermore, the method of acquiring multiple X-ray projection images at different incident angles and establishing an initial direction correspondence relationship with the tissue direction distribution in the reconstruction area according to preset angle parameters to generate a projection direction mapping matrix includes:

[0031] Based on the angle relationship between the main structure direction angle of each image pixel position in the tissue direction distribution and each incident angle, the projection angle correspondence with an angle exceeding a preset threshold value π / 8 is eliminated to retain incident angle information with high direction consistency;

[0032] For each retained incident angle, calculating a direction consistency response value of the image pixel position, the direction consistency response value being a direction cosine function value between the main structure direction angle and the incident angle;

[0033] Based on the directional consistency response values ​​at multiple incident angles and the magnitude of the change in the main structural direction of the pixel in its neighborhood, a local structural stability score is constructed to measure the degree to which the main structural direction of the pixel is maintained within the projection angle domain.

[0034] The structural stability score is subjected to direction-aware fusion processing at multiple spatial scales to form a scale-robust directional saliency score map, and the directional saliency score map is used in the pixel-level weighted calculation of generating the projection direction mapping matrix to output a projection direction mapping matrix that retains high directional consistency and takes into account structural stability.

[0035] First, for each image pixel position, its main structural direction angle is known. This angle is usually obtained through structural tensor calculation, main direction estimation or image gradient statistics, and is expressed as an absolute angle relative to the horizontal direction in radians. At the same time, each X-ray projection image corresponds to a fixed incident angle, which is also given in radians. For each pixel position and each incident angle, the angle between the main structural direction angle of the pixel and the projection incident angle is calculated. If the angle exceeds a preset direction threshold (for example, π / 8), the mapping relationship of the pixel under the projection angle will be eliminated to avoid introducing inconsistent interference information in the direction. This operation can be achieved by calculating the absolute value of the difference between the two angles and determining whether it exceeds the threshold.

[0036] For each projection angle that is not eliminated, continue to calculate its directional consistency response value. This response value is obtained by converting the main structure direction angle and the incident angle into two-dimensional unit vectors respectively, and calculating the dot product of these two unit vectors to obtain its direction cosine value. The direction cosine value is between -1 and 1. When the two directions are completely consistent, the value is 1, when they are completely orthogonal, the value is 0, and when the directions are opposite, the value is -1. Since the structure in the image usually only responds to consistent directions, only positive direction cosine values ​​(that is, cosine values ​​greater than zero) are retained and used as the directional consistency response value of the pixel at this projection angle. This calculation process can be performed cyclically at the pixel level, and finally a three-dimensional data volume is generated, which represents the directional consistency response value of each pixel at all valid projection angles.

[0037] Next, it is necessary to further evaluate the stability of the structural direction in the spatial domain at the pixel level. To this end, a local structural stability score is introduced. The calculation process of this score includes the following steps: first, with each pixel as the center, a neighborhood with a fixed radius around it is selected, such as a 3×3 or 5×5 window, and the main structural direction angles of all pixels in the neighborhood are extracted; then, the main structural direction angle of the central pixel is used as the benchmark, and the difference between the direction angles of all pixels in the neighborhood and the main structural direction angle is calculated, and the standard deviation or variance of these angle differences is taken as the directional fluctuation of the pixel. The directional fluctuation is reverse normalized (for example, the minimum value is first subtracted, and then divided by the difference between the maximum and minimum values) to obtain a structural stability score between 0 and 1. The closer the value is to 1, the more consistent the main structural direction is in the neighborhood, that is, the more stable the direction is. Otherwise, it means that the direction fluctuates greatly and the structure is unstable.

[0038] In order to enhance the adaptability of the structural stability score at different scales, the present invention introduces a multi-scale directional perception fusion mechanism. Specifically, the original stability score map is downsampled to multiple resolution levels (such as the original scale, 1 / 2 scale, and 1 / 4 scale) through Gaussian pyramid or mean pooling, and the local stability score calculation is repeated at each scale, and the score map at each scale is re-upsampled to the original image size. For each pixel, the scores obtained at all scales can be fused by weighted averaging, and the weights can be set based on the scale confidence, for example, the original scale weight is 0.5, the 1 / 2 scale is 0.3, and the 1 / 4 scale is 0.2, to ensure that neighboring details are prioritized while considering the continuity and consistency of the structure at different scales.

[0039] Finally, this fused multi-scale structural stability score map is combined with the aforementioned directional consistency response values ​​for each pixel at different projection angles to generate a directional saliency score map. Specifically, for each pixel and its corresponding retained incident angle, the directional consistency response value is multiplied by the structural stability score to obtain a weighted directional score. This score comprehensively considers the degree of directional matching for the pixel in the current orientation and the credibility of its local structural orientation. Normalizing the weighted scores across all orientations yields a directional mapping weighting factor for that pixel.

[0040] The above-mentioned set of scores ultimately constitutes the pixel-level directional weight map used to generate the projection direction mapping matrix. The projection direction mapping matrix is ​​constructed on a pixel-by-pixel basis. The directional consistency response value of a pixel at all retained projection angles is multiplied and summed with its corresponding weighted structural stability score to form the directional weight vector for that pixel. This is used to guide the subsequent distribution of the main directional response strength and the weighting of the regularization term in the tensor field.

[0041] In summary, through angle screening, direction cosine value calculation, local structural stability score assessment, scale domain fusion and direction weighted combination, the present invention specifically and systematically constructs a directional saliency score map for generating the projection direction mapping matrix, ensuring that the mapping matrix has both directional consistency recognition and structural stability regulation capabilities, providing a solid quantitative foundation for subsequent direction-aware tensor modeling.

[0042] Step S102: Based on the projection direction mapping matrix and the structural prior information of the reconstructed area, a high-order direction-aware tensor field that couples the main direction of the tissue and the propagation direction of the ray is constructed, and each tensor unit in the direction-aware tensor field is used to describe the dominant structural direction and anisotropic response characteristics at the corresponding image position.

[0043] The goal of step S102 is to construct a high-order direction-aware tensor field that couples the principal tissue directions and the ray propagation directions, based on the projection direction mapping matrix generated in step S101 and the structural prior information of the reconstruction region. This direction-aware tensor field is essentially a three- or four-dimensional data structure that covers the entire image reconstruction region. Each tensor unit is used to characterize the dominant structural direction and anisotropic response characteristics at that location, forming the basis for directional guidance, edge enhancement, and regularization in subsequent image reconstruction.

[0044] First, constructing a direction-aware tensor field requires obtaining two key inputs: a projection direction mapping matrix, which defines the quantitative correspondence between projection angles and structural directions at each spatial location; and structural prior information, which can be derived from directional distributions extracted from multimodal images acquired by external devices (such as MRI, ultrasound imaging, and optical imaging), or obtained through structural tensor analysis, gradient principal direction statistics, and local symmetry detection on preliminary reconstructed images. This structural prior information can be defined as a vector field in two- or three-dimensional space, with each location having a unit vector representing the dominant structural direction at that point.

[0045] Based on the two inputs above, a corresponding tensor unit is constructed at each pixel or voxel position (x, y) or (x, y, z) in the image reconstruction area. Specifically, this tensor unit is represented by a symmetric, positive-definite second-order tensor, which can be represented by a 2×2 or 3×3 real symmetric matrix. For example, in a two-dimensional image, the tensor T(x, y) can be expressed as:

[0046]

[0047] is the unit vector of the main direction of the structure. This is defined at the pixel point The unit vector is used to represent the dominant direction of the local tissue at that location. The direction of this vector can be obtained by solving the image grayscale gradient, structure tensor or texture direction estimation method. It usually refers to the direction perpendicular to the direction of maximum gradient change, that is, the edge extension direction. It is a two-dimensional column vector, denoted as:

[0048]

[0049] in is the main structural direction angle relative to The angle between the axes is usually expressed in radians. For example, if the structure extends horizontally, then .

[0050] yes The transpose of . is the projection vector in the principal direction. is the response strength in the main direction. This is a scalar coefficient that indicates the degree of response or penalty strength of the pixel in the main direction. The larger the value, the more important the direction is, and the stronger the constraint or preservation in this direction in the subsequent image regularization process. Its value can be set based on the following factors:

[0051] (1) The angular consistency score of the point in the projection direction mapping matrix (for example, the weight should be increased when the direction cosine value is greater than a certain threshold); (2) The structural gradient intensity is large, indicating that the edge is clear and the directional response should be improved; (3) The directional stability is high, indicating that the local texture has strong ductility and should be given a higher weight.

[0052] For example, if the point shows edge features that are highly consistent with the main direction of the tensor in multiple projection directions, you can set or higher; on the contrary, if the direction is unstable, it can be set to a lower value such as 0.2.

[0053] is a secondary direction unit vector orthogonal to the main direction, and this vector is Perpendicular, used to form an orthogonal basis. It usually represents the normal direction of the main direction, that is, the direction with the least structural change. , then:

[0054]

[0055] This definition ensures that and The inner product of is zero, ensuring orthogonality.

[0056] is the projection tensor in the orthogonal direction. The response intensity in the orthogonal direction is the response control coefficient in the non-main structural direction, which is used to suppress the non-structural noise that may appear in this direction. It should usually be set to be much smaller than , to highlight the information of the structural direction. For example, you can set Or smaller, especially in image areas where edge preservation is required. If the area is homogeneous within the tissue, the , enhancing overall smoothness.

[0057] For actual construction, the following steps can be performed at each pixel position: first, find the main direction unit vector of the position in the structural prior; then use the direction consistency score of the position at all projection angles in the projection direction mapping matrix to calculate the main response intensity in that direction At the same time, the response strength in the auxiliary direction is calculated based on the response variability or gradient variance of the point in other directions. Finally, the main direction is combined with two weights to generate the final tensor unit. This process is repeated to form a complete direction-aware tensor field in the entire image domain.

[0058] It is worth noting that in order to ensure that the tensor field has a strong expressive power for various structures, it should be spatially continuous and directionally stable. Therefore, it is recommended to perform spatial smoothing operations on the initially constructed tensor field, such as using Gaussian filtering or anisotropic diffusion to smooth the tensor parameters, to suppress sudden changes in the tensor direction caused by local abnormal gradients or outliers. At the same time, for the boundary regions of the structure, the sensitive variability of the main direction of the tensor should be preserved to facilitate the subsequent enhancement of edge response.

[0059] In terms of data organization, this direction-aware tensor field can be stored as a tensor image, with each pixel corresponding to a tensor structure containing the principal direction vector, orthogonal direction vectors, and their corresponding directional response weights. Alternatively, it can be compressed using an eigenvalue + eigenvector decomposition. Regardless of the structure used, the tensor should maintain a spatial coverage consistent with the image size to facilitate pixel-level access and operations in subsequent steps.

[0060] In summary, step S102 requires constructing a high-order directional-aware tensor field that couples the principal tissue direction and the ray propagation direction point by point within the image reconstruction region, based on the obtained projection direction mapping matrix and structural prior information. This tensor field, in the form of a symmetric positive definite matrix, records the dominant direction information and directional response characteristics at each location, serving as the fundamental data structure for subsequent directional enhancement, regularization, and objective function optimization.

[0061] Furthermore, the method of constructing a high-order direction-aware tensor field coupling the main direction of the tissue and the propagation direction of the ray based on the projection direction mapping matrix and the structural prior information of the reconstruction area includes:

[0062] Obtaining a directional consistency response value for each image pixel position in the projection direction mapping matrix under multiple incident angles, and generating a main direction performance stability coefficient for the pixel based on a weighted average method, wherein the directional consistency response value is a direction cosine function value between the main structure direction angle and the corresponding incident angle, and the main direction performance stability coefficient is used to adjust the initial amplitude of the main direction response intensity of the subsequent tensor;

[0063] Based on the stability coefficient, combined with the projection error residual values ​​of each image pixel position under the multiple incident angles, an independent response adjustment factor of the pixel in the main direction and the orthogonal direction is constructed, wherein the independent response adjustment factor in the main direction is used to set the main direction response strength in the tensor unit, and the independent response adjustment factor in the orthogonal direction is used to set the orthogonal direction response strength in the tensor unit, so as to achieve pixel-level adaptive control of the tensor anisotropic response;

[0064] Initializing the main structural direction angle of each pixel position in the structural prior information as the main direction vector of the tensor unit, and constructing a main direction iterative update path based on the gradient direction of the corresponding pixel position in the direction enhancement response map, and correcting the main direction vector in each iteration with the goal of minimizing the angle between the gradient direction and the main direction of the tensor until the change of the main direction vector of each pixel position is lower than a preset threshold;

[0065] A symmetric positive definite tensor unit is constructed for each pixel position using the converged main direction vector and the response adjustment factor. The tensor unit contains a weighted combination corresponding to the main direction vector and the orthogonal direction vector, which is used to characterize the directional guidance ability and anisotropic response characteristics of the position in the image, and form a direction-aware tensor field covering the entire image domain.

[0066] This paper proposes a pixel-level tensor modeling method that combines directional consistency response values, projection error residuals, structural prior directions, and a gradient feedback correction mechanism. The goal is to construct a set of tensor units with spatial adaptability, directional adjustability, and an error feedback mechanism to achieve high-precision direction-aware modeling. This process is described in detail below.

[0067] First, in the present invention, the response strength adjustment of the tensor unit no longer uses the traditional fixed weight setting method. Instead, the main direction performance stability coefficient is dynamically generated based on the directional consistency response values ​​under multiple incident angles. The so-called directional consistency response value refers to the degree of directional consistency between the main structural direction and the incident angle at each valid projection angle for each image pixel position. The calculation method is as follows: First, the main structural direction angle and the current incident angle are converted into two-dimensional unit vectors, and then the dot product of the two is calculated. The resulting cosine value is the directional consistency response value under this direction. Its value range is between -1 and 1, but in the present invention, only non-negative values ​​(i.e., direction cosines greater than or equal to zero) are retained for participating in the main direction evaluation. Next, the multiple directional consistency response values ​​at each pixel position are weighted averaged. The weight can be set as a constant or adjusted based on the incident angle distribution function. The final value of the main direction performance stability coefficient is between 0 and 1, which represents the overall level of structural direction consistency of the pixel in multiple directions. This coefficient will be used to adjust the initial amplitude of the main direction response strength of the pixel tensor, that is, the degree of penalty or retention in the main direction in the direction perception tensor unit.

[0068] Next, the present invention introduces a feedback mechanism for projection error residuals to construct independent response adjustment factors in the main direction and orthogonal directions. Specifically, the projection error residual refers to the difference between the current image estimate after the projection operation and the actual projected image at each incident angle. For each pixel position, its corresponding value in the projection residual map is recorded at multiple incident angles, and the statistical characteristics of these residual values, such as the mean, variance, or maximum value, are calculated. For the independent response adjustment factor in the main direction, the product of the direction consistency response value and the inverse function of the residual in that direction can be taken. That is, when the residual in that direction is smaller and the consistency is higher, the response adjustment factor is larger, indicating that the main direction is more reliable and the tensor should be given a stronger response; conversely, if the residual is large or the consistency is low, the main direction response factor decreases. For the independent response adjustment factor in the orthogonal direction, it can be directly set proportional to the residual. A large residual indicates a strong response in the non-structural direction and should be suppressed more strongly, that is, a smaller response intensity is set to form a strongly anisotropic tensor field. Through this mechanism, the main direction and the orthogonal direction are no longer simply bound to constant coefficients, but are response control functions based on real imaging errors, which improves the adaptability of tensor anisotropy modeling.

[0069] Then, when constructing the main direction vector of the tensor, the initial direction is taken from the main structural direction angle of each pixel in the structural prior information. The angle is converted into a two-dimensional unit vector, which is used as the initial main direction vector of the tensor. In order to further improve the stability of the direction field and the fit with the image content, the present invention adopts a feedback mechanism based on the gradient direction in the direction enhancement response map to perform fixed point iterative update on the main direction vector of the tensor. In each iteration, for each pixel, its main direction gradient direction vector in the direction enhancement response map is extracted, and the angle between the vector and the current main direction of the tensor is calculated. If the angle is greater than a certain set threshold (for example, π / 16), the main direction of the tensor is updated using linear interpolation to make it closer to the current response direction of the pixel. The update method can be to take the weighted average of the current main direction vector of the tensor and the gradient direction unit vector, and then normalize them as the main direction of the next round. It is iterated in this way until the main direction vector of all pixels changes less than the set threshold in the two rounds before and after, which is considered to be converged.

[0070] Finally, after the main direction converges, the main direction vector is combined with the corresponding independent response adjustment factor in the main direction and the independent response adjustment factor in the orthogonal direction to construct a symmetric positive definite tensor unit for each pixel. The tensor unit consists of two parts: one is the unit projection tensor of the main direction vector, which is the main direction unit vector multiplied by its own transpose; the other is the unit projection tensor of the orthogonal direction unit vector. The two are multiplied by the main direction response factor and the orthogonal direction response factor respectively, and then summed to obtain the final tensor unit of the pixel. This tensor unit has the characteristics of clear directional dominance, controllable anisotropy of response intensity, and closed-loop error feedback adjustment. It can effectively reflect the structural direction distribution and response characteristics of the position in the image.

[0071] The collection of tensor units at all pixel positions forms a direction-aware tensor field covering the entire image domain. This tensor field not only incorporates the coupling between the structural prior and the current image response, but also incorporates a feedback adjustment mechanism for multi-angle imaging errors. It is the core foundation for subsequent tensor-guided local gradient calculation, structural response enhancement, and tensor regularization constraints.

[0072] In summary, the present invention introduces a complete technical process in the process of constructing a direction-aware tensor field, which includes generating a main direction stability coefficient by weighted averaging of directional consistency responses, constructing a response adjustment factor based on projection residuals, using gradient feedback to iteratively update the main direction, and finally constructing a positive definite tensor unit.

[0073] Step S103: performing a tensor-guided local gradient calculation operation on each of the plurality of X-ray projection images to generate a direction enhancement response map, wherein the direction enhancement response map is combined with the main direction vector of the corresponding position in the direction-aware tensor field to achieve dynamic enhancement of the local edge area.

[0074] The purpose of step S103 is to perform tensor-guided local gradient calculation operations on multiple X-ray projection images respectively, so as to generate a direction-enhanced response map. This response map needs to be combined with the main direction vector of the corresponding position in the direction-aware tensor field constructed in the previous step to achieve dynamic enhancement of the local edge area. To this end, it is necessary to first clarify the input data and calculation target during the implementation process: the input includes multiple X-ray projection images with different incident angles obtained in step S101, and the direction-aware tensor field established in step S102. The output is a direction-enhanced response map corresponding to each projection image, with the same size as the original. Figure 1 Each pixel value represents the structural response intensity of the position in the main direction.

[0075] Specifically, when processing an X-ray projection image, the principal direction vector of each pixel in the image is first read from the direction-aware tensor field. This vector, typically expressed as a two-dimensional vector of unit length, describes the dominant structural extension direction of that pixel in image space. For example, in areas with horizontal edges, the vector points toward the x-axis; in areas with diagonal structures or textures, the vector points diagonally. This principal direction vector forms the basis for the direction of subsequent gradient calculations.

[0076] After obtaining the main direction vector, it is necessary to perform local gradient calculation along the main direction on the current image. To do this, a set of finite difference operators aligned with the main direction vector can be designed in the form of directional derivatives. For example, if the main direction vector is , we can set several neighborhood sampling points in that direction (for example, using the center pixel as the reference point and projecting coordinates one pixel forward and one pixel backward), calculate the forward difference or center difference in that direction, and form the main direction gradient estimate. To achieve sub-pixel direction tracking, bilinear interpolation can be performed on the image if necessary, so that pixel values ​​at non-integer positions can also be used for calculations.

[0077] This gradient calculation process must be repeated for every pixel in the image, ensuring that each location incorporates its own unique principal direction information, thereby generating a complete direction-enhanced response map. Each pixel value in this response map represents the intensity of the image gradient at that point in the principal direction, which has two meanings: on the one hand, it reflects the degree of local edge strength along the principal direction at that point; on the other hand, it also reflects the degree of consistency of the structure with the constructed tensor field.

[0078] To further improve the stability and discrimination of the response map, the initially obtained directional response map can be subjected to nonlinear transformations, such as normalization, sigmoid compression, or local contrast enhancement, to suppress spurious responses in noisy areas while amplifying the true response in the structural direction. Furthermore, response map information from multiple projection images can be superimposed, and directional enhancement maps at different angles can be integrated using weighted averaging, maximum response selection, or angular consistency-based fusion strategies to obtain a more comprehensive and robust representation of the structural response.

[0079] It's worth emphasizing that the direction-enhanced response map is not an edge map in the traditional sense, but rather a high-dimensional response map that combines information from the principal structural direction, projection angle consistency, and image gradient strength. Its core function is to preserve image detail while eliminating noise perturbations inconsistent with the principal direction, and to provide a strong quantitative foundation for the subsequent construction of structure-sensitive functions and tensor regularization. Therefore, in actual programming implementation, it is imperative to ensure that the orientation of each pixel is strictly consistent with the principal tensor direction. Estimation errors caused by directional offsets must be avoided during gradient calculations. It is recommended to use a high-precision interpolation algorithm to compensate for directional alignment errors.

[0080] In summary, step S103 generates a direction-enhanced response map on each X-ray projection image through the tensor-guided local gradient calculation method, fully combining the main direction vector information in the direction-aware tensor field, realizing the response enhancement of the dominant direction of the structure and the dynamic amplification of the edge area, laying a high-quality structural foundation for the subsequent anisotropic modeling and regularization guidance.

[0081] Furthermore, performing a tensor-guided local gradient calculation operation on each of the plurality of X-ray projection images to generate a direction enhancement response map includes:

[0082] Based on the principal direction vector of the tensor unit at each image pixel position in the direction-aware tensor field, a directional gradient operator is constructed at the pixel. The directional gradient operator uses a differentiable directional difference kernel set along the principal direction unit vector and obtains grayscale value differences with sub-pixel accuracy based on non-integer sampling point positions in the image through a bilinear interpolation method to achieve gradient approximation in a continuous space.

[0083] The anisotropy degree of the pixel is defined based on the ratio of the main direction response intensity to the orthogonal direction response intensity in the directional perception tensor field, and a local gradient enhancement coefficient is set accordingly. The gradient enhancement coefficient is set to have a large enhancement weight in areas with obvious main direction structures, and a small enhancement weight in areas with close main and orthogonal direction responses or unclear structures, so as to improve the directional response selectivity of the structural boundary area;

[0084] For each X-ray projection image, the local gradient value guided by the tensor is calculated at each pixel position, and the calculated directional response value is assigned to the pixel position in combination with the anisotropy degree and the directional enhancement coefficient to form a directional enhancement response map at a single angle. The directional enhancement response map is used to characterize the spatial distribution characteristics of the main directional gradient of the image at this incident angle;

[0085] Based on the directional consistency response value of each pixel in the projection direction mapping matrix under multiple incident angles, an angle weighting function is constructed, and all directional enhancement response maps are weightedly superimposed and fused to obtain a main direction enhancement response map that integrates all angle information.

[0086] The present invention proposes an image processing path based on principal direction unit vector control, sub-pixel gradient calculation, anisotropy adjustment enhancement, and multi-angle fusion mechanism. The following is a detailed description of this process.

[0087] First, in the process of generating the direction-enhanced response map, the core goal is to calculate the local gradient variation intensity of all pixels along their corresponding principal directions in each X-ray projection image, thereby reflecting the spatial distribution characteristics of the main structural directions of the image. To achieve this, it is necessary to rely on the principal direction vectors of the tensor units in the aforementioned direction-aware tensor field. Each pixel in the tensor field corresponds to a tensor unit, which contains a unit vector representing the principal structural direction. This principal direction unit vector will serve as the direction basis for the local gradient calculation.

[0088] In specific operations, it is necessary to construct a directional differential operator in the pixel coordinate system based on the main direction unit vector. This differential operator does not calculate the gradient along the horizontal or vertical direction of the image, but strictly samples along the direction indicated by the main direction unit vector. In order to support non-integer directions and sub-pixel level direction tracking, the present invention adopts a differentiable directional differential kernel when constructing the directional gradient operation operator. For example, assuming that the main direction unit vector has a horizontal component and a vertical component in the two-dimensional image coordinate system, the differential operation in this direction can be understood as extending a small distance in the main direction and the opposite direction on the basis of the current pixel position to form two sampling points, and then dividing the grayscale value difference at the two sampling points by the distance to obtain the gradient approximation in this direction. Since the main direction unit vector is usually not aligned with the image pixel grid, these two sampling points fall on non-integer coordinate positions most of the time, so the pixel values ​​in the image cannot be directly accessed. To address this issue, the present invention uses bilinear interpolation to obtain the grayscale value of a point. This method first determines the four adjacent integer pixels between which the point falls, then performs weighted interpolation based on horizontal and vertical distances to accurately estimate the image grayscale value at that location. This approach allows the image gradient response to be obtained with continuous spatial precision in any principal direction, achieving sub-pixel directional enhancement.

[0089] After completing the preliminary gradient estimation, it is necessary to moderately enhance or suppress the response based on the anisotropic characteristics of each pixel in the tensor unit. To this end, the present invention introduces the ratio of the main direction response intensity to the orthogonal direction response intensity as a measure of the degree of anisotropy. In the direction-aware tensor field, the main direction response intensity represents the structural clarity of the pixel in the main direction, while the orthogonal direction response intensity corresponds to its response tolerance in the non-structural direction. Dividing the two can obtain the anisotropy ratio. The higher the ratio, the more obvious the main direction structure and the stronger the directional guidance. A ratio close to 1 or lower indicates that the structural direction is not obvious or there is multi-directional texture, and the directional discrimination is weak. Based on this ratio, a local gradient enhancement coefficient can be set for each pixel position. This coefficient is used to control the amplification weight of its final directional response value. In areas with clear structure, that is, locations with a high anisotropy ratio, a larger enhancement weight is set to strengthen its performance in the directional enhancement response map; while in areas with blurred structure, a smaller enhancement weight is set to avoid excessive amplification of erroneous responses.

[0090] Subsequently, for each X-ray projection image, at each pixel position, a gradient is estimated based on the direction of its principal direction unit vector. The response value is adjusted based on the corresponding degree of anisotropy and enhancement coefficient, ultimately forming a directional enhancement response map for a single incident angle across the entire image. This response map is a two-dimensional matrix of the same size as the original image, in which each pixel value represents the directional enhancement intensity of that pixel along its principal direction at the current projection angle. It is a structural representation of the spatial distribution of the image's principal direction gradient. Because the principal direction is related to the actual tissue orientation in the image, this response map effectively characterizes the clarity and continuity of the image's structural orientation at that incident angle.

[0091] Since the present invention considers X-ray projection images with multiple incident angles, in order to construct a stable and angle-independent direction enhancement representation, it is necessary to fuse multiple direction enhancement response maps. To this end, the present invention further constructs an angle weighting function based on the direction consistency response value of each pixel in the aforementioned projection direction mapping matrix at different incident angles. This function is used to evaluate the degree of consistency matching of a certain incident angle with the main structural direction of the current pixel, and generally takes the direction cosine value as the weight factor. For a pixel position, its direction consistency response value at all retained projection angles is normalized and used as the weighting coefficient of the corresponding position in each angle direction enhancement response map. Finally, at all projection angles, the pixel value in each response map is weighted and summed to obtain a fused main direction enhancement response map. This response map fuses the main direction response information at multiple angles, has stronger direction consistency and noise suppression capabilities, and is the direct basis for subsequent structure-sensitive function construction and tensor regularization configuration.

[0092] In summary, in the process of generating direction-enhanced response maps, the present invention integrates tensor-guided direction tracking, sub-pixel gradient estimation, anisotropy adjustment strategy and multi-angle weighted fusion mechanism to form a complete set of continuous domain, direction-aware, high-resolution structural response map generation solutions.

[0093] Furthermore, the performing of a tensor-guided local gradient calculation operation on each of the plurality of X-ray projection images to generate a direction-enhanced response map further includes:

[0094] Before constructing the directional gradient operation operator, a directional stability smoothing process is performed on the main direction vector of the tensor unit at each image pixel position in the directional perception tensor field in a continuous domain. The directional stability smoothing process improves the spatial consistency and response stability of the direction field in the structural boundary area by performing a weighted averaging operation based on spherical distance in the main direction unit vector space, and the smoothed main direction vector is used as the direction basis for constructing a differentiable directional difference kernel;

[0095] After obtaining the grayscale value difference at the sub-pixel precision, performing a nonlinear normalization operation based on response consistency on the difference value, wherein the nonlinear normalization operation uses the angle consistency between the main direction vector of the tensor unit of the pixel and the direction vector of its neighborhood in the direction perception tensor field as an adjustment factor to suppress the response error in the direction inconsistent area and improve the robustness of the structural response map in terms of spatial continuity;

[0096] In the process of constructing the direction-enhanced response map, a structural density weighting term is further introduced into the response value of each pixel in the direction-enhanced response map. The structural density weighting term is based on the pixel value of the pixel in the structure-sensitive function map and the local statistical distribution of its gradient direction, and is used to adjust the response balance between the high-frequency area and the low-texture area of ​​the image, so as to prevent the response value of the edge details from being excessively amplified by noise;

[0097] When fusing all directional enhancement response maps to form the main directional enhancement response map that integrates all-angle information, a structural consistency mask is introduced as the masking factor of the angle weighting function. The structural consistency mask is constructed according to the consistency of the response trend of each pixel in the directional enhancement response map under multiple incident angles, and only assigns high weights to areas with highly consistent response trends, thereby improving the reliability of directional recognition of the fused image in complex texture areas.

[0098] First, before constructing the directional gradient operator, a continuous domain directional stability smoothing process is performed on the principal direction vectors of the tensor units at each image pixel in the directional-aware tensor field. The principal direction vector is a two- or three-dimensional vector of unit length that represents the dominant structural direction of the current pixel in image space. Because this direction vector is inferred based on the local image structure, it is susceptible to edge perturbations or noise, and its direction may exhibit discontinuous jumps, particularly in boundary regions. Therefore, the goal of smoothing is to enhance the spatial continuity of the direction field, ensuring consistent direction within the same structure and a natural transition at boundaries. To achieve this, the present invention employs a weighted averaging strategy based on spherical distance for vector domain smoothing. Specifically, the method involves selecting all principal direction unit vectors within a fixed window (e.g., a 3×3 or 5×5 neighborhood) centered on the current pixel. The angles between these neighborhood directions and the central direction are calculated, and these angle differences are converted into weights. The weights are constructed using cosine or Gaussian functions, giving directions with smaller angles greater weights. Subsequently, all neighboring direction vectors are weighted and renormalized to form the smoothed main direction vector. This vector not only takes into account the original direction estimate of the current point but also integrates the directional commonalities of its neighbors, making it more resistant to noise and continuous, and can be directly used to construct the direction basis for the subsequent directional gradient operator.

[0099] After obtaining the grayscale value difference under sub-pixel precision, in order to avoid excessive amplification of the response value by local noise or direction estimation error, the present invention introduces a nonlinear normalization operation based on response consistency. The core of this operation is to use the angle consistency between the main direction vector of the tensor unit and the main direction vector of the neighborhood as an adjustment factor. In the specific implementation, first, in the neighborhood of the current pixel, the main direction vectors of all neighboring points are extracted, and the angle is calculated one by one with the main direction vector of the current pixel. The smaller the angle, the higher the direction consistency. The cosine value can be used as the direction consistency measure, and all neighborhood consistency scores are weighted averaged to obtain the direction consistency index of the pixel. Subsequently, the grayscale difference value calculated in the previous step is nonlinearly adjusted according to the index. The adjustment method can use a Sigmoid function, an exponential decay function or a piecewise linear function, so that the response value of the area with high direction consistency remains large, while the response value of the area with poor consistency is suppressed. This method helps to filter out the error response in the local direction chaos area and enhance the stability of the response map in terms of structural continuity.

[0100] When constructing the directional enhancement response map, in order to avoid relying solely on local gradients and causing excessive amplification of edge structures or lack of response to uniform areas, the present invention further introduces a structural density weighting term. The weighting term consists of two parts: one is the numerical value of the pixel in the structure sensitivity function map, which represents the response intensity of the point in the main direction of the structure; the other is the local statistical distribution of the pixel in the direction of its main direction, such as the local gradient standard deviation or mean. The weighting factor can be constructed by multiplying the pixel structure value and its directional gradient intensity, or by combining it through an adaptive adjustment function, so that the response at the structural boundary is moderately enhanced, while in uniform areas or high-frequency interference areas, the response is moderately compressed. After the gradient response value is calculated, the structural density weighting term will be multiplied with it or used as a coefficient to participate in the response value construction, thereby achieving a dynamic balance of the response intensity in space and effectively suppressing the error accumulation caused by excessive amplification of texture edges or background noise.

[0101] Finally, when performing weighted superposition fusion on multiple directional enhancement response maps to generate a main directional enhancement response map that incorporates all-angle information, the present invention introduces a structural consistency mask, based on the existing angle-weighting function, as a masking factor for the angle-weighting function. This mask is generated based on the following principle: for each image pixel position, its directional enhancement response value will form a response sequence under all known incident angles. The trend consistency between the response values ​​in this sequence is statistically analyzed, such as directional monotonicity, consistency slope change, and the angular concentration of the maximum response, to construct a directional trend consistency score for the pixel in the angular domain. Only when this score exceeds a certain threshold is the pixel allowed to retain all weighting coefficients during the angular fusion process; otherwise, the fusion weight for that position is set to a smaller value or cleared. This structural consistency mask ensures that the final fused image assigns high-confidence responses to regions with stable responses and clear directions at multiple angles, while imposing restrictions on regions with ambiguous structures, divergent responses, or directional drift, thereby improving the directional discrimination ability and structural reconstruction quality of the fused image.

[0102] In summary, by introducing continuous domain directional smoothing, response consistency normalization, structure density response adjustment and multi-angle consistency mask mechanism, a highly adaptive, structure-aware, multi-scale fusion direction-enhanced response map generation strategy was constructed, which significantly improved the accuracy, stability and noise robustness of the main structure direction extraction during image reconstruction.

[0103] Step S104: constructing a structure sensitivity function map based on the local structure response intensity extracted from the direction enhancement response map, wherein the structure sensitivity function map is used to describe the anisotropic response degree of each image position.

[0104] In the present invention, the core goal of step S104 is to construct a structure-sensitive function map. This map is used to characterize the degree of anisotropic response of each pixel in the image along the main structural direction, and serves as a weighting factor to guide the spatial distribution of the tensor regularization term during the subsequent image reconstruction process. Therefore, to achieve this goal, it is necessary to extract the local structural response intensity at each position in the image based on the direction-enhanced response map generated in the previous step, and then generate the structure-sensitive function map based on this.

[0105] The directional enhancement response map is essentially an intermediate image, representing the intensity of the image gradient response at each pixel along its principal structural direction, guided by a tensor. Higher pixel values ​​indicate more pronounced structural edges along the principal direction at that point, indicating greater directional consistency and structural clarity in space. Conversely, lower response values ​​often indicate weak structural changes, unclear edges, and even areas of homogeneous texture or noise. This response intensity can be obtained using a local difference operator guided by the principal direction or directly read from the directional enhancement response map, eliminating the need for repeated calculations.

[0106] To construct the structure-sensitivity function map, the raw response intensity values ​​of each pixel in the direction-enhanced response map must be normalized to a uniform and stable numerical scale, typically set between 0 and 1. This normalization can be achieved in a variety of ways, such as linear scaling (based on the maximum and minimum values ​​of the entire image), histogram equalization, or nonlinear compression functions (such as the sigmoid function). Nonlinear compression is preferred because it has an edge saturation effect, which can significantly increase the numerical contrast between structured regions and the background while suppressing false responses in noisy areas.

[0107] After normalization, a numerical coefficient is obtained at each pixel position in the image. This value is the grayscale value in the structure sensitivity function map. The final structure sensitivity function map is a two-dimensional grayscale image of the same size as the original image. Each pixel value represents the structural significance of that point, ranging from 0 to 1. Values ​​close to 1 indicate clear structure and significant direction, while values ​​close to 0 indicate weak or unclear structure. In the image, this structure sensitivity function map shows a distribution state with higher grayscale (bright) in areas such as tissue edges and organ outlines, and lower grayscale (dark) in areas within the tissue or without obvious structure. The distribution strength of the structure in the image can be visually identified.

[0108] To further enhance the robustness and spatial continuity of the function graph, a spatial filtering process can be introduced after its generation. For example, Gaussian filtering can be used to smooth local numerical variations and avoid misleading responses caused by isolated points. Alternatively, bilateral filtering can be employed to suppress local noise while preserving edge features. This processing is particularly suitable near tissue boundaries, effectively preventing issues such as edge breakage and structural extension interruptions during subsequent regularization.

[0109] In the reconstruction of multi-angle X-ray projection images, if a directional enhancement response map is constructed for each projection angle and the corresponding extraction is performed, multiple structural sensitivity function maps will be obtained. These maps can then be further integrated by taking a weighted average of the structural response coefficients at multiple angles, taking the maximum value, or performing directional coupling fusion based on the degree of consistency between the projection direction and the main structural direction. The resulting unified structural sensitivity function map can be used as a global weight distribution map to accurately guide the spatial adaptability of anisotropic regularization in the image domain.

[0110] For example, consider a pixel in a lung X-ray image. If the pixel is located at the edge of a lung lobe, its value in the direction enhancement response map is 0.88, which becomes 0.95 after Sigmoid normalization. This indicates that there is a clear boundary in the main direction at this point, and the regularization strength should be reduced to preserve structural details. Therefore, the value in the structure sensitivity function map is set to 0.95. For another pixel in the center of the lung tissue, its response value is 0.14, which is 0.12 after normalization. This means that the structure at this location is not obvious, and regularization can be strengthened to suppress reconstruction artifacts. Therefore, the value of this point in the structure sensitivity function map is set to 0.12.

[0111] In summary, the structure-sensitive function map is a structural saliency distribution map generated based on the directional enhancement response map. It realizes the quantitative encoding of the structural differences of the image in the spatial domain by extracting the response intensity in the main direction of each pixel and expressing it in a normalized manner. This map not only has the advantages of high precision and stable distribution, but also serves as a regularization weighting basis in the image reconstruction objective function, which can effectively distinguish between structural and non-structural areas and achieve a dynamic balance between directional protection and noise suppression. Therefore, the structure-sensitive function map plays a key role as a bridge connecting response extraction and regularization term adjustment in the reconstruction process of the present invention, and is a basic technical component for image detail preservation and noise robustness optimization.

[0112] Step S105: Using the structure-sensitive function graph as a weighting factor to guide the construction of a tensor regularization term, and combining the direction-aware tensor field to construct an image reconstruction objective function, wherein the objective function takes minimizing projection error and direction consistency loss as optimization goals.

[0113] The purpose of this step is to use the structure-sensitive function map as a weighting factor to guide the construction of the tensor regularization term, and to combine it with the direction-aware tensor field to jointly establish the image reconstruction objective function, where the objective function is optimized to minimize the projection error and directional consistency loss. In practice, the validity of the two input items should be confirmed first: the structure-sensitive function map and the direction-aware tensor field, which come from steps S104 and S102 respectively. The former expresses the structural salience weight of each location in the image, and the latter describes the dominant structural direction and anisotropic response characteristics of each location.

[0114] When constructing the tensor regularization term, it is necessary to design a type of regularization constraint mechanism with direction selectivity in the image space based on the direction-aware tensor field. This mechanism is different from the traditional isotropic regularization term, such as the L2 norm or isotropic total variation. Its core idea is to use tensor guidance to only perform smoothness penalties in the main direction of the image structure, thereby avoiding blurring effects in the direction of tissue boundaries. To achieve this goal, a direction-selective differential operator can be defined to apply a gradient operation aligned with the main direction of its tensor to each pixel in the image, and then use the directional gradient as the core metric of the regularization term. Specifically, for a certain pixel point (x, y), its directional regularization term can be expressed as a tensor-guided gradient norm, such as ,in represents the tensor-guided directional derivative operator, The image to be optimized.

[0115] In order to make the regularization term spatially adaptable, a structure-sensitive function map needs to be introduced as its weighting factor. In actual construction, the regularization term of each pixel will be multiplied by the weight coefficient of the corresponding position in the structure-sensitive function map. For areas with high structural significance, the weight value is small, suppressing the strong regularization effect, thereby protecting clear edges; while for areas with insignificant structure or dominated by noise, the weight value is large, strengthening the regularization strength to enhance smoothness and robustness. In summary, the tensor regularization term should be adaptive in spatial distribution and selective in directional distribution, and be able to adjust the regularization strength and directional response according to the structural characteristics of the image itself.

[0116] After the tensor regularization term is designed, it must be combined with the data consistency term to construct the image reconstruction objective function. The data consistency term's fundamental purpose is to minimize the projection error between the current estimated image and the original X-ray projection image. A common approach is to use a forward projection operator based on the Radon transform or its numerical analog (such as the projection matrix) to project and reconstruct the current estimated image and then calculate the difference between it and the true projection image to form a residual term. This residual term is typically measured using the L2 norm or Huber function to constrain the final reconstructed image to preserve the physical consistency of the original measurement data in the projection space.

[0117] During image reconstruction, it is necessary not only to minimize the reconstruction error in the projection domain, but also to maintain the consistency of the image's spatial structure to avoid structural distortion or directional drift. Therefore, a directional consistency loss term is introduced into the objective function to measure whether the structural direction of the current reconstructed image is consistent with the preset direction-aware tensor field.

[0118] The directional consistency loss is constructed by extracting the local image gradient direction for each pixel in the image and comparing it with the principal direction defined in the direction-aware tensor field at that pixel. A smaller angle between the two indicates higher directional consistency; a larger angle indicates that the image structure deviates from the expected principal direction. Cosine similarity can be used to measure angular consistency, and a penalty term can be designed through a function, added as a loss term to the overall objective function.

[0119] After integrating the above items, the complete image reconstruction objective function is as follows:

[0120]

[0121] Each of these items has the following meaning:

[0122] : The image to be optimized (i.e. the current reconstructed image).

[0123] :For images The simulated projection image obtained by the forward projection operation is usually implemented using Radon transform or sparse angle simulated projection operator.

[0124] : The original X-ray projection image data obtained by actual acquisition is a reference used to constrain the consistency of the reconstructed image and the actual measurement data.

[0125] : Data consistency term, that is, the square error between the reconstructed image and the true projection, reflects the matching degree of the reconstructed image in the physical observation domain.

[0126] : Position in the structure-sensitive function graph The pixel weight at , usually ranges from 0 to 1. A high value indicates that the point has a clear structure and significant directional features, and regularization should be weakened; a low value indicates that the point has a fuzzy structure or is dominated by noise, and regularization should be strengthened.

[0127] : Tensor-guided gradient, representing the image gradient computed along the principal directions defined by the direction-aware tensor field. This gradient-guided regularization constrains the image to act only along the local principal directions, suppressing ineffective smoothing along unstructured directions.

[0128] : The strength of the tensor regularization term, used to adjust the direction selectivity of structure edge preservation and noise suppression.

[0129] : Directional consistency deviation metric function, used to penalize the consistency deviation between the local gradient direction of the image and the main direction of the tensor field. It can be defined as follows: calculate the angle between the gradient direction and the main direction of the tensor , then use or As the consistency penalty. The larger the value, the more serious the direction deviation and the greater the loss.

[0130] : The weight coefficient of the data consistency term, often used to control the matching priority between the reconstructed image and the observed data. The recommended value range is 10-100.

[0131] : The weight coefficient of the tensor regularization term, which is used to adjust the balance between structure preservation and noise suppression in the reconstructed image. The recommended value range is 0.1-10.

[0132] γ: Weight coefficient for the directional consistency loss term, used to enforce consistency constraints between the image gradient direction and the tensor direction, improving the credibility of the structural orientation. The recommended value range is 0.1–5.

[0133] In summary, step S105 introduces the structure-sensitive function graph into the weighted mechanism of the tensor regularization term, and combines it with the direction-aware tensor field to establish an image reconstruction objective function with spatial adaptability and direction consistency. This objective function simultaneously minimizes the projection error and direction deviation, effectively improving the detail preservation ability and structural credibility of the reconstructed image, and providing a rigorous and effective mathematical basis for the subsequent joint optimization iterative process.

[0134] Step S106: performing a joint optimization operation on the image reconstruction objective function, dynamically updating the directional consistency constraint in the tensor regularization term using the directional response distribution of the current reconstructed image, and iterating until the reconstructed image converges to a solution with optimal directional detail preservation and noise suppression effects, thereby obtaining the final reconstructed image.

[0135] The purpose of step S106 is to perform a joint optimization operation on the image reconstruction objective function. This image reconstruction objective function, constructed in the previous steps, consists of three key components: a projection error term, a tensor regularization term, and a directional consistency loss term. Its optimization goal is to restore the original X-ray projection data while preserving the image's directional structural details as much as possible and effectively suppressing image noise. Therefore, in this step, the objective function is numerically solved, and the directional consistency constraints in the tensor regularization term are dynamically updated during the solution process, resulting in a final reconstructed image that optimizes both directional detail preservation and noise suppression.

[0136] In practical implementation, the image reconstruction variables should first be initialized. Initialization can be done by setting all pixels to zero, or by using a preliminary image obtained using a fast reconstruction algorithm (such as filtered backprojection) as an initial estimate. Based on this initial image, the constructed orientation-aware tensor field and structure-sensitive function graph are used to compute the initial tensor regularization term and the orientation consistency loss term. These terms are then combined with the projection error term computed from the forward projection to form the complete loss function expression.

[0137] Optimization can be performed using iterative variational methods or gradient-based numerical optimization algorithms, such as gradient descent, quasi-Newton method, alternating direction method of multipliers (ADMM), or iterative shrinkage-thresholding algorithm (ISTA). In each iteration, the tensor field and structure-sensitive function graph are fixed, and the gradient information of the loss function is calculated based on the current image state, thereby updating the image variables. After the image update is completed, the structural direction distribution of the current image must be re-evaluated, and the dominant direction field of the current image must be recalculated through local gradient direction analysis or principal direction estimation methods.

[0138] After obtaining the dominant direction of the current image, it is compared with the direction-aware tensor field initially constructed in step S102. Based on the directional deviation between the two, the directional consistency constraint in the tensor regularization term is updated. Specifically, at each pixel position, the angular difference between the local gradient direction of the current image and the dominant direction defined in the tensor field is calculated. This difference is used to construct a new penalty weight, or direction adjustment factor, to dynamically adjust the response strength of the current tensor unit to that direction. The more consistent the direction, the smaller the penalty, while vice versa, the penalty is increased, pushing the image to converge toward the dominant structural direction.

[0139] This dynamic update mechanism ensures that the tensor regularization term remains synchronized with the directional information of the current image state throughout the optimization process, avoiding directional shifts or structural loss caused by inaccurate initial tensor fields. Furthermore, this mechanism is adaptive, automatically adjusting the regularization strength based on the current image features, even in areas with large image content changes or weak boundary information, enabling more detailed and targeted optimization control.

[0140] The entire iterative process should be performed with appropriate convergence criteria. Common methods include ensuring that the pixel difference between two iterations of the current image is below a set threshold, or that the decrease in the objective function is less than a set ratio. Once the convergence criteria are met, the optimization process is terminated and the final image is output as the reconstruction result.

[0141] The final reconstructed image should meet the following goals simultaneously: first, its projection data should be highly consistent with the original X-ray projection image under the error norm, ensuring that the physical measurement data is accurately reconstructed; second, the structural edges in the image should be distributed along the main directions defined by the direction-sensing tensor field, and the directional information should remain clear and coherent; third, the noise in the non-structural areas of the image should be effectively suppressed, and the background part should be smooth and consistent without artifacts or accumulation of reconstruction errors.

[0142] In summary, step S106 achieves high-precision image reconstruction by performing a joint optimization operation during image reconstruction and dynamically updating the directional consistency constraint in the tensor regularization term. Throughout the iterative process, directional response information is continuously re-estimated and fed back into the regularization term, ensuring that the optimized direction remains consistent with the true structure, effectively improving the ability to preserve image detail and the stability of noise suppression.

[0143] The following is the reference implementation code of the image reconstruction method provided in this embodiment:

[0144] import numpy as np

[0145] import math

[0146] # --------- Step S101 ----------

[0147] def compute_direction_mapping_matrix(projection_angles, structure_orientation_map):

[0148] Input: projection_angles: projection angle sequence, in radians, length N, θ_i, structure_orientation_map: the main structural direction angle φ(x, y) at each pixel of the image, in radians, shape (H, W); Output: direction_mapping_matrix: mapping matrix M(x,y,i) = cos(θ_i -φ(x,y)), shape (H, W, N)

[0149] H, W = structure_orientation_map.shape

[0150] N = len(projection_angles)

[0151] mapping_matrix = np.zeros((H, W, N))

[0152] for i in range(N):

[0153] theta_i = projection_angles[i]# The incident angle of the i-th projection image

[0154] for x in range(H):

[0155] for y in range(W):

[0156] phi_xy = structure_orientation_map[x, y] #Main structure orientation angle φ(x,y)

[0157] delta = theta_i - phi_xy

[0158] mapping_matrix[x, y, i]=math.cos(delta) #Directional consistency measure

[0159] return mapping_matrix

[0160] # --------- Step S102 ------------

[0161] def build_tensor_field(structure_orientation_map, direction_mapping_matrix):

[0162] Construct direction-aware tensor field T(x,y)

[0163] H, W = structure_orientation_map.shape

[0164] tensor_field = np.zeros((H, W, 2, 2)) # A 2x2 tensor at each position

[0165] for x in range(H):

[0166] for y in range(W):

[0167] phi = structure_orientation_map[x, y]

[0168] cos_phi = math.cos(phi)

[0169] sin_phi = math.sin(phi)

[0170] v1 = np.array([[cos_phi], [sin_phi]])# Main direction vector v1

[0171] v2 = np.array([[-sin_phi], [cos_phi]])# Orthogonal direction vector v2

[0172] # Set response strength based on directional consistency and prior

[0173] lambda_1 = 0.9# can be adjusted according to the consistency value in the mapping matrix

[0174] lambda_2 = 0.05

[0175] # Build tensor

[0176] T = lambda_1 * (v1 @ v1.T) + lambda_2 * (v2 @ v2.T)

[0177] tensor_field[x, y] = T

[0178] return tensor_field

[0179] # ------------ Step S103 -----------

[0180] def directional_gradient(image, tensor_field):

[0181] Perform tensor-guided gradient calculation on the image to obtain a direction-enhanced response map

[0182] H, W = image.shape

[0183] response_map = np.zeros((H, W))

[0184] for x in range(1, H - 1):

[0185] for y in range(1, W - 1):

[0186] T = tensor_field[x, y]

[0187] # Extract the main direction component

[0188] eigvals, eigvecs = np.linalg.eigh(T)

[0189] principal_dir = eigvecs[:, np.argmax(eigvals)]

[0190] dx = principal_dir[0]

[0191] dy = principal_dir[1]

[0192] # Finite differences along the principal directions

[0193] val_center = image[x, y]

[0194] val_forward = image[min(H - 1, int(x + dx)), min(W - 1, int(y+ dy))]

[0195] val_backward = image[max(0, int(x - dx)), max(0, int(y -dy))]

[0196] # Central difference as the main direction response strength

[0197] grad = (val_forward - val_backward) / 2.0

[0198] response_map[x, y] = abs(grad)

[0199] return response_map

[0200] # ---------- Step S104 ----------

[0201] def build_structure_sensitivity_map(response_map):

[0202] Construct a structure-sensitive function graph, normalize the response value and enhance edge contrast

[0203] min_val = np.min(response_map)

[0204] max_val = np.max(response_map)

[0205] norm_map = (response_map - min_val) / (max_val - min_val + 1e-6)

[0206] # Sigmoid compression to enhance response differences in edge areas

[0207] sigmoid_map = 1 / (1 + np.exp(-10 * (norm_map - 0.5)))

[0208] return sigmoid_map

[0209] # -------------- Step S105 ------------

[0210] def compute_total_loss(f, g, P_f, w_map, tensor_field, alpha=50, beta=1.0, gamma=0.5):

[0211] # Calculate the data consistency term of the objective function E(f)

[0212] data_loss = alpha * np.sum((P_f - g) ** 2)

[0213] # Tensor regularization term

[0214] tensor_loss = 0.0

[0215] H, W = f.shape

[0216] for x in range(1, H - 1):

[0217] for y in range(1, W - 1):

[0218] T = tensor_field[x, y]

[0219] w = w_map[x, y]

[0220] # Calculate directional derivatives using the principal directions of the tensor

[0221] eigvals, eigvecs = np.linalg.eigh(T)

[0222] principal_dir = eigvecs[:, np.argmax(eigvals)]

[0223] dx, dy = principal_dir[0], principal_dir[1]

[0224] val_forward = f[min(H - 1, int(x + dx)), min(W - 1, int(y+ dy))]

[0225] val_backward = f[max(0, int(x - dx)), max(0, int(y -dy))]

[0226] grad = (val_forward - val_backward) / 2.0

[0227] tensor_loss += beta * w * (grad ** 2)

[0228] # Directional consistency loss term (using the angle between the main direction of the tensor and the direction of the image gradient)

[0229] direction_loss = 0.0

[0230] fx = np.gradient(f, axis=0)

[0231] fy = np.gradient(f, axis=1)

[0232] for x in range(H):

[0233] for y in range(W):

[0234] gx, gy = fx[x, y], fy[x, y]

[0235] norm_degree = math.sqrt(gx**2 + gy**2) + 1e-6

[0236] degree_dir = np . array ( [ gx , gy ]) / norm_degree

[0237] T = tensor_field[x, y]

[0238] eigvals, eigvecs = np.linalg.eigh(T);

[0239] main_dir = eigvecs[:, np.argmax(eigvals)]

[0240] cos_theta = np.dot(grad_dir, main_dir)

[0241] angle_penalty = ( 1 - cos_theta ) # angle_penalty sin 2 (θ)conditioning

[0242] direction_loss += gamma * angle_penalty

[0243] return data_loss + tensor_loss + direction_loss

[0244] # ------------ Step S106 -----------

[0245] def optimize_image(initial_image, projection_data, project_operator,structure_orientation_map,

[0246] projection_angles, num_iterations=50, alpha=50,beta=1.0, gamma=0.5, step_size=0.1):

[0247] Perform the complete tensor-based image reconstruction optimization process

[0248] Parameter description: initial_image: initial image estimation (can be obtained by methods such as filtered back projection) projection_data: original X-ray projection image (g) project_operator: projection operation function, defined as P(f) structure_orientation_map: main structure direction φ(x,y) at each pixel

[0249] projection_angles: all incident angles θ_i sequence num_iterations: maximum number of iterations; alpha, beta, gamma: weighted coefficients of each loss; step_size: step size of each round of gradient descent

[0250] # Initialize variables

[0251] f = initial_image.copy()

[0252] H, W = f.shape

[0253] # Step S101: Direction Mapping Matrix

[0254] direction_mapping_matrix = compute_direction_mapping_matrix(projection_angles, structure_orientation_map)

[0255] # Step S102: Construct tensor field

[0256] tensor_field = build_tensor_field(structure_orientation_map,direction_mapping_matrix)

[0257] for iteration in range(num_iterations):

[0258] print(f is iterating {iteration + 1} / {num_iterations} times...)

[0259] # Step S103: Generate direction enhancement response map

[0260] response_map = directional_gradient(f, tensor_field)

[0261] # Step S104: Construct structure-sensitive function graph

[0262] w_map = build_structure_sensitivity_map(response_map)

[0263] # Step S105: Calculate the loss function E(f)

[0264] projected_f = project_operator(f)

[0265] loss = compute_total_loss(f, projection_data, projected_f, w_map, tensor_field, alpha, beta, gamma)

[0266] print(f current loss value E(f): {loss:.4f})

[0267] Gradient descent updates the image f (more complex derivative formulas can actually be used)

[0268] grad_f = np.zeros_like(f)

[0269] # Back-projection of data-consistent gradient (P(f) - g)

[0270] error_proj = projected_f - projection_data

[0271] backprojected_error = project_operator(error_proj, adjoint=True)

[0272] grad_f += 2 * alpha * backprojected_error

[0273] # Tensor regularization directional gradient term (partial derivative of directional derivative)

[0274] fx = np.gradient(f, axis=0)

[0275] fy = np.gradient(f, axis=1)

[0276] for x in range(1, H - 1):

[0277] for y in range(1, W - 1):

[0278] T = tensor_field[x, y]

[0279] eigvals, eigvecs = np.linalg.eigh(T)

[0280] v = eigvecs[:, np.argmax(eigvals)]

[0281] dx, dy = v[0], v[1]

[0282] forward = f[min(H - 1, int(x + dx)), min(W - 1, int(y+ dy))]

[0283] backward = f[max(0, int(x - dx)), max(0, int(y -dy))]

[0284] direction_grad = (forward - backward) / 2.0

[0285] grad_f[x, y] += beta * w_map[x, y] * direction_grad

[0286] # Directional consistency loss gradient (simplified to directional projection error)

[0287] fx = np.gradient(f, axis=0)

[0288] fy = np.gradient(f, axis=1)

[0289] for x in range(H):

[0290] for y in range(W):

[0291] gx, gy = fx[x, y], fy[x, y]

[0292] norm_grad = math.sqrt(gx**2 + gy**2) + 1e-6

[0293] grad_dir = np.array([gx, gy]) / norm_grad

[0294] T = tensor_field[x, y]

[0295] eigvals, eigvecs = np.linalg.eigh(T)

[0296] v = eigvecs[:, np.argmax(eigvals)]

[0297] cos_theta = np.dot(grad_dir, v)

[0298] # The greater the direction inconsistency, the heavier the penalty

[0299] angle_penalty_grad = -1.0 * (1 - cos_theta)

[0300] grad_f[x, y] += gamma * angle_penalty_grad

[0301] # Perform gradient descent to update the image

[0302] f -= step_size * grad_f

[0303] return f

[0304] A second embodiment of the present application provides an electronic device, comprising:

[0305] processor;

[0306] The memory is used to store a program, which, when read and executed by the processor, executes an X-ray image reconstruction method based on direction-aware tensor modeling provided in the first embodiment of the present application.

[0307] The third embodiment of the present application provides a computer-readable storage medium having a computer program stored thereon. When the program is executed by a processor, the program executes an X-ray image reconstruction method based on direction-aware tensor modeling provided in the first embodiment of the present application.

[0308] Although the present application is disclosed as above with the preferred embodiments, it is not intended to limit the present application. Any person skilled in the art may make possible 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 based on the scope defined by the claims of the present application.

Claims

1. An X-ray image reconstruction method based on direction-aware tensor modeling, characterized in that: include: Acquire multiple X-ray projection images at different incident angles, establish an initial direction correspondence relationship with the tissue direction distribution within the reconstruction area based on preset angle parameters, and generate a projection direction mapping matrix; Based on the projection direction mapping matrix and structural prior information of the reconstruction area, a high-order direction-aware tensor field coupling the main direction of the tissue and the propagation direction of the ray is constructed; performing a tensor-guided local gradient calculation operation on each of the plurality of X-ray projection images to generate a direction-enhanced response map; Constructing a structure sensitivity function map based on the local structure response intensity extracted from the direction enhancement response map, wherein the structure sensitivity function map is used to characterize the anisotropic response degree of each image position; The structure-sensitive function map is used as a weighting factor to guide the construction of a tensor regularization term, and the image reconstruction objective function is constructed in combination with the direction-aware tensor field, wherein the objective function takes minimizing the projection error and the direction consistency loss as an optimization goal; A joint optimization operation is performed on the image reconstruction objective function, and the directional consistency constraint in the tensor regularization term is dynamically updated using the directional response distribution of the current reconstructed image. The process is iterated until the reconstructed image converges to a solution that optimizes directional detail preservation and noise suppression, thereby obtaining the final reconstructed image.

2. The X-ray image reconstruction method based on direction-aware tensor modeling according to claim 1, characterized in that: The method of acquiring multiple X-ray projection images at different incident angles, establishing an initial direction correspondence relationship with the tissue direction distribution within the reconstruction area according to preset angle parameters, and generating a projection direction mapping matrix includes: Based on the angle relationship between the main structure direction angle of each image pixel position in the tissue direction distribution and each incident angle, the projection angle correspondence with an angle exceeding a preset threshold value π / 8 is eliminated to retain incident angle information with high direction consistency; For each retained incident angle, calculating a direction consistency response value of the image pixel position, the direction consistency response value being a direction cosine function value between the main structure direction angle and the incident angle; Based on the directional consistency response values ​​at multiple incident angles and the magnitude of the change in the main structural direction of the pixel in its neighborhood, a local structural stability score is constructed to measure the degree to which the main structural direction of the pixel is maintained within the projection angle domain. The structural stability score is subjected to direction-aware fusion processing at multiple spatial scales to form a scale-robust directional saliency score map, and the directional saliency score map is used in the pixel-level weighted calculation for generating the projection direction mapping matrix to output the projection direction mapping matrix.

3. The X-ray image reconstruction method based on direction-aware tensor modeling according to claim 1, characterized in that: The method of constructing a high-order direction-aware tensor field coupling the main direction of the tissue and the propagation direction of the ray based on the projection direction mapping matrix and the structural prior information of the reconstruction area includes: Obtaining a directional consistency response value for each image pixel position in the projection direction mapping matrix under multiple incident angles, and generating a main direction performance stability coefficient for the pixel based on a weighted average method, wherein the directional consistency response value is a direction cosine function value between the main structure direction angle and the corresponding incident angle, and the main direction performance stability coefficient is used to adjust the initial amplitude of the main direction response intensity of the subsequent tensor; Based on the stability coefficient, combined with the projection error residual values ​​of each image pixel position under the multiple incident angles, an independent response adjustment factor of the pixel in the main direction and the orthogonal direction is constructed, wherein the independent response adjustment factor in the main direction is used to set the main direction response strength in the tensor unit, and the independent response adjustment factor in the orthogonal direction is used to set the orthogonal direction response strength in the tensor unit, so as to achieve pixel-level adaptive control of the tensor anisotropic response; Initializing the main structural direction angle of each pixel position in the structural prior information as the main direction vector of the tensor unit, and constructing a main direction iterative update path based on the gradient direction of the corresponding pixel position in the direction enhancement response map, and correcting the main direction vector in each iteration with the goal of minimizing the angle between the gradient direction and the main direction of the tensor until the change of the main direction vector of each pixel position is lower than a preset threshold; A symmetric positive definite tensor unit is constructed for each pixel position using the converged main direction vector and the response adjustment factor. The tensor unit contains a weighted combination corresponding to the main direction vector and the orthogonal direction vector, which is used to characterize the directional guidance ability and anisotropic response characteristics of the position in the image, and form a direction-aware tensor field covering the entire image domain.

4. The X-ray image reconstruction method based on direction-aware tensor modeling according to claim 1, characterized in that: The performing of a tensor-guided local gradient calculation operation on each of the plurality of X-ray projection images to generate a direction enhancement response map includes: Based on the principal direction vector of the tensor unit at each image pixel position in the direction-aware tensor field, a directional gradient operator is constructed at the pixel. The directional gradient operator uses a differentiable directional difference kernel set along the principal direction unit vector and obtains grayscale value differences with sub-pixel accuracy based on non-integer sampling point positions in the image through a bilinear interpolation method to achieve gradient approximation in a continuous space. The anisotropy degree of the pixel is defined based on the ratio of the main direction response intensity to the orthogonal direction response intensity in the directional perception tensor field, and a local gradient enhancement coefficient is set accordingly. The gradient enhancement coefficient is set to have a large enhancement weight in areas with obvious main direction structures, and a small enhancement weight in areas with close main and orthogonal direction responses or unclear structures, so as to improve the directional response selectivity of the structural boundary area; For each X-ray projection image, the local gradient value guided by the tensor is calculated at each pixel position, and the calculated directional response value is assigned to the pixel position in combination with the anisotropy degree and the directional enhancement coefficient to form a directional enhancement response map at a single angle. The directional enhancement response map is used to characterize the spatial distribution characteristics of the main directional gradient of the image at this incident angle; Based on the directional consistency response value of each pixel in the projection direction mapping matrix under multiple incident angles, an angle weighting function is constructed, and all directional enhancement response maps are weightedly superimposed and fused to obtain a main direction enhancement response map that integrates all angle information.

5. The X-ray image reconstruction method based on direction-aware tensor modeling according to claim 4, characterized in that: The step of performing a tensor-guided local gradient calculation operation on each of the plurality of X-ray projection images to generate a direction enhancement response map further includes: Before constructing the directional gradient operation operator, a directional stability smoothing process is performed on the main direction vector of the tensor unit at each image pixel position in the directional perception tensor field in a continuous domain. The directional stability smoothing process improves the spatial consistency and response stability of the direction field in the structural boundary area by performing a weighted averaging operation based on spherical distance in the main direction unit vector space, and the smoothed main direction vector is used as the direction basis for constructing a differentiable directional difference kernel; After obtaining the grayscale value difference at the sub-pixel precision, performing a nonlinear normalization operation based on response consistency on the difference value, wherein the nonlinear normalization operation uses the angle consistency between the main direction vector of the tensor unit of the pixel and the direction vector of its neighborhood in the direction perception tensor field as an adjustment factor to suppress the response error in the direction inconsistent area and improve the robustness of the structural response map in terms of spatial continuity; In the process of constructing the direction-enhanced response map, a structural density weighting term is further introduced into the response value of each pixel in the direction-enhanced response map. The structural density weighting term is based on the pixel value of the pixel in the structure-sensitive function map and the local statistical distribution of its gradient direction, and is used to adjust the response balance between the high-frequency area and the low-texture area of ​​the image, so as to prevent the response value of the edge details from being excessively amplified by noise; When fusing all directional enhancement response maps to form the main directional enhancement response map that integrates all-angle information, a structural consistency mask is introduced as the masking factor of the angle weighting function. The structural consistency mask is constructed according to the consistency of the response trend of each pixel in the directional enhancement response map under multiple incident angles, and only assigns high weights to areas with highly consistent response trends, thereby improving the reliability of directional recognition of the fused image in complex texture areas.

Images