Color image restoration method, terminal equipment and storage medium

Abstract

The invention relates to a color image restoration method, terminal equipment and a storage medium. The method comprises the following steps: modeling a to-be-restored image into a three-order observation tensor; performing TR decomposition on the observation tensor to obtain a core tensor; on the basis of the core tensor, the to-be-restored image modeling is optimized through an optimization model, and a target tensor is obtained; and obtaining an image restoration result of the to-be-restored image based on the target tensor, the optimization model being used for calculating the target tensor so that the target tensor satisfies a low-rank constraint term of model expansion of a minimized TR factor, a fitting error of an approximate tensor and a data driving prior realized based on FFDNet. The image restoration effect of the optimization model provided by the invention is superior to that of an existing image completion model.

Description

Technical Field

[0001] This invention relates to the field of image processing, and more particularly to a color image restoration method, terminal device, and storage medium. Background Technology

[0002] Compared to two-dimensional grayscale images, 3D color images possess richer information and higher redundancy, which is beneficial for describing realistic scenes. However, due to factors such as sensor errors, interference during signal transmission, or damage to the storage medium, 3D color images are inevitably affected by noise (such as Gaussian noise and impulse noise). Noise in 3D color images not only affects image quality but also hinders subsequent applications such as image fusion, video restoration, image segmentation, and pattern recognition. Therefore, image denoising is an important research topic in image processing.

[0003] The core idea of ​​image denoising is to utilize various characteristics of an image to achieve the purpose of noise reduction. In recent years, many image denoising methods have been proposed, which can be roughly divided into two categories: one is based on channel-by-channel two-dimensional image processing, and the other is based on cross-channel third-order tensor image denoising.

[0004] Two-dimensional image processing methods are a classic approach in image processing. Related two-dimensional image processing methods include Total Variation (TVA) methods and sparse representation methods. However, when the noise level is high, these two-dimensional image processing methods often fail to achieve satisfactory denoising results.

[0005] Third-order tensor image denoising methods, while preserving cross-channel correlations better than traditional channel-by-channel two-dimensional processing methods by modeling color images as third-order tensors and utilizing their low-rank properties for restoration, still have significant drawbacks. First, most methods (such as those based on Tucker or CP decomposition) often require expanding the tensor into a matrix when applying low-rank constraints. This process disrupts the spatial-color structural integrity of the original data, leading to information loss. Second, even with more advanced tensor ring (TR) decomposition to avoid expansion, traditional TR models still primarily rely on single-module expansion or kernel norm constraints on the entire tensor. This makes them prone to oversmoothing due to rank selection sensitivity when facing strong noise or high missing rates, failing to effectively restore high-frequency details, sharp edges, and rich textures. Ultimately, this results in blurred and distorted restorations, making it difficult to meet the demands of high-quality image processing. Summary of the Invention

[0006] To address the aforementioned problems, this application provides a color image restoration method, a terminal device, and a storage medium.

[0007] One embodiment of this application is as follows:

[0008] A color image restoration method includes: modeling the image to be restored as a third-order observation tensor; optimizing the modeling of the image to be restored based on the observation tensor using an optimization model to obtain a target tensor; and obtaining an image restoration result of the image to be restored based on the target tensor, wherein the optimization model is expressed as:

[0009]

[0010] Wherein, min represents taking the minimum value; Represent the target tensor; This represents the sequence of TR factors obtained after performing TR decomposition on the target tensor. Represents the k-th TR factor; Represents TR factor The nth modulus expansion matrix; n represents the modulus index; k represents the TR factor index; K represents the total number of TR factors; ||.|| * denoted by λ; denoted by λ; denoted by TR(.); denoted by ||.||2; denoted by l2 norm; denoted by δ; denoted by ψ(.); denoted by FFDNet-based image local information restoration model; denoted by st; denoted by Ω; This represents the projection operator, used to retain elements in the index set while setting the elements in the complement of the index set to zero; This represents the observation tensor.

[0011] In some specific implementation schemes, the optimization of the modeling of the image to be restored by optimizing the model includes: introducing auxiliary variables to transform the optimization model into an augmented Lagrange form, and then using the alternating direction multiplier method to solve iteratively.

[0012] In some specific implementation schemes, when using the alternating direction multiplier method for iterative solution, the stopping condition of the iteration includes: the relative change in the L2 norm of the target tensor obtained from two consecutive iterations is less than the change threshold.

[0013] One embodiment of this application is as follows:

[0014] A color image restoration terminal device includes a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements any of the aforementioned color image restoration methods.

[0015] One embodiment of this application is as follows:

[0016] A computer-readable storage medium storing a computer program that, when executed by a processor, implements any of the aforementioned color image restoration methods.

[0017] This application provides the above-mentioned technical solution, combining model-driven TR decomposition with data-driven deep learning regularization. By introducing an energy functional regularization term based on the Fast and Flexible Denoising Convolutional Neural Network (FFDNet) architecture, the robustness of rank selection is enhanced while improving global low-rank and local detail preservation capabilities. By assuming that the expansion matrix of the TR factor has low-rank properties, a kernel norm regularization constraint is imposed on the TR factor to enhance its global low-rank characteristics. Local details of the target tensor are preserved by introducing a deep prior regularization term derived from the FFDNet network. Attached Figure Description

[0018] Figure 1 The diagram shown is a flowchart of the method in the embodiment.

[0019] Figure 2 The image shown is a schematic diagram of the test image in the embodiment.

[0020] Figure 3 The image shown is a schematic diagram of the processing result of the "person" image in Example 1.

[0021] Figure 4 The image shown is a schematic diagram of the processing result of the "chili pepper" image in Example 1.

[0022] Figure 5 The image shown is a schematic diagram of the processing result of the "butterfly" image in Example 1.

[0023] Figure 6 The image shown is a schematic diagram of the processing result of the "house" image in Example 2.

[0024] Figure 7 The image shown is a schematic diagram of the processing result of the "sailboat" image in Example 2.

[0025] Figure 8 The image shown is a schematic diagram of the processing result of the "airplane" image in Example 2.

[0026] Figure 9 The figure shown is a schematic diagram of the hyperparameter sensitivity curve in Example 4. Detailed Implementation

[0027] To further illustrate the various embodiments, this application provides accompanying drawings. These drawings are part of the disclosure of this application and are mainly used to illustrate the embodiments, and can be used in conjunction with the relevant descriptions in the specification to explain the operating principles of the embodiments. With reference to these drawings, those skilled in the art should be able to understand other possible implementations and the advantages of the present invention.

[0028] The present invention will now be further described in conjunction with the accompanying drawings and specific embodiments.

[0029] To facilitate description and make the technical solutions of this disclosure easier to understand, background knowledge related to this disclosure will be introduced before describing the technical solutions of this disclosure.

[0030] (1) Symbols and preliminary explanation

[0031] Scalars, vectors, matrices, and tensors are represented by x, x, X, respectively. Representation. For a K-order tensor use Tensor The (i1,i2,",i K ) elements. The l2 norm is defined as Tensor Sequence Abbreviated as

[0032] (2) TR decomposition model

[0033] TR decomposition aims to represent high-order (or high-dimensional) tensors through a sequence of cyclically multiplied third-order tensors. Specifically, let... This represents a value of size I1×I2×…×I K The K-order tensor is denoted as TR decomposition will It is decomposed into a series of core tensors (i.e., TR factors). These core tensors can be represented in element-wise form, that is:

[0034]

[0035] in, Tensor The (i1,i2,",i K ) elements. Tr represents the trace of the matrix. G (k) (i k ) represents the core tensor The i-th k There are 1 side slice matrix of size R. k ×R k+1 Because any two adjacent core tensors and They all have the same modulus R in their corresponding modes. k+1 Therefore, the last core tensor The size is R K ×I K ×R1, i.e., R K+1=R1, thus ensuring the product of the above matrices It is a square matrix. For example, the core tensor... It can also be called the kth nucleus.

[0036] r = [R1, R2, "R K ] T Let represent the rank of the TR decomposition. From equation (1), we know that... Equivalent to matrix {G (k) (i k The trace of the sequential product of}. To further describe this concept, equation (1) is rewritten in index form, i.e.:

[0037]

[0038] in, k represents the index of the tensor modulus. r k Indicates the index of the potential modulus. i k Indicates the index of the data module.

[0039] Equation (2) can also be expressed in tensor form, i.e.:

[0040]

[0041] Among them, symbols Represents the outer product of vectors. g (k) (r k ,r k+1 ) represents tensor g (k) of (r) k ,r k+1 The second-order fiber is a 2-order tensor. Equation (3) shows that the entire tensor... It can be decomposed into the sum of the outer products of rank-1 tensors. The number of parameters in the TR representation is... It is linearly related to the tensor order K.

[0042] Definition 1 (Inverse Modular Expansion): The inverse modular expansion matrix of tensor R is expressed as a matrix of size I. k ×∏ j≠k I j R [k] It indicates that its elements are defined as:

[0043]

[0044] Definition 2 (Sequential Modulus k Expansion): The sequential modulus k expansion matrix of tensor R is expressed as a matrix of size I. k ×∏ j≠k I j R (k) It is represented and defined as:

[0045]

[0046] in, Defined as:

[0047]

[0048] Definition 3 (Merging Subchains of Adjacent Core Factors): Let For a K-order tensor TR decomposition, Tensor TR nuclei. Adjacent TR nuclei and (The k-th core and the (k+1)-th core) have the same modulus R. k+1 And can be merged into a single subchain using multilinear products. subchain The horizontal slice matrix is ​​represented as:

[0049]

[0050] Similarly, the subchain tensor is obtained by merging all kernels except the k-th kernel (i.e., The subchain tensor can be represented as... The horizontal slice matrix of a subchain tensor is defined as follows:

[0051]

[0052] (3) Least squares algorithm for TR decomposition

[0053] The main concept of the alternating least squares algorithm is to optimize one core while keeping the others fixed. This process is repeated until a certain convergence criterion is met. Given a K-order tensor... The goal is to optimize the kernel with a given TR rank r, i.e.:

[0054]

[0055] Theorem 1. Given a TR decomposition Its inverse modulus k expansion matrix can be expressed as:

[0056]

[0057] in, Let K be the subchain obtained by merging K-1 cores, as defined in equation (8).

[0058] Proof: According to the definition of TR in equation (1), we can obtain:

[0059]

[0060] therefore, The inverse modulus k expansion matrix can be represented as:

[0061]

[0062] Then equation (10) holds true.

[0063] Figure 1 A color image restoration method according to one embodiment of this disclosure is shown. Figure 1 The method shown includes steps S110 to S130.

[0064] In step S110, the image to be restored is modeled as a third-order observation tensor.

[0065] In step S120, based on the observation tensor, the target tensor is obtained by optimizing the model to model the image to be restored through optimization.

[0066] In step S130, the image restoration result of the image to be restored is obtained based on the target tensor.

[0067] The optimization model used in this application abandons the use of the classic tensor decomposition completion model and instead selects a TR model that applies low-rank constraints to each TR kernel. Subsequently, in order to recover the detailed texture of the image to be recovered, FFDNet data-driven prior is introduced to explore the depth prior information of the image to be recovered, thereby improving the quality of the image recovery results. The construction process of the optimization model (hereinafter referred to as the TR-DD (Tensor Ring Data Driving) model) is described below.

[0068] The classic decomposition and completion model can be described as follows:

[0069]

[0070] Where Ω represents the index set; This represents the projection operator, used to retain elements in the index set while setting the elements in the complement of the index set to zero; Represents the observation tensor; ||·|| * The nuclear norm matrix is ​​represented by λ; the equilibrium parameter is represented by ||.||2, which represents the l2 norm. Represents the target tensor.

[0071] Classical decomposition typically requires mode k-matrix transformation, which may disrupt the intrinsic structure of the image to some extent, fail to guarantee the low-rank structure of the internal tensors, and result in a large number of parameters. To address these limitations, this application's embodiments abandon the use of the classical tensor decomposition completion model and instead employ the TR model.

[0072] As one possible implementation, a low-rank constraint is imposed on each TR factor, and equation (13) can be rewritten as follows:

[0073]

[0074] in, represents the k-th TR factor; st represents the constraint condition; TR(.) represents TR decomposition.

[0075] Theorem 1 states that tensors Rank sum TR factor The relationship between ranks allows us to obtain: tensor The upper bound of the rank of the modulo k expansion is the corresponding TR factor. The rank of the matrix under modulo 2 expansion. Therefore, in this embodiment, for each TR factor... By applying a low-rank constraint, the above model can be rewritten as:

[0076]

[0077] in, Represents TR factor The modulo-2 expansion matrix.

[0078] Formula (15) imposes tensor kernel norm constraints on the modulo 2 expansion of each TR factor, which can avoid the destruction of the image structure to a certain extent and reduce the computational complexity.

[0079] Furthermore, embodiments of this application also consider imposing low-rank constraints (nuclear norm constraints) on the additional two modulo expansions of the TR factor, i.e., the TR factor is expanded along modulo 1 and modulo 3, which can be expressed as: The optimization model can be represented as:

[0080]

[0081] When solving the optimization model, the kernel norm of the modulus n expansion rank of the TR factor and the fitting error of the approximate tensor are minimized simultaneously. This implementation ensures that the initial TR rank serves as an upper bound on the true tensor rank, thereby enhancing the robustness of the optimization model in selecting the rank.

[0082] To recover image detail textures from low-rank constraints that are difficult to recover, one possible implementation incorporates FFDNet-based data-driven priors into the optimization model to explore deeper prior information about the image, thereby improving the quality of the image restoration results. In the optimization model, low-rank constraints from TR decomposition are first used to recover the missing image, followed by an FFDNet-based image local information recovery model to recover image details. Based on this, the optimization model can be rewritten as follows:

[0083]

[0084] Where δ represents the regularization parameter, used to balance the low-rank model driving force. and data-driven priors implemented based on FFDNet

[0085] As one possible implementation, the optimization model is used to model the image to be restored. This includes: introducing auxiliary variables to transform the optimization model into an augmented Lagrangian form, and then using the alternating direction multiplier method (ADMM) for iterative solution. The solution process will be described in detail below.

[0086] First, introduce auxiliary variables. The optimization model is rewritten as follows:

[0087]

[0088] in, express Auxiliary variables.

[0089] Subsequently, the optimization model can be simplified, that is:

[0090]

[0091] in, denoted as Lagrange multiplier; μ>0 denotes the quadratic penalty parameter.

[0092] For k = 1, 2, ..., K, n = 1, 2, 3, and The three factors are independent of each other, and the optimization model is finally solved using the alternating direction multiplier method. During the solution process, the following steps are taken: and The four factors are updated alternately until the stopping condition is met.

[0093] (1) The subproblem can be described as follows:

[0094]

[0095] in, Is with The other irrelevant Lagrangian function parts, i.e., the constant term. Equation (20) can be simplified and then written in matrix form, i.e.:

[0096]

[0097] Equation (21) is simplified and optimized by transposing both sides of the equation, as shown below:

[0098]

[0099] make We can obtain:

[0100]

[0101] Then, by optimizing equation (23) and combining like terms, we can obtain:

[0102]

[0103] Then, by transposing both sides of equation (24), we get:

[0104]

[0105] Then we have:

[0106]

[0107] Where I represents the identity matrix.

[0108] Finally, by reassembling the matrix form into a tensor form, we obtain:

[0109]

[0110] (2) The subproblem can be described as follows:

[0111]

[0112] The objective function of equation (28) above contains three subproblems. Each sub-problem is described below:

[0113]

[0114] First, rewrite equation (29) in matrix form, that is:

[0115]

[0116] Equation (30) is solved using the singular value threshold, and the solution is:

[0117]

[0118] Where D(·) represents the singular value thresholding operation; fold n Let represent an nth-order folding operator that converts the nth-order expansion matrix into its tensor form.

[0119] (3) The subproblem can be described as follows:

[0120]

[0121] Equation (32) is simplified to:

[0122]

[0123] make Equation (33) can be rewritten as:

[0124]

[0125] Equation (34) is optimized and solved using the antecedent-consequent splitting algorithm. The solution process consists of two steps.

[0126] Antecedent subproblems The update is determined by the observations in the corresponding index, and then the missing items are approximated using the updated TR factor, resulting in:

[0127]

[0128] in, express Update of the preceding subproblem. Ω c It is the complement of Ω, representing the missing index value. Then, it is updated based on the previous item. Further updates

[0129] Updated The previous problem used a plug-and-play framework, FFDnet. The recovered R is shown below:

[0130]

[0131] Among them, Ω c As the complement of Ω, FFDNet represents a denoising neural network, derived from data. The driver is φ, which is a model hyperparameter.

[0132] (4) The subproblems are described as follows: n = 1, 2, 3

[0133]

[0134] Where k = 1, 2, ..., K, n = 1, 2, 3.

[0135] Lagrange multipliers Updated to:

[0136]

[0137] Since the parameter μ restricts the penalty term of the Lagrange function, μ is passed through μ + =min(ρμ,μ)max Update: ρ is one of the tuning hyperparameters.

[0138] In summary, the solution scheme based on the alternating direction multiplier method was iteratively updated. In one possible implementation, two iteration stopping conditions were considered: the maximum number of iterations and the difference between two iterations. In another possible implementation, when considering the difference between two iterations, the relative change in the L2 norm of the target tensor obtained from the two iterations can be set to be less than a threshold change, and the corresponding calculation formula is expressed as: in, This represents the target tensor obtained in the next iteration. Let A represent the target tensor obtained in the previous iteration, and let A represent the change threshold. For example, the change threshold can be set to 10. -5 .

[0139] This application introduces deep learning-based energy functional regularization into the TR decomposition framework, proposing an optimization model that combines model-driven and data-driven approaches. In this optimization model, regularization techniques are first introduced to provide robustness for the selection of the TR rank, enhancing the global low-rank nature and local detail recovery capability of the target tensor. Then, a data-driven deep learning network is employed to enhance the robustness to model parameter selection, while simultaneously capturing image details and textures that are difficult to capture due to low-rank constraints.

[0140] This application's embodiments experimentally validate the performance of the proposed optimized model (TR-DD model) and compare it with tensor decomposition models based on different tensor ranks, namely, the TMac model based on Tucker rank, the Transformer Neural Network (TNN) model based on tube rank, the 3DlogTNN model based on fiber rank, the Tensor Ring Low Rank Factor (TRLRF) model based on TR rank, and the Gradient Factor Regularization (TR-GFR) model based on tensor ring decomposition. Specifically, color image completion experiments were first conducted on color images with different missing rates, and then the above model was applied to a color image graffiti removal application. Finally, the parameter sensitivity of the proposed optimized model was analyzed. To visually demonstrate the experimental results, peak signal-to-noise ratio and structural similarity index were used to evaluate the model performance in this application's embodiments. To test the model's completion capability for different images, six 256×256 test images were selected, such as... Figure 2 As shown, Figure (a) is a "person", Figure (b) is a "sailboat", Figure (c) is a "house", Figure (d) is a "bell pepper", Figure (e) is a "butterfly", and Figure (f) is an "airplane".

[0141] Example 1

[0142] This embodiment experimentally evaluates the proposed method under different scenarios. Experiments were conducted on a desktop computer equipped with 32GB of memory and an Intel Xeon(R) CPU (clock frequency: 3.5GHz) using MATLAB 2017b. To evaluate the performance of the proposed model, a portion of image data was randomly deleted from six test images. Color image completion was performed with a missing data rate ranging from 20% to 80%. The proportion of missing data to the total data is the missing rate. The experimental results are summarized in Tables 1 and 2, where Table 1 shows the PSNR (Peak Signal-to-Noise Ratio) values ​​for color image completion, and Table 2 shows the SSIM (Structural Similarity) values ​​for color image completion.

[0143] As shown in Table 1, the TR-DD model provided in this application exhibits the best performance, with a significantly higher peak signal-to-noise ratio than the TMac and TR models. Compared to the TMac_DP3 model, the TR-DD model also demonstrates improved performance, attributed to the TR decomposition factor effectively preserving the internal structure of the image. For the TR-GFR model based on TR decomposition, the TR-DD model achieves good completion results because the depth prior recovers detailed textures that are difficult to capture using low-rank constraints. Figure 3 (It should be noted that,) Figures 3-8 The images in the dataset, ordered by ai, are: original image, noisy image, TMac processed image, TNN processed image, TRLRF processed image, TR-GFR processed image, 3DlogTNN processed image, TMac_DP3 processed image, and TR-DD processed image. Under the condition of a certain missing rate, all models generally recovered clear and good images with prominent details. However, when the missing rate increases, such as... Figure 4 As shown, in the "chili pepper" image with a 50% missing pixel rate, the TMac, TNN, and TRLFR models clearly missed pixels, resulting in a blurry image and loss of detail. Although the TR-GFR and 3DLogTNN models performed well overall, the images restored by the deep learning-based TMac_DP3 and TR-DD models were smoother. In the "butterfly" image with an 80% missing pixel rate, the TMac_DP3 and TR-DD models were still able to recover image texture information, such as... Figure 5 As shown, the TMac, TNN, and TRLFR models exhibit numerous artifacts, resulting in the loss of all background details. TR-GFR shows poor recovery, with white spots appearing in some images due to missing data. While the 3DLogTNN model achieves good overall image recovery, some details on the butterfly wings are still missing, and the image contains numerous noise specks. The images recovered by the TMac_DP3 and TR-DD models not only contain significant information but are also very smooth. Overall, the TR-DD model outperforms the TMac_DP3 model, providing satisfactory results for high missing data rates.

[0144] Table 1. PSNR (Peak Signal-to-Noise Ratio) values ​​for color image completion

[0145]

[0146]

[0147] Table 2 SSIM (Structural Similarity) values ​​for color image completion

[0148]

[0149]

[0150] Example 2

[0151] To further evaluate the performance of the TR-DD model, this embodiment applies the TR-DD model to graffiti color image restoration, which includes removing irregular graffiti, grids, and letters. The selected test images include "houses," "sailboats," and "airplanes."

[0152] Figure 6 This is the result of graffiti removal from the image of a "house". For example... Figure 6 As shown, TMac_DP3, TR-DD, TR-GFR, and 3DlogTNN effectively removed random graffiti. However, traces of graffiti remained in TMac, TNN, and TRLRF, resulting in poorer repair performance.

[0153] Figure 7 This is the result of mesh removal processing for the "sailboat" element. For example... Figure 7 As shown, TMac, TNN, and TRLRF exhibit numerous mesh cracks, making it impossible to repair damaged pixels. Clearer but less noticeable mesh traces are observed in TR-GFR and 3DlogTNN. Compared to other models, TMac_DP3 and TR-DD perform better in repairing pixels damaged by mesh graffiti, despite some blurred mesh traces.

[0154] Figure 8 This is the result of letter removal processing on the image of an "airplane". For example... Figure 8 As shown, some artifacts exist in TR-GFR, 3DlogTNN, TMac, TNN, and TRLRF in terms of letter removal.

[0155] Example 3

[0156] This embodiment uses the TR-DD model to explore the impact of TR rank on image completion. The test images are "bell peppers" and "sailboats" with a missing rate of 60%. Table 3 shows the tensor completion results for different tensor ranks (TR rank) at a missing rate of 60%. As the TR rank increases, the completion performance gradually improves. This is because a higher rank represents more initial information. However, as the amount of initial information increases, the time cost rises rapidly. In Table 3, when the TR rank is greater than 16, the improvement in completion performance is minimal with increasing rank, while the time increases significantly. When the TR rank is 24, although the time doubles, the performance remains almost unchanged. Therefore, a TR rank between 16 and 20 should be selected to ensure good completion results within an acceptable time cost range.

[0157] Table 3. Tensor completion results for different tensor ranks (TR rank) when the missing rate is 60%.

[0158]

[0159] Example 4

[0160] This embodiment discusses the influence of the hyperparameter φ on the TR-DD model. φ can be adjusted using δ, and the test image is a "house" image.

[0161] like Figure 9 The diagram illustrates the sensitivity curve of the hyperparameter δ. When other parameters remain constant, the final effect initially increases and then decreases as δ increases. This is because the FFDNet network can recover image details, making edges sharper. However, as the value of the hyperparameter φ increases, color artifacts appear in the image, making it look unrealistic and overly smooth, thus offsetting the final effect. Therefore, choosing an appropriate hyperparameter φ is crucial.

[0162] The results of the above embodiments show that the optimized model provided in this application is superior to existing image completion models.

[0163] Although the invention has been specifically shown and described in conjunction with preferred embodiments, those skilled in the art should understand that various changes in form and detail may be made to the invention without departing from the spirit and scope of the invention as defined in the appended claims, all of which shall be within the scope of protection of the invention.

Claims

1. A method for restoring a color image, characterized in that, include: The image to be restored is modeled as a third-order observation tensor; Based on the observed tensor, the model of the image to be restored is optimized by an optimization model to obtain the target tensor; as well as The image restoration result of the image to be restored is obtained based on the target tensor. The optimization model is expressed as follows: Wherein, min represents taking the minimum value; Represent the target tensor; This represents the sequence of TR factors obtained after performing TR decomposition on the target tensor. Represents the k-th TR factor; Represents TR factor The nth modulus expansion matrix; n represents the modulus index; k represents the TR factor index; K represents the total number of TR factors; ||.|| * denoted by λ; denoted by λ; denoted by TR(.); denoted by ||.||2; denoted by l2 norm; denoted by δ; denoted by ψ(.); denoted by FFDNet-based image local information restoration model; denoted by st; denoted by Ω; This represents the projection operator, used to retain elements in the index set while setting the elements in the complement of the index set to zero. This represents the observation tensor.

2. The method according to claim 1, characterized in that: The optimization of the modeling of the image to be restored by optimizing the model includes: After introducing auxiliary variables to transform the optimization model into an augmented Lagrangian form, the alternating direction multiplier method is used for iterative solution.

3. The method according to claim 2, characterized in that: In the iterative solution using the alternating direction multiplier method, the stopping conditions for the iteration include: The relative change in the L2 norm of the target tensor obtained from the two iterations is less than the change threshold.

4. A color image restoration terminal device, characterized in that: The method includes a processor, a memory, and a computer program stored in the memory and running on the processor, wherein the processor executes the computer program to implement the color image restoration method as described in any one of claims 1 to 3.

5. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by the processor, it implements the color image restoration method as described in any one of claims 1 to 3.

Images