A method for high missing color image restoration based on GLSKF-tSVD

Abstract

The present application relates to the field of image processing and computer vision, and provides a kind of based on GLSKF-tSVD's high missing color image restoration method, the method includes: obtaining the color image to be completed and its corresponding mask tensor, color image is represented as three-order tensor, define observation index set to construct corresponding projection operator and its complement projection operator, initialize the complete tensor to be recovered, global component and local residual component;Global-local additive completion model is constructed, t-SVD low rank structure based on t-product is used to parameterize representation for global component, structured covariance matrix is used to model for local residual component;Minimization objective function is constructed to solve model parameters;Alternating minimization strategy is used to solve minimization objective function, when meeting convergence condition or reaching maximum iteration number, output final completion tensor and restore to color image.The present application realizes the high-fidelity completion of color image under extreme high missing rate.

Description

Technical Field

[0001] This invention relates to the fields of image processing and computer vision technology, and in particular to a method for restoring highly missing color images based on GLSKF (Generalized Least Squares Kernelized Tensor Decomposition)-tSVD. Background Technology

[0002] In fields such as computer vision, remote sensing imaging, and medical image analysis, visual data such as color images and video sequences can be mathematically represented as third-order or higher-order tensors. However, in actual data acquisition, transmission, or storage, sensor malfunctions, occlusions (such as clouds), transmission packet loss, or physical damage (such as damaged old photographs) often result in a large amount of missing data, with only a very small portion of effective pixels (e.g., less than 10%) being obtained. Under such conditions of extremely high missing rates, reconstructing a complete and clear image from extremely sparse observations, requiring not only the restoration of the overall image structure but also the preservation of the authenticity of local details, has always been a core challenge in image processing and computer vision.

[0003] Existing image completion methods mainly revolve around two categories: matrix completion and tensor completion. Early methods were mostly based on matrix completion, processing multidimensional tensors by expanding them into two-dimensional matrices. Although these methods are theoretically mature, their dimensionality reduction inevitably disrupts the inherent spatial structure and local correlations of the image, leading to visual distortions or texture discrepancies in the restored image, especially under high missing rates. To overcome the limitations of matrix models, tensor completion methods emerged, operating directly in high-dimensional space and better preserving the multidimensional correlations of the data. Tensor decomposition-based models, such as CP decomposition and Tucker decomposition, improve the ability to restore structural consistency to some extent by utilizing global low-rank priors of the data. However, traditional methods such as CP decomposition often treat spatial and channel dimensions indiscriminately when processing color images (third-order tensors), failing to fully model the strong correlations between RGB channels, resulting in color distortion or color block effects in the restored image. When observations are extremely sparse, the errors of such models are further amplified, severely affecting visual quality.

[0004] Furthermore, natural images contain both low-rank global structures and rich local details (such as edges and textures). While traditional global low-rank tensor completion methods can reconstruct the overall contour, they often over-smooth the image, resulting in the loss of high-frequency information. On the other hand, methods that rely solely on local interpolation or block-based approaches struggle to infer a reasonable macroscopic layout when the missing regions are extremely large, easily leading to structural breaks or discontinuities.

[0005] Therefore, exploring a tensor completion method that can more accurately express channel correlation and take into account both global structure restoration and local detail reconstruction has important practical application value. Summary of the Invention

[0006] To address the above issues, this invention introduces t-SVD as a global low-rank prior to enhance cross-channel correlation modeling. It also combines a phased update and a rigorous observation projection alternating iterative solution strategy to achieve high-fidelity completion of color images under extremely high missing rates. This significantly improves the accuracy of color restoration and macroscopic structure recovery while ensuring the algorithm's strong generalization ability, excellent numerical stability, and superior visual reconstruction quality.

[0007] According to an embodiment of the present invention, a method for restoring highly missing color images based on GLSKF-tSVD is provided.

[0008] In a first aspect of the invention, a method for restoring highly missing color images based on GLSKF-tSVD is provided. The method includes:

[0009] Step S01: Obtain the color image to be completed and its corresponding mask tensor, represent the color image as a third-order tensor, define the observation index set to construct the corresponding projection operator and its complement projection operator, and initialize the complete tensor to be restored, the global component and the local residual component.

[0010] Step S02: Construct a global-local additive completion model. The global components are parameterized using a t-SVD low-rank structure based on t-product, and the local residual components are modeled using a structured covariance matrix.

[0011] Step S03: Construct a minimum objective function to solve for the model parameters:

[0012] ,

[0013] in, For global factor tensors, for Diagonal tensor For local residual components, For the set of observation indexes The corresponding projection operator, for The identity matrix, For global tubal-rank, For regularization weight parameters, Here is the covariance matrix used for the global components. Describing the Frobenius norm, The structured covariance matrix of the local residual components;

[0014] Step S04: Solve the minimization objective function using an alternating minimization strategy. When the convergence condition is met or the maximum number of iterations is reached, output the final completed tensor and restore it to a color image.

[0015] Furthermore, the global-local additive completion model described in step S02 specifically involves representing the complete tensor to be recovered as the sum of global components and local residual components:

[0016] ,

[0017] in, To capture the global low-rank components of the overall image structure and cross-channel coupling correlations. To capture relevant residual components of local texture details.

[0018] Furthermore, the parameterization representation of the global components using a t-SVD low-rank structure based on t-product described in step S02 specifically involves: And constrain its rank .

[0019] Furthermore, the modeling of the local residual components using a structured covariance matrix in step S02 specifically involves using a structured covariance matrix. Model it and constrain it to conform to the covariance norm. ,Will The structure is in the form of a separable Kronecker product: ,in, and Used to represent the correlation in the spatial dimensions of an image. Used to represent the correlation between color channels.

[0020] Furthermore, in step S04, the alternating minimization strategy is used to solve the minimization objective function. In this iteration, the following sub-steps are specifically executed:

[0021] Step S041: While holding Under unchanged conditions, with As input for this round, the updated global components are obtained by solving the global subproblem. ;

[0022] Step S042: After obtaining Then, construct the prediction tensor. Then, observation consistency hard projection is performed to satisfy... ,calculate: ;

[0023] Step S043: When season ;when When that time comes, proceed to step S044; where, The threshold for the number of rounds in each stage;

[0024] Step S044: While holding Under unchanged conditions, with As input, solving the local subproblem yields ;

[0025] Step S045: After obtaining Then construct a new prediction tensor And perform observation consistency hard projection operation to calculate .

[0026] Furthermore, the updated global components described in step S041 are solved using the Fourier transform domain:

[0027] Perform a Fast Fourier Transform on the residual tensor along the third dimension;

[0028] At each forward slice in the frequency domain, the frequency domain factor is solved using the conjugate gradient method. The system of linear equations, and update the diagonal tensor. ;

[0029] The updated factors are transformed back to the time domain using the inverse fast Fourier transform to reconstruct the global components. .

[0030] Furthermore, the specific implementation of the observation consistency hard projection described in step S045 is as follows: the predicted tensor is calculated using the updated components. Then, the projected tensor is calculated using the following formula. :

[0031] .

[0032] Among them, among them, For observation index set The supplement, To observe the tensor In the observation index set The projection results on To predict tensors In the unobserved index set The projection results on.

[0033] Furthermore, the step S04, which involves outputting the final completed tensor and restoring it to a color image, comprises: calculating the complete tensor obtained from two adjacent iterations. relative error Determine whether the relative error is less than the convergence threshold. Or reach the maximum number of iterations If the stopping condition is not met, then let Return to step S04 to continue iteration; if the stopping condition is met, stop the iteration and output the final completed tensor. Then, the tensor data is restored to a color image file format.

[0034] In a second aspect of the invention, an apparatus for restoring highly missing color images based on GLSKF-tSVD is provided. The apparatus includes:

[0035] Initialization module: used to obtain the color image to be completed and its corresponding mask tensor, represent the color image as a third-order tensor, define the observation index set to construct the corresponding projection operator and its complement projection operator, and initialize the complete tensor to be restored, global components and local residual components;

[0036] Model building module: used to build a global-local additive completion model. The global components are parameterized using a t-SVD low-rank structure based on t-product, and the local residual components are modeled using a structured covariance matrix.

[0037] Model Solver Module: Used to construct a minimum objective function to solve for the model parameters.

[0038] ,

[0039] in, For global factor tensors, for Diagonal tensor For local residual components, For the set of observation indexes The corresponding projection operator, for The identity matrix, For global tubal-rank, For regularization weight parameters, Here is the covariance matrix used for the global components. Describing the Frobenius norm, The structured covariance matrix of the local residual components;

[0040] Image output module: Used to solve the minimization objective function using an alternating minimization strategy. When the convergence condition is met or the maximum number of iterations is reached, the final completed tensor is output and restored to a color image.

[0041] This invention introduces t-SVD as a global low-rank prior to enhance cross-channel correlation modeling, and combines a phased update and rigorous observation projection alternating iterative solution strategy to achieve high-fidelity completion of color images under extremely high missing rates. This significantly improves the accuracy of color restoration and macroscopic structure recovery, while ensuring the algorithm's strong generalization ability, excellent numerical stability, and superior visual reconstruction quality.

[0042] It should be understood that the description in the Summary of the Invention is not intended to limit the key or essential features of the embodiments of the present invention, nor is it intended to restrict the scope of the invention. Other features of the invention will become readily apparent from the following description.

[0043] The beneficial effects of this invention are:

[0044] 1. Using tensor singular value decomposition (t-SVD) based on t-product as a global low-rank prior, the modeling ability of cross-channel correlation is significantly enhanced by co-processing color channels in the Fourier transform domain. This effectively improves color fidelity and reduces distortion while restoring the macroscopic structure of the image.

[0045] 2. An alternating iterative solution strategy combining phased updates and temporal observation projection is designed. This strategy does not rely on pre-trained data and has good generalization ability. By prioritizing the stabilization of the global structure and strictly maintaining known observations, regularization bias is avoided, thereby achieving higher accuracy reconstruction and better visual effects under high missing rate. Attached Figure Description

[0046] The above and other features, advantages, and aspects of the various embodiments of the present invention will become more apparent from the accompanying drawings and the following detailed description. Wherein:

[0047] Figure 1 A flowchart of a method for restoring highly missing color images based on GLSKF-tSVD according to an embodiment of the present invention is shown;

[0048] Figure 2 The original complete color image of the Airplane selected in Embodiment 1 of the present invention;

[0049] Figure 3 This is the observed color image obtained in Embodiment 1 of the present invention under the condition of a pixel missing rate of 90%;

[0050] Figure 4 In Embodiment 1 of the present invention, the method of the present invention is used to... Figure 3 The image shown is the result of restoring the observed color image;

[0051] Figure 5This is a comparison chart of the completion effect of the method of the present invention and other existing tensor completion methods under the condition of 90% pixel loss;

[0052] Figure 6 A block diagram of an apparatus for restoring highly missing color images based on GLSKF-tSVD according to an embodiment of the present invention is shown. Detailed Implementation

[0053] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0054] According to an embodiment of the present invention, a method for restoring highly missing color images based on GLSKF-tSVD is proposed. By introducing t-SVD as a global low-rank prior to enhance cross-channel correlation modeling, and combining an alternating iterative solution strategy of phased updates and rigorous observation projection, high-fidelity completion of color images under extremely high missing rates is achieved, significantly improving the accuracy of color restoration and macroscopic structure recovery, while ensuring the algorithm's strong generalization ability, excellent numerical stability, and superior visual reconstruction quality.

[0055] The principles and spirit of the present invention will be explained in detail below with reference to several representative embodiments.

[0056] This embodiment selects a color image of an airplane from the USC-SIPI Image Database as the object to be restored, and its image resolution is [resolution missing]. ,like Figure 2 As shown. A random missing mask is constructed on the original complete image, such that each tensor element is sampled at a certain rate. Independently observed, resulting in an observed color image with a pixel loss rate of 90%, such as... Figure 3 As shown.

[0057] Step S01: Obtain the color image to be completed and its corresponding mask tensor, represent the color image as a third-order tensor, define the observation index set to construct the corresponding projection operator and its complement projection operator, and initialize the complete tensor to be restored, the global component and the local residual component.

[0058] Specifically, obtain the color image to be completed and its corresponding mask tensor, and represent the color image as a third-order tensor. ,in These are the image pixel height and width, respectively. Define the number of color channels; define the set of observation indices. Construct the corresponding projection operator and its complement projection operator Initialize the complete tensor to be recovered. satisfy and initialize global components. With local residual components .

[0059] In this embodiment, the observed color image to be completed is represented as a third-order observation tensor. Define the observation index set based on the position of the observed pixels. Construct the corresponding projection operator and its complement projection operator .

[0060] Initialize the complete tensor to be recovered To satisfy And fill the unobserved locations with the mean. Initialize the local residual components. Simultaneously, the global factor tensor is randomly initialized. , ,and diagonal tensor Thus, the initial global components are obtained: .

[0061] The algorithm parameters are set as follows: Regularization parameters , The optimal combination for recovery is selected as the parameter setting for this embodiment; the taper range is fixed at 30. Global tubal-rank The threshold for the number of rounds in each stage is taken as follows: The maximum number of iterations is taken as The convergence threshold is taken as .

[0062] Step S02: Construct a global-local additive completion model. The global components are parameterized using a t-SVD low-rank structure based on t-product, and the local residual components are modeled using a structured covariance matrix.

[0063] Specifically, the complete tensor to be recovered is represented as the sum of the global components and the local residual components:

[0064] ,

[0065] in, To capture the global low-rank components of the overall image structure and cross-channel coupling correlations. To capture relevant residual components of local texture details.

[0066] For global components The parameterized representation is achieved using a t-product-based t-SVD low-rank structure:

[0067] ,

[0068] in, , For global factor tensors, for Diagonal tensor It represents t-product (t-product).

[0069] For local residual components Using structured covariance matrix Model it and constrain it to conform to the covariance norm. To reduce the computational complexity of processing high-dimensional tensors, The structure is in the form of a separable Kronecker product: ,in, and Used to represent the correlation in the spatial dimensions of an image. Used to represent the correlation between color channels.

[0070] Step S03: Construct a minimum objective function to solve for the model parameters:

[0071] ,

[0072] in, For regularization weight parameters, This is the covariance matrix used for the global components.

[0073] Specifically, the first term is a fidelity term based on the observed data, while the second and third terms are regularization terms for the global factor and the local residual components, respectively.

[0074] Step S04: Solve the minimization objective function using an alternating minimization strategy. When the convergence condition is met or the maximum number of iterations is reached, output the final completed tensor and restore it to a color image.

[0075] The objective function is solved by using an alternating minimization strategy. In the next iteration ( , (To determine the maximum number of iterations), the following sub-steps are executed.

[0076] Step S041: While holding Under unchanged conditions, with As input for this round, the updated global components are obtained by solving the global subproblem. The global update corresponds to in - Fitting global components under low-rank SVD constraints, making It can prioritize characterizing the overall structure of the image and the cross-channel coupling correlation.

[0077] Specifically, global components The update is solved in the Fourier transform domain:

[0078] Perform a Fast Fourier Transform (FFT) on the residual tensor along the third dimension (color channel);

[0079] At each forward slice in the frequency domain, the frequency domain factor is solved using the conjugate gradient method (CG). The system of linear equations, and update the diagonal tensor. ;

[0080] The updated factors are transformed back to the time domain using the inverse fast Fourier transform (iFFT) to reconstruct the global components. .

[0081] Step S042: After obtaining Then, construct the prediction tensor. Then, observation consistency hard projection is performed to satisfy... ,calculate:

[0082] .

[0083] Through the above projection operations, it is explicitly guaranteed that... At the observation location and the observation tensor Completely consistent, that is, satisfying .

[0084] Step S043: When To prioritize stabilizing the overall structure, local updates will not be introduced at this time. ;when Then, proceed to step S044, where local texture details are restored after the global structure has stabilized relatively. This is the threshold for the number of rounds in each stage.

[0085] Step S044: While holding Under unchanged conditions, with As input, solving the local subproblem yields Local updates constrain locally correlated residuals through a structured covariance matrix, making... It can compensate for local high-frequency details such as edges and textures and suppress noise and artifacts.

[0086] Step S045: After obtaining Then construct a new prediction tensor And perform the projection operation again to calculate This ensures the complete complement tensor output in this iteration. At the observation location, always with Consistency, that is, satisfaction .

[0087] The predicted tensor is obtained by calculating the updated components. Then, the projected tensor is calculated using the following formula. :

[0088] ,

[0089] This step explicitly ensures that the values ​​of the completed results at the observation locations are always equal to the original observation data. And it does not shift with the regularization term.

[0090] Finally, the complete tensor obtained from two adjacent iterations is calculated. relative error Determine whether the relative error is less than the convergence threshold. Or reach the maximum number of iterations If the stopping condition is not met, then let Return to step S04 to continue iteration. If the stopping condition is met, stop the iteration and output the final completed tensor. And restore the tensor data to a color image file format, such as Figure 4 As shown.

[0091] Depend on Figure 2 , Figure 3 and Figure 4 It can be seen that even with a pixel loss rate of 90%, the method described in this invention can still restore the main outline, wing edges, and color continuity of the background area of ​​the Airplane image relatively well. This indicates that the method of this invention can effectively restore local texture and edge details while maintaining global structural consistency.

[0092] To further verify the effectiveness and superiority of the method of the present invention, seven classic color images from the USC-SIPI Image Database were used as test data: Tree, Female, House256, Sailboat, Peppers, House512, and Airplane. The first three images have a resolution of [missing information - likely a resolution value]. The last four images have a resolution of The experiments were conducted in... , and The sampling was performed at three different sampling rates, corresponding to pixel missing rates of 80%, 90%, and 95%, respectively. HaLRTC, SPC, GLTC-TNN, and GLSKF were selected as comparison methods, with Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity-Induced Simulation (SSIM) used as objective evaluation metrics. The comparison results are shown in Table 1 (best results are highlighted in bold).

[0093] Table 1

[0094]

[0095] As shown in Table 1, under conditions of 80%, 90%, and 95% pixel loss, the GLSKF- proposed in this invention... The SVD method outperforms the comparison method overall across all test images, demonstrating that the present invention replaces the global component representation with a CP-based representation. - The low-rank representation of SVD can more fully characterize the coupling correlation between RGB color channels, thereby obtaining more stable global structure recovery capability and better color consistency under high missing rate conditions.

[0096] In an Airplane image, when At that time, the PSNR / SSIM of the method of the present invention reached 28.86 / 0.864, which is better than the comparative methods such as HaLRTC, SPC, GLTC-TNN and GLSKF.

[0097] Visual pairs under 90% missing condition Figure 5 As shown, compared with HaLRTC, SPC, GLTC-TNN and GLSKF methods, the method of the present invention restores the image more closely to the original image, can better maintain the main structure, edge contour and color consistency of the image, and effectively reduce blur and artifacts.

[0098] In summary, the GLSKF-based method proposed in this invention... The SVD method for restoring high-missing color images has good effectiveness, stability and superiority in the task of restoring high-missing-rate color images. The restored images are relatively closer to the original clear images in terms of color fidelity and detail contours.

[0099] Based on the same inventive concept, this invention also proposes a device for restoring highly missing color images based on GLSKF-tSVD. The implementation of this device can be found in the implementation of the method described above; repeated details will not be repeated. Figure 6 As shown, the device 100 includes:

[0100] Initialization module 101: used to obtain the color image to be completed and its corresponding mask tensor, represent the color image as a third-order tensor, define the observation index set to construct the corresponding projection operator and its complement projection operator, and initialize the complete tensor to be restored, global components and local residual components.

[0101] Model building module 102: Used to build a global-local additive completion model. The global components are parameterized using a t-SVD low-rank structure based on t-product, and the local residual components are modeled using a structured covariance matrix.

[0102] Model Solver Module 103: Used to construct a minimum objective function to solve for the model parameters.

[0103] ,

[0104] in, For global factor tensors, for Diagonal tensor For local residual components, For the set of observation indexes The corresponding projection operator, for The identity matrix, For global tubal-rank, For regularization weight parameters, Here is the covariance matrix used for the global components. Describing the Frobenius norm, The structured covariance matrix of the local residual components;

[0105] Image output module 104: Used to solve the minimization objective function using an alternating minimization strategy. When the convergence condition is met or the maximum number of iterations is reached, it outputs the final completed tensor and restores it to a color image.

[0106] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the described module can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0107] Furthermore, although the operations are described in a specific order, this should be understood as requiring that such operations be performed in the specific order shown or in sequential order, or requiring that all illustrated operations be performed to achieve the desired result. In certain environments, multitasking and parallel processing may be advantageous. Similarly, although several specific implementation details are included in the above discussion, these should not be construed as limiting the scope of the invention. Certain features described in the context of individual embodiments may also be implemented in combination in a single implementation. Conversely, various features described in the context of a single implementation may also be implemented individually or in any suitable sub-combination in multiple implementations.

[0108] Although the subject matter has been described using language specific to structural features and / or methodological logic, it should be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or actions described above. Rather, the specific features and actions described above are merely illustrative examples of implementing the claims.

Claims

1. A method for restoring highly missing color images based on GLSKF-tSVD, characterized in that, The method includes: Step S01: Obtain the color image to be completed and its corresponding mask tensor, represent the color image as a third-order tensor, define the observation index set to construct the corresponding projection operator and its complement projection operator, and initialize the complete tensor to be restored, the global component and the local residual component. Step S02: Construct a global-local additive completion model. The global components are parameterized using a t-SVD low-rank structure based on t-product, and the local residual components are modeled using a structured covariance matrix. Step S03: Construct a minimum objective function to solve for the model parameters: ， Among them, is the global factor tensor, is the diagonal tensor, is the local residual component, is the set of observation indices the corresponding projection operator, is the identity matrix of, is the global tubal-rank, is the regularization weight parameter, is the covariance matrix for the global component, denotes the Frobenius norm, is the structured covariance matrix of the local residual component; Step S04: Solve the minimization objective function using an alternating minimization strategy. When the convergence condition is met or the maximum number of iterations is reached, output the final completed tensor and restore it to a color image.

2. The method for restoring highly missing color images based on GLSKF-tSVD according to claim 1, characterized in that, The global-local additive completion model described in step S02 specifically involves representing the complete tensor to be recovered as the sum of global components and local residual components. ， in, To capture the global low-rank components of the overall image structure and cross-channel coupling correlations. To capture relevant residual components of local texture details.

3. The method for restoring highly missing color images based on GLSKF-tSVD according to claim 1, characterized in that, The parameterization representation of the global component described in step S02 using the t-SVD low-rank structure based on the t-product is specifically as follows: , and its tube rank is constrained .

4. The method for restoring highly missing color images based on GLSKF-tSVD according to claim 1, characterized in that, The modeling of the local residual component using the structured covariance matrix described in step S02 is specifically as follows: The structured covariance matrix is used for modeling, and it is constrained to conform to the covariance norm . is constructed in a separable Kronecker product form: , where and are used to represent the correlation in the image spatial dimension, and is used to represent the correlation between color channels.

5. The method for restoring highly missing color images based on GLSKF-tSVD according to claim 1, characterized in that, The method described in step S04, which employs an alternating minimization strategy to solve the minimization objective function, is as follows: In this iteration, the following sub-steps are specifically executed: Step S041: While keeping unchanged, use as the input for this round, and solve the global sub-problem to obtain the updated global component ; Step S042: After obtaining , construct the prediction tensor , and then perform an observation consistency hard projection to satisfy , calculate: ; Step S043: When occurs, let ; when occurs, proceed to Step S044; where is the threshold of the phased round number; Step S044: While keeping unchanged, use as the input to solve the local sub-problem and obtain ; Step S045: After obtaining Then construct a new prediction tensor And perform observation consistency hard projection operation to calculate .

6. The method for restoring highly missing color images based on GLSKF-tSVD according to claim 5, characterized in that, The updated global components described in step S041 are solved using the Fourier transform domain: Perform a Fast Fourier Transform on the residual tensor along the third dimension; At each forward slice in the frequency domain, the frequency domain factor is solved using the conjugate gradient method. The system of linear equations, and update the diagonal tensor. ; The updated factors are transformed back to the time domain using the inverse fast Fourier transform to reconstruct the global components. .

7. The method for restoring highly missing color images based on GLSKF-tSVD according to claim 1, characterized in that, The specific implementation of the observation consistency hard projection described in step S045 is as follows: the predicted tensor is calculated using the updated components. Then, the projected tensor is calculated using the following formula. : 。 in, For observation index set The supplement, To observe the tensor In the observation index set The projection results on To predict tensors In the unobserved index set The projection results on.

8. The method for restoring highly missing color images based on GLSKF-tSVD according to claim 1, characterized in that, The step S04, which involves outputting the final completed tensor and restoring it to a color image, is as follows: Calculate the complete tensor obtained from two adjacent iterations. relative error Determine whether the relative error is less than the convergence threshold. Or reach the maximum number of iterations ; If the stopping condition is not met, then let Return to step S04 to continue iteration; if the stopping condition is met, stop the iteration and output the final completed tensor. Then, the tensor data is restored to a color image file format.

9. A device for restoring highly missing color images based on GLSKF-tSVD, characterized in that, The device implements the method as described in any one of claims 1 to 8, comprising: Initialization module: used to obtain the color image to be completed and its corresponding mask tensor, represent the color image as a third-order tensor, define the observation index set to construct the corresponding projection operator and its complement projection operator, and initialize the complete tensor to be restored, global components and local residual components; Model building module: used to build a global-local additive completion model. The global components are parameterized using a t-SVD low-rank structure based on t-product, and the local residual components are modeled using a structured covariance matrix. Model Solver Module: Used to construct a minimum objective function to solve for the model parameters. ， in, For global factor tensors, for Diagonal tensor For local residual components, For the set of observation indexes The corresponding projection operator, for The identity matrix, For global tubal-rank, For regularization weight parameters, Here is the covariance matrix used for the global components. Describing the Frobenius norm, The structured covariance matrix of the local residual components; Image output module: Used to solve the minimization objective function using an alternating minimization strategy. When the convergence condition is met or the maximum number of iterations is reached, the final completed tensor is output and restored to a color image.

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