Image compression and reconstruction system based on matrix singular value decomposition

Abstract

The application discloses an image compression and reconstruction system based on matrix singular value decomposition, and relates to the technical field of image processing, comprising: a feature extraction module: used for acquiring a to-be-processed image and extracting an inertia tensor thereof, determining a global principal axis direction of the image according to the inertia tensor, mapping the to-be-processed image to a fractional order transform domain, and acquiring an initial fractional order matrix; an alignment decomposition module: used for generating a rotation compensation operator according to the global principal axis direction, and performing singular value decomposition on the initial fractional order matrix by using the rotation compensation operator to obtain a left singular vector set, a singular value matrix and a right singular vector set; and a feature compression module: used for performing compression processing on the singular value matrix to retain core components; the application has the beneficial effects that the most distortion-resistant projection plane can be adaptively found, and high-proportion and high-geometric-consistency reconstruction of a rotating image is realized at a low code rate.

Description

Technical Field

[0001] This invention relates to the field of image processing technology, and in particular to an image compression and reconstruction system based on matrix singular value decomposition. Background Technology

[0002] This invention relates to the fields of digital signal processing and computer vision technology, specifically to an image compression and reconstruction system based on matrix singular value decomposition. With the rapid development of ultra-high-definition video and high-precision remote sensing image technology, the amount of image data is growing explosively. How to achieve high-ratio image compression and maintain high-quality reconstruction under extremely low bandwidth has become a hot research topic in the industry. Matrix singular value decomposition (SVD), as an important algebraic decomposition method, is widely used in the fields of image dimensionality reduction, denoising and compression because it can extract the core feature energy of the image matrix.

[0003] However, existing image processing schemes based on singular value decomposition (SVD) have significant limitations when facing complex geometric transformations (especially rotational transformations). Traditional SVD compression methods typically perform energy truncation within a fixed spatial domain or standard frequency domain, lacking the ability to perceive the image's own geometric topology. When the image to be processed has angular deviations or is in an unsteady projection space, simple singular value energy filtering can lead to obvious geometric distortions such as jagged edges and texture misalignment in the reconstructed image. More importantly, the feedback adjustment mechanisms of existing technologies mostly only involve fine-tuning the compression ratio (the number of singular values ​​retained) in a single dimension, failing to fundamentally correct structural distortions caused by improper selection of the mathematical projection plane. This "black box" unidirectional compression process makes it difficult for the system to adaptively find the optimal transformation operator that balances compression efficiency and geometric fidelity under different rotational orientations and complex texture environments, thus limiting the application of image compression technology in precision medical imaging and high-robustness transmission scenarios. Summary of the Invention

[0004] In view of the above-mentioned prior art, this application is hereby proposed. Embodiments of this application provide an image compression and reconstruction system based on matrix singular value decomposition, which can maintain extremely high geometric fidelity and effectively solve the problem of blurred edges of key lesions in medical images.

[0005] According to one aspect of this application, an image compression and reconstruction system based on matrix singular value decomposition is provided, comprising:

[0006] Feature extraction module: used to acquire the image to be processed and extract its inertial tensor, determine the global principal axis direction of the image based on the inertial tensor, map the image to be processed to the fractional transformation domain, and obtain the initial fractional matrix;

[0007] Alignment decomposition module: used to generate a rotation compensation operator based on the global principal axis direction, and use the rotation compensation operator to perform singular value decomposition on the initial fractional matrix to obtain a left singular vector set, a singular value matrix and a right singular vector set;

[0008] Feature compression module: used to compress the singular value matrix to retain the core components, and to construct a compressed bitstream by combining the left singular vector set and the right singular vector set;

[0009] Reconstruction evaluation module: used to perform inverse transformation on the compressed bitstream to restore the image, obtain the reconstructed image, calculate the geometric structure entropy of the reconstructed image relative to the image to be processed, and obtain the geometric distortion index;

[0010] Judgment module: used to determine whether the geometric distortion index exceeds a preset threshold;

[0011] If the judgment result is yes, then the transformation order corresponding to the current initial fractional matrix and the rotation angle of the current rotation compensation operator are corrected according to the geometric distortion index feedback. Based on the corrected transformation order and rotation angle, the fractional transformation, singular value decomposition and reconstruction process are re-executed on the current image to be processed until the geometric distortion index reaches the preset requirements.

[0012] If the judgment result is negative, then the current compressed bitstream is determined as the output result.

[0013] Compared with existing technologies, the image compression and reconstruction system based on matrix singular value decomposition according to the embodiments of this application constructs a feedback loop containing the transformation order and rotation compensation angle, enabling the system to dynamically find the mathematical projection plane that best matches the topological features of each image to be processed. This allows the reconstructed image to maintain extremely high geometric fidelity even when facing rotational transformations, effectively solving the problem of blurred edges of key lesions in medical images. Furthermore, it makes the energy distribution of the initial fractional-order matrix more concentrated. Under the same reconstruction quality, this invention can represent more image energy with fewer singular value components, greatly improving the compression ratio and meeting the real-time transmission requirements of medical images in wireless network environments.

[0014] Using geometric entropy as a distortion evaluation index, the system can accurately capture minute changes in the spatial topology of images. Through closed-loop control with preset thresholds, the system can automatically execute a recursive process of "optimization-reconstruction-reevaluation" to ensure that the output compressed bitstream meets the preset robustness standard in the geometric dimension, providing more valuable high-quality reconstructed data for clinical diagnosis. The system employs fractional-order transform and singular vector structure alignment technology, which has natural resistance to noise and angular rotation. Whether it is grayscale ultrasound images or color pathological slide images with complex textures, the system can complete high-quality compression through an adaptive feedback mechanism without manual intervention, demonstrating excellent cross-scenario application performance. Attached Figure Description

[0015] The above and other objects, features, and advantages of this application will become more apparent from the more detailed description of the embodiments of this application in conjunction with the accompanying drawings. The drawings are provided to further illustrate the embodiments of this application and form part of the specification. They are used together with the embodiments of this application to explain this application and do not constitute a limitation thereof. In the drawings, the same reference numerals generally represent the same components or steps.

[0016] Figure 1 This is a schematic diagram of the overall process of the image compression and reconstruction system based on matrix singular value decomposition of the present invention.

[0017] Figure 2 This is a schematic diagram of the compression process of the image compression and reconstruction system based on matrix singular value decomposition of the present invention.

[0018] Figure 3 This is a schematic diagram of the singular value decomposition of the image compression and reconstruction system based on matrix singular value decomposition according to the present invention. Detailed Implementation

[0019] Hereinafter, exemplary embodiments according to this application will be described in detail with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of this application, and not all embodiments of this application. It should be understood that this application is not limited to the exemplary embodiments described herein.

[0020] Reference Figures 1-3 As an embodiment of the present invention, an image compression and reconstruction system based on matrix singular value decomposition is provided, including: a feature extraction module, an alignment decomposition module, a feature compression module, a reconstruction evaluation module, and a judgment module.

[0021] Figure 1 The figure illustrates an image compression and reconstruction system based on matrix singular value decomposition according to an embodiment of this application, including:

[0022] Feature extraction module: used to acquire the image to be processed and extract its inertia tensor, and determine the global principal axis direction of the image based on the inertia tensor;

[0023] Specifically, the system first acquires the image to be processed, which serves as the initial data source for this solution. This image can be digital medical image data generated during medical diagnosis or image sequences with complex texture features used in teaching demonstrations. After acquiring the image, the system extracts its inertia tensor through a feature extraction module. The inertia tensor is a physical mapping quantity that characterizes the spatial distribution and aggregation characteristics of image pixels. In practical implementation, the system treats each pixel of the image to be processed as a mass unit, with pixel coordinates corresponding to its spatial position and pixel grayscale values ​​corresponding to its mass attributes. By performing a second-order central moment operation on all pixels of the image, a second-order square matrix is ​​constructed, which is the inertia tensor. This inertial tensor can eliminate the influence of image translation on geometric description and extract the overall shape distribution features of the image from a statistical perspective. The global principal axis direction refers to the geometric reference direction that can represent the main direction of the image energy distribution. Specifically, the system performs feature decomposition operation on the inertial tensor constructed above and extracts the feature vector corresponding to its maximum feature value. The straight line direction defined by this feature vector in the two-dimensional image space is determined as the global principal axis direction of the image to be processed. This step transforms the abstract image content into directional geometric parameters, providing an objective physical reference for the subsequent generation of rotation compensation operators and structural alignment.

[0024] The image to be processed is mapped to the fractional transform domain to obtain the initial fractional matrix.

[0025] It should be noted that obtaining the initial fractional matrix includes:

[0026] The radial energy distribution features of the image to be processed are extracted. Specifically, the system performs a two-dimensional Fourier transform on the image I(x,y) to the frequency space F(u,v) and calculates the spatial frequency radius. Average energy intensity on the circumference The calculation formula is as follows:

[0027] ;

[0028] in, The spatial frequency radius is The average energy intensity on the circumference, The radius represents the spatial frequency, and its dimension is the reciprocal of the length. The two-dimensional Fourier spectrum function representing the image. Represents the rotation angle in polar coordinates. 0 and 0 represent the upper and lower limits of integration, respectively, in radians;

[0029] The specific formula for calculating the information concentration of radial energy distribution characteristics at different spatial frequencies is as follows:

[0030] ;

[0031] in, For information concentration, Represents a infinitesimal element in the radial direction. This is the maximum spatial frequency cutoff value;

[0032] Based on the energy peak offset of the information concentration on the spatial frequency axis, the initial transform order corresponding to the image to be processed is obtained, and the specific formula is as follows:

[0033] ;

[0034] in, Let the initial transformation order be . The preset baseline image information concentration;

[0035] Within the fractional transform domain, a fractional kernel operator is constructed using the initial transform order, and the image to be processed is convolved with the fractional kernel operator to obtain an initial fractional matrix. This process, through pre-rotation alignment of the mathematical plane, ensures that the image features are in the most energy-concentrated projection state before entering singular value decomposition, thereby achieving the preset robustness requirements with a faster convergence speed in subsequent reconstruction evaluation and feedback.

[0036] Alignment decomposition module: used to generate rotation compensation operators based on the global principal axis direction. The core of this step is to transform the physical geometric pose of the image into a mathematical transformation matrix, thereby aligning the image features with the decomposition basis vectors. The specific implementation is as follows;

[0037] Calculate the angular displacement between the global principal axis direction and the preset reference axis to determine the target rotation angle; construct a two-dimensional rotation transformation matrix with orthogonal constraint characteristics based on the target rotation angle, as the rotation compensation operator; wherein, the rotation compensation operator is used to correct the set of singular vectors obtained by the initial fractional matrix to an orthogonal coordinate system aligned with the global principal axis by performing rotation mapping on the projected basis vectors when performing singular value decomposition on the initial fractional matrix;

[0038] After determining the global principal axis direction of the image to be processed, the system calculates the angle between this principal axis direction and a preset reference axis (usually the horizontal X-axis or vertical Y-axis of the image coordinate system) through the alignment decomposition module, thus obtaining the target rotation angle. To achieve geometric consistency in the subsequent singular value decomposition process, the system is based on the target rotation angle. The rotation compensation operator is constructed, and the specific formula is as follows:

[0039] ;

[0040] in, For rotation compensation operator, it is a An orthogonal matrix is ​​used to perform rotation transformations on coordinate space or matrix basis vectors;

[0041] The technical function of this rotation compensation operator is that it mathematically records the random rotation deviation generated during the image acquisition process. In subsequent steps, by applying the rotation compensation operator to the singular value decomposition process of the initial fractional matrix, the singular vectors generated by the decomposition can be "corrected" to the standard coordinate system consistent with the global principal axis. This processing method ensures that even if the same target is photographed at different angles, the feature vectors extracted by the system can maintain the consistency of the topological structure after being adjusted by the rotation compensation operator, thus effectively solving the reconstruction distortion problem caused by rotation in the existing technology.

[0042] The initial fractional matrix is ​​decomposed into singular values ​​using a rotation compensation operator to obtain the left singular vector set, the singular value matrix, and the right singular vector set.

[0043] It should be noted that the singular value decomposition of the initial fractional matrix includes:

[0044] An orthogonal basis alignment transformation is performed on the initial fractional matrix using a rotation compensation operator to align the energy distribution axis of the initial fractional matrix with the global principal axis. It should be noted that the orthogonal basis alignment transformation refers to rotating the mathematical basis vectors of the initial fractional matrix to a coordinate system consistent with the physical principal axis of the image through matrix mapping. Specifically, let the initial fractional matrix be A, and the specific formula for the transformed target matrix is ​​as follows:

[0045] ;

[0046] in, To perform the orthogonal basis alignment transformation on the target matrix, a rotation compensation operator is used. The active compensation cancels out the random rotation of the image during acquisition, so that the energy distribution axis (mathematical feature direction) of the aligned target matrix A' coincides with the global principal axis direction (physical geometric direction) in mathematical expression;

[0047] Under the constraint of satisfying the global principal axis direction, it should be noted that satisfying the constraint of satisfying the global principal axis direction means that during the decomposition process, the direction domain of the left singular vector must be located in the orthogonal space defined by the global principal axis. Singular value decomposition is performed on the transformed initial fractional matrix (i.e., the aligned target matrix A') to obtain the set of left singular vectors, the singular value matrix, and the set of right singular vectors. The decomposition formula is as follows:

[0048] ;

[0049] in, Let be a set of left singular vectors, whose column vectors form an orthogonal basis that satisfies the global principal axis direction constraints. Let be a singular value matrix, and let be a diagonal matrix whose diagonal elements are singular values ​​arranged in descending order. For the set of right singular vectors, Let be the transpose of the right singular vector set.

[0050] In this embodiment, by transforming the originally blind mathematical decomposition process into a controlled decomposition with geometric prior constraints, since the singular vector set is extracted in the aligned space, this ensures that even if the same image to be processed is rotated, the compressed bitstream generated by the system still has a high degree of structural consistency, thereby significantly reducing the feedback correction pressure of subsequent geometric distortion indicators.

[0051] Feature compression module: This module compresses the singular value matrix to retain its core components and combines the left and right singular vector sets to construct a compressed bitstream. The core of this step is to achieve data dimensionality reduction through energy filtering and integrate the scattered feature matrices into a standardized transmission format. The specific implementation is as follows:

[0052] First, the singular value matrix is ​​compressed to retain its core components. Given a diagonal matrix, the elements on its diagonal are... (Singular values) are arranged in descending order and represent the energy intensity of the image in different feature dimensions. Preserving the core components means setting an energy contribution rate threshold to retain only the top k largest singular values, while setting the remaining smaller singular values ​​to zero or discarding them. To determine the optimal number of singular values ​​to retain, k, the system calculates the cumulative contribution rate, using the following formula:

[0053] ;

[0054] in, For cumulative contribution rate, Let be the i-th singular value in the singular value matrix, k be the number of core components retained, and n be the total number of singular values;

[0055] Secondly, a compressed bitstream is constructed by combining the left singular vector set, the right singular vector set, and the compressed singular values. The compressed bitstream refers to a binary data stream encapsulated according to a preset protocol, which can be used for storage or transmission. In specific implementation, the system extracts the first k columns of the left singular vector set U, denoted as... Extract the first k columns of the right singular vector set V, denoted as and the vector consisting of the k singular values ​​that are retained. The system encapsulates the above data according to specific serialization rules, as follows:

[0056] ;

[0057] in, For the final generated compressed bitstream, This is the bitstream header information, including image size and data offset. It is a cyclic redundancy check code used for error correction during transmission.

[0058] The reconstruction evaluation module is used to perform an inverse transform on the compressed bitstream to restore the image and obtain the reconstructed image. The specific implementation is as follows;

[0059] The system parses the received compressed bitstream and extracts the filtered core components, left singular vector set, right singular vector set, transform order, and rotation compensation operator. It backfills the core components based on their index positions in the original singular value set and sets the non-core component positions to zero, thereby reconstructing the compressed singular value matrix. Then, it performs matrix multiplication using the left singular vector set, the reconstructed singular value matrix, and the transpose of the right singular vector set to obtain the preliminary restored matrix in the transform domain. Next, it multiplies the transpose of the rotation compensation operator (i.e., the inverse rotation matrix) with the preliminary restored matrix to cancel the angle compensation applied in the decomposition stage, allowing the matrix features to return to their original orientation in the coordinate space. Finally, based on the extracted transform order, it performs a negative fractional-order transform of the corresponding order on the phase-decoupled matrix. Since fractional-order transforms satisfy the additive law at the operator level, by applying an inverse transform in the opposite direction to the encoding stage, the system reprojects the image features from the fractional-order domain back to the original spatial geometric domain and outputs the reconstructed image.

[0060] Calculate the geometric structure entropy of the reconstructed image relative to the image to be processed to obtain the geometric distortion index;

[0061] The geometric distortion indices are obtained, including:

[0062] Feature probability distribution mappings of the image to be processed and the reconstructed image in the fractional transform domain are constructed respectively. A kernel density estimation algorithm is used to extract the first structural probability density of the image to be processed on the local feature manifold, and the second structural probability density of the reconstructed image on the local feature manifold. The relative structural information gain of the reconstructed image relative to the image to be processed is calculated based on the first and second structural probability densities, using the following formula:

[0063] ;

[0064] in, For relative structural information gain, The first structure probability density, This represents the probability density of the second structure.

[0065] By combining the relative structural information gain with the joint probability distribution of the edge gradient direction, a geometric structure entropy function is constructed, and the geometric structure entropy is calculated.

[0066] It should be noted that the construction of the geometric structure entropy function includes:

[0067] Calculate the tangent space mapping of the first structure probability density and the second structure probability density in the feature manifold space, and obtain the geodesic distance of the tangent space mapping in the edge gradient direction;

[0068] An exponential evolution operator with respect to relative structural information gain is constructed based on geodesic distance to extract curvature perturbation factors;

[0069] The construction of the exponential evolution operator includes:

[0070] The Riemannian metric correction coefficients for the manifold space are determined based on the energy distribution ratio of the singular values ​​in the singular value matrix, using the following formula:

[0071] ;

[0072] in, This represents the Riemann metric correction coefficient. The argument for the singular value index, The upper limit for truncation of singular values. The index of all components in the singular value matrix is ​​represented by the index argument. The total order of the singular value matrix is ​​. Let i be the i-th singular value in the singular value matrix. Let j be the j-th singular value in the singular value matrix;

[0073] Using Riemannian metric correction factors to determine geodesic distance Perform scaling to construct a dynamic mapping basis. (Right now Using the dynamic mapping basis as the exponential parameter, an exponential power-law transformation is performed on the relative structural information gain to generate an exponential evolution operator (i.e., curvature perturbation factor), the specific formula of which is as follows:

[0074] ;

[0075] in, For exponential evolution operators;

[0076] A functional convolution mapping of the measure space is performed on the curvature perturbation factor and the joint probability distribution to obtain the geometric structure entropy function. The geometric structure entropy is then used to quantify the structural integrity of the reconstructed image under rotation and scaling transformations, yielding the geometric distortion index, as shown in the following formula:

[0077] ;

[0078] in, Indicates geometric distortion index, For geometric structure entropy, This represents the joint probability distribution of the edge gradient directions. Represents local measure variables in the manifold space. This represents the global extent of the defined local feature manifold. Represents the differential measure element of the manifold space.

[0079] Judgment module: Used to determine whether the geometric distortion index exceeds the preset threshold.

[0080] Preset threshold The determination process for whether the geometric distortion index of the reconstructed image meets the standard is as follows:

[0081] The system first selects a set of calibration images with standard geometric structures as reference samples. Under initial transformation order and rotation angle, it performs a compression reconstruction process. The system determines the upper limit of acceptable physical parameters such as edge position error and angular deviation in the reconstructed image through manual evaluation or reference to high-precision measurements. The system then calculates the geometric entropy of the reconstructed image relative to the original image under this upper limit condition, obtaining the baseline index distribution and setting a preset threshold. The calculation formula is as follows:

[0082] ;

[0083] in, Let be the mean geometric entropy of the baseline sample set under qualified reconstruction conditions. The standard deviation of the geometric entropy of the benchmark sample set. For the mean operator, For the standard deviation operator, It is the set of geometric entropy of the benchmark sample set.

[0084] If the judgment result is yes, then the transformation order (i.e., the initial transformation order P) corresponding to the current initial fractional matrix and the rotation angle of the current rotation compensation operator are corrected according to the geometric distortion index feedback. Based on the corrected transformation order and rotation angle, the fractional transformation, singular value decomposition and reconstruction process are re-executed on the current image to be processed until the geometric distortion index reaches the preset requirements.

[0085] It should be noted that the corrections to the transformation order (i.e., the initial transformation order P) and the rotation angle include:

[0086] Based on the partial derivatives of the geometric distortion index with respect to the transformation order and rotation angle, a distortion gradient mapping matrix is ​​constructed.

[0087] Furthermore, regarding the construction of the distortion gradient mapping matrix, since there is an implicit nonlinear mapping between the image geometric entropy and the transformation parameters, the system cannot directly derive it analytically. Therefore, while keeping the current input image unchanged, the system establishes two virtual detection branches, including:

[0088] A first small perturbation is applied to the current transformation order, and a second small perturbation is applied to the current rotation angle. The geometric entropy variable of the reconstructed image under the perturbation state is then obtained. Specifically:

[0089] The first detection branch applies a small perturbation to the current transformation order p. The reconstructed image under the first perturbation state is obtained by performing fractional-order transformation, singular value decomposition, and inverse transformation; the second detection branch detects the current rotation angle. Apply a second small perturbation By updating the rotation compensation operator The decomposition and reconstruction process is then re-executed to obtain the reconstructed image under the second perturbation state;

[0090] Calculate the geometric structure entropy of the reconstructed image relative to the original image under each of the two perturbation states to obtain the geometric structure entropy variable. Specifically, denote the entropy value under the current state as... The corresponding geometric structure entropy variables are as follows:

[0091] and ;

[0092] The first rate of change of the geometric structure entropy variable relative to a first small perturbation and the second rate of change relative to a second small perturbation are calculated. It should be noted that the first and second rates of change are used to characterize the sensitivity of the geometric distortion index to parameter changes. The specific formulas are as follows:

[0093] ;

[0094] ;

[0095] in, Let be the first rate of change of the geometric structure entropy variable relative to the first small perturbation. Let be the second rate of change of the geometric structure entropy variable relative to the second small perturbation. for , Let be the geometric entropy variable under the action of the second small perturbation;

[0096] Based on the first rate of change Second rate of change Construct a distortion gradient mapping matrix that characterizes the correlation between spatial projection stability and geometric distortion. ;

[0097] The total correction energy is determined using the distortion gradient mapping matrix, which is determined by the current geometric distortion index S. Based on the weighted distribution of the influence of transformation order and rotation angle on geometric distortion, the total correction energy is allocated to the first correction step size of the transformation order and the second correction step size of the rotation compensation operator, as shown in the following formula:

[0098] ;

[0099] ;

[0100] in, The first correction step size is the transformation order. This is the second correction step size for the rotation compensation operator. For total correction energy, ;

[0101] Incremental compensation is performed on the current transform order based on the first correction step size, and phase correction is performed on the current rotation angle simultaneously based on the second correction step size, generating a new set of updated parameters. Subsequently, the system triggers a recursive processing mechanism, using the updated parameter set to restart the compression and reconstruction process on the original image to be processed. The specific implementation is as follows:

[0102] The system utilizes the corrected rotation angle Regenerate the rotation compensation operator and combine it with the corrected transformation order. A new round of fractional-order transform and controlled singular value decomposition is performed on the image to be processed. Since the order of the transform plane and the rotation compensation angle have been finely adjusted according to the gradient feedback of the previous round, the newly generated singular value matrix will better fit the physical principal axis of the image in terms of energy distribution, while the left and right singular vector sets will have stronger geometric and topological robustness. Then, the system performs an inverse transform on the newly generated compressed bitstream to obtain a new round of reconstructed image, and recalculates the geometric distortion index of the reconstructed image relative to the image to be processed. ;

[0103] The system uses built-in loop judgment logic to determine the current geometric distortion index. With preset threshold Perform real-time comparison: If This indicates that the current reconstruction quality has not yet reached the preset geometric fidelity standard. The system will maintain the current iteration state and continue with this iteration. The aforementioned distortion gradient mapping matrix construction and step size allocation process is triggered again based on the baseline, entering the next round of iterative correction; if If the geometric consistency of the reconstructed image has met the expected requirements, the system will terminate the iteration and determine the current compressed bitstream as the final output result.

[0104] In this process, the judgment logic for determining whether the geometric distortion index reaches the preset requirements can be based not only on the absolute threshold, but also by introducing the convergence slope. As an auxiliary criterion, the specific formula is as follows:

[0105] ;

[0106] in, This represents the improvement in geometric distortion between two adjacent iterations (i.e., the convergence slope). Let represent the geometric distortion index obtained in the t-th iteration. For the first The geometric distortion index obtained in the second iteration; this invention transforms the image compression process from the traditional open-loop unidirectional mapping to closed-loop parameter evolution. This index-driven repetitive execution mechanism ensures that the system can automatically lock the most suitable transformation order and rotation angle for the specific geometric distribution of each image to be processed. This depth adaptive capability enables the system to maintain extremely high reconstruction fidelity when processing medical images with large-angle rotation or complex deformation, effectively solving the structural distortion problem caused by fixed compression parameters in the prior art.

[0107] If the judgment result is negative, the current compressed bitstream is determined as the output result; at this time, the system determines the current transform order p and rotation angle. The optimal (or suboptimal) matching state has been achieved through feedback correction. The geometric topology of the reconstructed image has been accurately restored to the original image within the allowable error range. The system then stops iterative calculation and determines the compressed bitstream containing the core components generated in the current iteration cycle as the final output result.

[0108] The adaptive feedback correction scheme for transform order and rotation angle in this application is based on the introduction of a closed-loop adjustment mechanism from control theory. This transforms image compression from a traditional open-loop unidirectional mapping to parameter evolution driven by indices. Since there is an implicit nonlinear mapping between the geometric topological features of complex images such as medical images and compression parameters, the system cannot directly obtain the optimal solution through analytical methods. Therefore, the embodiments of this application adopt a gradient optimization strategy based on numerical detection. Its technical advantage is that it can automatically lock the most suitable transform order and rotation angle for the specific geometric distribution of each image to be processed. While ensuring an extremely high compression ratio, it restores the key geometric features of the image such as edges and textures to the maximum extent, solving the reconstruction distortion problem caused by parameter fixation in the prior art.

[0109] For example, suppose the object currently being processed by this system is a set of rotational medical CT image data containing the edges of minute lesions. In the initial stage (the first... (in the second iteration), the system obtains the initial transformation order based on the preliminary feature extraction. And the initial rotation compensation angle After completing the first round of reconstruction, the reconstruction evaluation module calculates the geometric distortion index. This value is significantly higher than the preset threshold. This triggers the feedback and correction process;

[0110] During the detection phase, the system uses two virtual detection branches to acquire gradient information: the first detection branch applies a small perturbation to the transformation order. A decrease in geometric entropy was observed, and the first rate of change was calculated. The second detection branch applies a second small perturbation to the rotation angle. An increase in geometric entropy was observed, and the second rate of change was calculated. The distortion gradient mapping matrix constructed based on the aforementioned rate of change shows that increasing the order p has a positive contribution to reducing distortion, while the current angle Over-compensation exists;

[0111] During the allocation and correction phase, the system adjusts the total correction energy. (From the current) (Decision) Perform weight calculation to obtain the first correction step size. Second correction step size The parameters are then updated to ;

[0112] Entering the second iteration (the After one iteration, the system re-executes the fractional-order transform and controlled singular value decomposition using the updated parameters. At this point, the geometric distortion index of the reconstructed image is reduced to [a value missing]. The system further calculates the convergence slope. This indicates that the corrected parameters significantly improved the reconstruction quality. At this point, due to If the termination condition is met, the system will stop iterating and output the compressed bitstream generated based on the optimal parameter alignment as the final result. Through the above closed-loop operation, this invention replaces the computationally intensive exhaustive grid search method and the poorly adaptable fixed parameter method, and achieves the optimal balance between reconstruction quality and computational efficiency.

[0113] like Figure 2 As shown, this application further proposes a compression process for the singular value matrix to retain core components, which also includes:

[0114] The set of singular values ​​is obtained from the singular value matrix. The set of singular values ​​is:

[0115] This refers to the diagonal matrix The set of all diagonal elements extracted represents the energy amplitude of the image signal in each decomposition dimension;

[0116] Based on the left singular vector set and the right singular vector set, the geometric structure contribution of each singular value in the singular value set is calculated. It should be noted that the geometric structure contribution refers to the importance index of a specific singular value component for maintaining the geometric topological features of the image (such as edges and contours).

[0117] Specifically, the acquisition of geometric contribution includes:

[0118] Construct the corresponding orthogonal basis space projection using the left and right singular vector sets, and calculate the rate of change of spatial curvature of each singular value in the singular value set under the orthogonal basis space projection. The specific formula is as follows:

[0119] ;

[0120] in, Let be the spatial curvature change rate matrix corresponding to the i-th singular value. The Laplacian operator is used to extract second-order differential features, i.e., curvature features. Let be the i-th left singular vector, and be a column vector. For the i-th singular value, Let be the transpose of the i-th right singular vector, and be a row vector;

[0121] Extract the local edge gradient vector G from the image to be processed, calculate the cosine similarity between the rate of change of spatial curvature and the local edge gradient vector, and determine the cosine similarity as the geometric structure contribution of the corresponding singular value. The specific formula is as follows:

[0122] ;

[0123] in, The geometrical contribution of the i-th singular value. The inner product operation represents the rate of change of spatial curvature κi and the local edge gradient vector G. Rate of change of spatial curvature The Frobenius norm, Let G be the magnitude of the local edge gradient vector; by comparing the overlap between the component curvature direction and the original edge gradient direction, the singular value components that play a key supporting role in the image structural features are identified.

[0124] Generate geometric energy distribution sequence ;

[0125] Based on the geometric energy distribution sequence, singular values ​​in the singular value set are filtered, and singular values ​​with a contribution higher than a preset geometric energy threshold are retained to form core components. The specific implementation is as follows:

[0126] The system is pre-set with a geometric energy threshold. The geometric energy threshold As a boundary condition for determining whether singular value components possess critical topological support, their value range is typically set between [0.6, 0.95]. The specific value is determined by the edge complexity requirements of the image. The system extracts the indices of all singular values ​​that satisfy the determination condition by traversing the geometric energy distribution sequence.

[0127] ;

[0128] in, This represents the set of core component indices to be retained. Indicates the order index of the singular value;

[0129] Subsequently, the system uses the core component index set From the original singular value set Extract the corresponding elements to form the core components. In this screening process, the system does not simply truncate and eliminate outliers based on their magnitude. Instead, it dynamically retains outliers based on the goodness of fit of each component to the local edge gradient of the image, even if a certain outlier is removed. The value is small, but if its corresponding geometric structure contribution is small... Higher than This indicates that the component carries subtle but crucial geometric texture information in the image (such as the boundary of a small lesion in a medical image), and the system will still classify it as a core component and retain it. Finally, the system will select the core components. Fill in the corresponding positions of the diagonal matrix and set the non-core component positions to zero to generate the compressed singular value matrix. Through this adaptive screening mechanism based on geometric contribution, the present invention can accurately lock the geometric skeleton information required for image reconstruction while eliminating a large amount of redundant background noise.

[0130] It should be noted that the geometric energy threshold The process for determining singular value components that provide core topological support is as follows:

[0131] The system determines the threshold by analyzing the correlation distribution between the image gradient field and the rate of change of spatial curvature. The system first considers the geometric contribution of the singular value components. The images are sorted in descending order to construct a cumulative contribution curve. The inflection point of the cumulative contribution curve is then identified; that is, when the increase in image edge energy begins to significantly decrease after adding a certain singular component, the contribution value corresponding to that point is used as the initial reference value. To balance detail preservation and bandwidth constraints in medical images, a geometric energy threshold is used. The final formula is as follows:

[0132] ;

[0133] in, Here, m represents the preset fidelity weighting coefficient, and m represents the total number of components included when the cumulative contribution reaches 90% in the initial screening state. The geometric structural contribution of the i-th singular value is calculated by statistically analyzing the average contribution level of most structural components in the image and using a fidelity weighting coefficient. The rigor of the screening process can be dynamically adjusted; when dealing with extremely detailed pathological sections, the rigor can be increased. improve This is done to force the retention of more singular value components with high similarity, ensuring the absolute integrity of geometric features.

[0134] The core idea of ​​the scheme for compressing singular value matrices to retain core components in this application is to upgrade traditional energy-driven compression to geometry-semantics-driven compression. In conventional singular value decomposition, small singular values ​​are usually considered to represent noise or redundancy. However, in scenarios such as medical imaging where geometric topology requirements are extremely high, large singular values ​​often only represent the energy of smooth background regions, while the information that truly carries key geometric features such as lesion edges and fine blood vessels is often hidden in low-energy components.

[0135] Therefore, this embodiment constructs the rate of change of spatial curvature under orthogonal basis spatial projection. Furthermore, it performs an inner product operation with the local edge gradient vector G of the original image to obtain cosine similarity, thereby establishing a geometric structure contribution evaluation system that transcends the magnitude of singular values. The technical advantage of this operation is that it breaks the inherent limitation of thinking that large values ​​are equivalent to important features in linear space. By comparing the directionality of second-order differential features (curvature), it identifies the singular value components that play a key supporting role in the image structure features, ensuring that the geometric skeleton of the image is accurately preserved under extremely high compression ratios. Compared with traditional global hard threshold truncation techniques or information entropy-based compression techniques, this scheme adaptively calibrates the geometric energy threshold. This achieves deep preservation of geometric details while eliminating redundant background noise;

[0136] For example, suppose the object being processed by this system is a mammogram containing microcalcifications. After performing singular value decomposition, the system obtains a set of singular values. This includes components with larger values ​​(such as...) (representing the smoothed background area) and smaller components (such as...) (representing the edge of a microcalcification point).

[0137] During the contribution acquisition phase: for large amounts The system calculates its rate of change of spatial curvature. It was found that its distribution was relatively flat, and its cosine similarity (i.e., geometric contribution) to the local edge gradient vector G was only [missing information]. For small portions Although its energy amplitude is small, its rate of change of spatial curvature is... The calcification point region exhibits characteristics highly consistent with the original gradient, and its geometric contribution is calculated to be... ;

[0138] In the threshold calibration and screening stage: the system analyzes the inflection point of the cumulative contribution curve, combined with the fidelity weighting coefficient. Determine the current geometric energy threshold. According to the filtering rules: because , quantity It was determined to be a non-core component, and because , quantity Precisely locked and stored in the core component index set ;

[0139] Ultimately, the system will include The core components, including those in the image, are backfilled into the diagonal matrix, while high-energy background or noise components that do not provide structural support are set to zero. The reconstruction results show that, compared with the traditional compression method that truncates by numerical value, the calcification point outlines reconstructed by this method are clearer, and the edge sharpness is fully preserved, which significantly improves the clinical diagnostic value of compressed images.

[0140] like Figure 3 As shown, this application further proposes singular value decomposition of the initial fractional matrix, and also includes:

[0141] The gradient field of the image to be processed is obtained, and the local orientation field representing the local geometry of the image is calculated based on the gradient field. It should be noted that the gradient field refers to the set of vectors representing the changes in the gray values ​​of image pixels in the spatial dimension. The system calculates the first-order partial derivatives of the image I(x,y) in the horizontal and vertical directions. and To construct, local directional field This reflects the microscopic direction of the image's internal texture and edges. The specific formula is as follows:

[0142] ;

[0143] in, Let be the local orientation angle of the image at pixel (x, y). These represent the gradient components of the image in the horizontal and vertical directions, respectively;

[0144] Calculate the angular deviation field between the local direction field and the global principal axis direction, and generate a local geometric weight matrix based on the angular deviation field. It should be noted that the angular deviation field... To quantify the deviation of local texture from the overall image pose, the system utilizes local orientation fields. With respect to the aforementioned determined global principal axis direction Performing the difference operation yields:

[0145] Subsequently, the system constructs a local geometric weight matrix W based on the angle deviation field, with the specific formula as follows:

[0146] ;

[0147] in, Let be the weight values ​​of the local geometric weight matrix at coordinates (x, y). W represents the angular deviation between the local direction and the global principal axis. W is a dimensionless matrix whose values ​​are distributed in the interval (0,1]. Physically, when the local direction is more consistent with the global principal axis, the weight is closer to 1, and vice versa, the weight is reduced, which plays a role in suppressing local distortion interference.

[0148] The local geometric weight matrix is ​​applied to the initial fractional matrix to obtain the target matrix after local geometric pre-compensation. Specifically, the system performs a Hadamard product (element-wise multiplication) operation between the initial fractional matrix A and the local geometric weight matrix W to obtain the target matrix. This step, through weight allocation, suppresses noise or local distortion components that do not conform to global geometric features in the transform domain in advance, so that the matrix energy is further aligned with the global principal axis.

[0149] Using rotation compensation operators on the target matrix Performing singular value decomposition yields the left singular vector set, the singular value matrix, and the right singular vector set, as shown in the following formula:

[0150] ;

[0151] For the set of left singular vectors, It is a singular value matrix. For the set of right singular vectors, Let be the transpose of the right singular vector set;

[0152] The extended implementation scheme for singular value decomposition of the initial fractional matrix in this application is based on the core concept of introducing microscopic geometric consistency to pre-verify and intervene in the global decomposition process. In conventional fractional singular value decomposition, the system often relies solely on the global principal axis direction for overall rotation and alignment. However, when processing images containing complex textures or local nonlinear distortions, the local texture orientation (microscopic) within the image may deviate significantly from the overall image pose (macroscopic). This is addressed by calculating the local orientation angle Φ(x,y) of each pixel relative to the global principal axis direction. The bias is used to identify structural outliers that do not conform to global geometric features. A local geometric weight matrix W, obtained by mapping the angular bias field ΔΦ(x,y), is used to perform a Hadamard product operation on the initial fractional matrix. Essentially, this is a geometric filtering step before singular value decomposition. Through this local pre-compensation mechanism, the target matrix is ​​forced to conform to the geometric weight matrix. The energy distribution further converges towards the global principal axis;

[0153] It can automatically suppress non-uniform components caused by sensor noise or local scanning distortion, so that the left and right singular vector sets obtained by decomposition are... , It can more purely characterize the global topological skeleton of an image without being disturbed by local disordered textures, achieving a leap from coarse alignment to fine compensation; by pre-assigning weights in the transform domain, the generated singular value matrix is ​​made more efficient. It has a higher energy concentration, thus enabling higher quality image reconstruction with fewer core components in the subsequent feature compression stage;

[0154] In terms of technological alternatives, this solution can effectively replace the following existing technologies: First, it replaces the traditional "global rotation windowing" technique. Traditional windowing methods often use fixed Gaussian or rectangular windows, which cannot be dynamically adjusted according to the actual texture direction inside the image. This solution achieves on-demand weighting through the angle deviation field. Second, it replaces complex nonlinear geometric correction preprocessing algorithms. Existing nonlinear correction usually involves a large amount of coordinate resampling, which easily introduces calculation errors and interpolation noise. This solution directly achieves geometric enhancement at the matrix operator level through weight mapping, which not only ensures the linearity and simplicity of calculation, but also avoids secondary damage to the original pixel data. This pre-compensation mechanism based on orientation field guidance provides a solid operator foundation for high-fidelity compression of rotated medical images.

[0155] The basic principles of this application have been described above with reference to specific embodiments. However, it should be noted that the advantages, benefits, and effects mentioned in this application are merely examples and not limitations, and should not be considered as essential features of each embodiment of this application. Furthermore, the specific details disclosed above are for illustrative and facilitative purposes only, and are not limitations. These details do not restrict the application from being implemented using the specific details described above.

[0156] The block diagrams of devices, apparatuses, devices, and systems involved in this application are merely illustrative examples and are not intended to require or imply that they must be connected, arranged, or configured in the manner shown in the block diagrams. As those skilled in the art will recognize, these devices, apparatuses, devices, and systems can be connected, arranged, and configured in any manner. Words such as “comprising,” “including,” “having,” etc., are open-ended terms meaning “including but not limited to,” and are used interchangeably with them. The terms “or” and “and” as used herein refer to the terms “and / or,” and are used interchangeably with them unless the context clearly indicates otherwise. The term “such as” as used herein refers to the phrase “such as but not limited to,” and is used interchangeably with it.

[0157] It should also be noted that in the apparatus, equipment, and methods of this application, the components or steps can be disassembled and / or recombined. These disassemblies and / or recombinations should be considered as equivalent solutions of this application.

[0158] The above description of the disclosed aspects is provided to enable any person skilled in the art to make or use this application. Various modifications to these aspects will be readily apparent to those skilled in the art, and the general principles defined herein can be applied to other aspects without departing from the scope of this application. Therefore, this application is not intended to be limited to the aspects shown herein, but rather to be accorded the widest scope consistent with the principles and novel features disclosed herein.

[0159] The above description has been given for purposes of illustration and description. Furthermore, this description is not intended to limit the embodiments of this application to the forms disclosed herein. Although numerous exemplary aspects and embodiments have been discussed above, those skilled in the art will recognize certain variations, modifications, alterations, additions, and sub-combinations thereof.

Claims

1. An image compression and reconstruction system based on matrix singular value decomposition, characterized in that, include: Feature extraction module: used to acquire the image to be processed and extract its inertial tensor, determine the global principal axis direction of the image based on the inertial tensor, map the image to be processed to the fractional transformation domain, and obtain the initial fractional matrix; Alignment decomposition module: used to generate a rotation compensation operator based on the global principal axis direction, and use the rotation compensation operator to perform singular value decomposition on the initial fractional matrix to obtain a left singular vector set, a singular value matrix and a right singular vector set; Feature compression module: used to compress the singular value matrix to retain the core components, and to construct a compressed bitstream by combining the left singular vector set and the right singular vector set; Reconstruction evaluation module: used to perform inverse transformation on the compressed bitstream to restore the image, obtain the reconstructed image, calculate the geometric structure entropy of the reconstructed image relative to the image to be processed, and obtain the geometric distortion index; Judgment module: used to determine whether the geometric distortion index exceeds a preset threshold; If the judgment result is yes, then the transformation order corresponding to the current initial fractional matrix and the rotation angle of the current rotation compensation operator are corrected according to the geometric distortion index feedback. Based on the corrected transformation order and rotation angle, the fractional transformation, singular value decomposition and reconstruction process are re-executed on the current image to be processed until the geometric distortion index reaches the preset requirements. If the judgment result is negative, then the current compressed bitstream is determined as the output result.

2. The image compression and reconstruction system based on matrix singular value decomposition according to claim 1, characterized in that, The compression process of the singular value matrix to retain core components also includes: Obtaining the set of singular values ​​based on the singular value matrix; Based on the left singular vector set and the right singular vector set, calculate the geometric structure contribution of each singular value in the singular value set to generate a geometric energy distribution sequence. Based on the geometric energy distribution sequence, the singular values ​​in the singular value set are filtered, and the singular values ​​with a contribution higher than the preset geometric energy threshold are retained to form the core components.

3. The image compression and reconstruction system based on matrix singular value decomposition according to claim 2, characterized in that, The acquisition of the geometric structure contribution includes: Construct a corresponding orthogonal basis space projection using the left singular vector set and the right singular vector set, and calculate the rate of change of spatial curvature of each singular value in the singular value set under the orthogonal basis space projection. Extract the local edge gradient vector of the image to be processed, calculate the cosine similarity between the spatial curvature change rate and the local edge gradient vector, and determine the cosine similarity as the geometric structural contribution of the corresponding singular value.

4. The image compression and reconstruction system based on matrix singular value decomposition according to claim 1, characterized in that, The singular value decomposition of the initial fractional matrix further includes: The gradient field of the image to be processed is obtained, and the local orientation field characterizing the local geometry of the image is calculated based on the gradient field. Calculate the angular deviation field between the local direction field and the global principal axis direction, and generate a local geometric weight matrix based on the angular deviation field; Applying the local geometric weight matrix to the initial fractional matrix yields the target matrix after local geometric pre-compensation. The singular value decomposition is performed on the target matrix using the rotation compensation operator to obtain the left singular vector set, the singular value matrix, and the right singular vector set.

5. The image compression and reconstruction system based on matrix singular value decomposition according to claim 1, characterized in that, Corrections for transformation order and rotation angle include: Based on the partial derivatives of the geometric distortion index with respect to the transformation order and rotation angle, a distortion gradient mapping matrix is ​​constructed. The total correction energy is determined using the distortion gradient mapping matrix, and based on the weight distribution of the influence of the transformation order and rotation angle on geometric distortion, the total correction energy is allocated to the first correction step size of the transformation order and the second correction step size of the rotation compensation operator. Incremental compensation is performed on the current transformation order based on the first correction step size, and phase correction is performed on the current rotation angle simultaneously based on the second correction step size.

6. The image compression and reconstruction system based on matrix singular value decomposition according to claim 5, characterized in that, The construction of the distortion gradient mapping matrix includes: A first small perturbation is applied to the current transformation order, and a second small perturbation is applied to the current rotation angle, to obtain the geometric entropy variable of the reconstructed image under the perturbation state; Calculate the first rate of change of the geometric entropy variable relative to the first small perturbation, and the second rate of change relative to the second small perturbation; Based on the first rate of change and the second rate of change, a distortion gradient mapping matrix is ​​constructed to characterize the correlation between spatial projection stability and geometric distortion.

7. The image compression and reconstruction system based on matrix singular value decomposition according to claim 1, characterized in that, The generation of rotation compensation operator includes: Calculate the angular displacement between the global main axis direction and the preset reference axis to determine the target rotation angle; Based on the target rotation angle, a two-dimensional rotation transformation matrix with orthogonal constraint properties is constructed as the rotation compensation operator; wherein, the rotation compensation operator is used to correct the set of singular vectors obtained by the decomposition to an orthogonal coordinate system aligned with the global principal axis by performing rotation mapping on the projected basis vectors when performing singular value decomposition on the initial fractional matrix.

8. The image compression and reconstruction system based on matrix singular value decomposition according to claim 1, characterized in that, The obtained geometric distortion index includes: The feature probability distribution mappings of the image to be processed and the reconstructed image under the fractional transform domain are constructed respectively. The kernel density estimation algorithm is used to extract the first structure probability density of the image to be processed on the local feature manifold and the second structure probability density of the reconstructed image on the local feature manifold. The relative structural information gain of the reconstructed image relative to the image to be processed is calculated based on the first structural probability density and the second structural probability density. The geometric structure entropy function is constructed by combining the relative structural information gain with the joint probability distribution of the edge gradient direction, and the geometric structure entropy is calculated. The geometric distortion index is obtained by using the geometric entropy quantization to reconstruct the structural integrity of the image under rotation and scaling transformations.

9. The image compression and reconstruction system based on matrix singular value decomposition according to claim 8, characterized in that, The construction of the geometric structure entropy function includes: Calculate the tangent space mapping between the first structure probability density and the second structure probability density in the feature manifold space, and obtain the geodesic distance of the tangent space mapping in the edge gradient direction; Based on the geodesic distance, an exponential evolution operator with respect to the relative structural information gain is constructed to extract the curvature perturbation factor; Perform a functional convolution mapping of the measure space on the curvature perturbation factor and the joint probability distribution to obtain the geometric entropy function.

10. The image compression and reconstruction system based on matrix singular value decomposition according to claim 9, characterized in that, The construction of the exponential evolution operator includes: Based on the energy distribution ratio of the singular values ​​in the singular value matrix, the Riemannian metric correction coefficients of the manifold space are determined. The geodesic distance is scaled using the Riemannian metric correction coefficients to construct a dynamic mapping basis. Using the dynamic mapping basis as the exponential parameter, an exponential power-law transformation is performed on the relative structural information gain to generate an exponential evolution operator.

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