Tensor recovery method fusing non-convex low-rank minimization and depth prior

Abstract

The invention discloses a tensor recovery method fusing non-convex low-rank minimization and depth prior. The method comprises the following steps: obtaining an observation tensor, and an index set, a prior set and reversible transformation corresponding to the observation tensor; inputting the acquired data into a constructed tensor recovery model, and outputting an initial recovery tensor; the construction of the tensor recovery model comprises the following steps: carrying out differential processing on a multi-order tensor to obtain a gradient tensor; constructing a TCTV regular term according to a tensor non-convex norm corresponding to the gradient tensor; building a tensor recovery model based on a TCTV regular term; and inputting the initial recovery tensor into the convolutional neural network model, and outputting a final recovery tensor. According to the method, the image recovery capability is enhanced, the recovery performance in an extreme environment is more remarkable, and the method plays a key role in coping with loss or damage of high-dimensional data; and the accuracy of downstream tasks based on image processing, such as face recognition, target tracking and the like, can be ensured.

Description

Technical Field

[0001] The present invention relates to the field of image processing technology, and more specifically to a tensor recovery method integrating non-convex low-rank minimization and depth prior. Background Art

[0002] Tensor recovery technology is a data processing method widely used in many fields, which includes tensor data completion and denoising. Tensors are mathematical representations of multidimensional arrays, covering the generalization from scalars (0 dimensions), vectors (1 dimensions), matrices (2 dimensions) to higher dimensions. Compared with matrices, tensors can retain more structural information and perform better when dealing with multidimensional data processing. In the actual data acquisition process, due to complex situations such as occlusion, noise interference, and transmission packet loss, the data is usually incomplete or contaminated by noise. Therefore, it is necessary to complete some missing data or restore the original signal through denoising methods. Both tasks involve reconstructing high-dimensional tensors from partial observations or damaged data.

[0003] Tensor completion is a technique for inferring and recovering missing data from partial observations. The mainstream method is based on the low-rank decomposition model of tensors. The low-rank property of a tensor is similar to the low-rank of a matrix, that is, it can be approximated by decomposing it into multiple simple factors. Techniques based on this idea include CP (CANDECOMP / PARAFAC) decomposition, Tucker decomposition, etc. CP decomposition approximates a tensor by decomposing it into the outer product of a set of vectors, while Tucker decomposition represents a tensor through a core tensor and its product with a set of factors. These decomposition methods are widely used in theory and practice, and can effectively recover the original tensor from incomplete observations. However, tensor decomposition is non-unique and has high computational complexity. Low-rank tensor recovery methods face great challenges when processing large-scale data.

[0004] Another commonly used tensor completion method is the recovery technology based on compressed sensing. The theory of compressed sensing was originally applied to signal processing. By exploiting the sparsity of data, the signal can be recovered from a small amount of sampled data. In tensor recovery, the compressed sensing method uses the sparse representation or low-rank characteristics of the tensor to reconstruct the original tensor from some observations. This type of method usually requires that the tensor has sparsity in a certain transform domain, such as Fourier transform, discrete cosine transform, etc., so that better recovery effects can be obtained with less observation data. However, the compressed sensing method relies on the prior sparsity assumption of the tensor, which is difficult to meet in some application scenarios.

[0005] In addition, the nuclear norm minimization method has been extended on the basis of matrix completion and is also widely used in the field of tensor completion. Nuclear norm minimization utilizes the multilinear low-rank structure of the tensor and achieves recovery by minimizing the nuclear norm of the tensor. The advantage of this method is that it can utilize the multidimensional structural information of the tensor, making it more restorative than a single matrix completion technique. However, the computational complexity of nuclear norm minimization is high, and the tensor nuclear norm is not the tightest convex relaxation of the tensor rank, and its performance in tensor recovery is poor.

[0006] Tensor principal component analysis (TPCA) is a denoising technique widely used in high-dimensional data processing, which aims to extract the original low-dimensional structural information from noise-contaminated observational data. It achieves denoising by assuming that the original data of the tensor has a low-rank structure, while the noise part often appears as a high-rank component. The goal of TPCA is to separate the low-rank main components from the observational data, suppress the influence of high-rank noise, and thus restore a tensor close to the original signal. In actual operation, multilinear singular value decomposition (HOSVD) is a commonly used method. HOSVD decomposes the tensor in different dimensions and extracts the principal components in each dimension. This process is similar to the way PCA performs singular value decomposition (SVD) on the matrix. HOSVD can effectively utilize the multi-dimensional structure of the tensor to help separate the low-dimensional signal from the high-noise data. In addition, the tensor nuclear norm minimization method can also constrain its low-rank property by minimizing the nuclear norm of the tensor and further remove noise. The nuclear norm minimization technique helps to maintain the low-rank structure of the tensor, suppress the complex high-rank part introduced by noise, and improve the denoising effect.

[0007] In recent years, learning-based tensor recovery techniques have gradually become a research hotspot in the field of tensor recovery, and have shown significant performance advantages when facing complex and high-dimensional data. Unlike traditional model-driven methods such as low-rank decomposition and compressed sensing, learning-based tensor recovery methods mainly rely on data-driven strategies. Through machine learning techniques such as deep learning, they automatically extract high-order structural information from the data, thereby performing tensor recovery more effectively. As a common deep learning model, convolutional neural network (CNN) can effectively capture local features in tensor data. By designing a neural network architecture suitable for tensor input, CNN can learn the potential high-dimensional structure from partial observation data and then recover the complete tensor. Learning-based tensor recovery methods have high flexibility and adaptability. They do not need to rely on explicit low-rank or sparsity assumptions, and can automatically learn complex data distributions and structures through a large amount of training data. However, such methods usually require a large amount of labeled data for training, and the model training and inference process is also relatively complex, requiring high computing resources.

[0008] At present, tensor recovery technology has been widely used in many fields. In the field of image and video processing, tensor recovery is used for image restoration, super-resolution reconstruction and video completion; in medical imaging, it helps to repair missing MRI data or CT images; in recommendation systems, it is used to recover potential preferences from sparse user-item interaction matrices; in wireless communications, signal processing and other fields, it is used for compressed sensing, signal reconstruction and multi-dimensional channel estimation. In addition, tensor recovery technology is also used in social network analysis, environmental monitoring and multimodal data fusion to help extract valuable information from partial observation data.

[0009] The significance of tensor recovery technology lies in its ability to efficiently handle the incomplete and noisy problems of high-dimensional data that are prevalent in real life. For many applications, the direct use of missing or noisy data will lead to incorrect or inefficient decisions. Through tensor completion and denoising technology, we can maximize the use of partially observed data and recover key information in the data, thereby improving the performance of the model. This has significant practical value in applications such as recommendation systems, medical diagnosis, and video restoration. The successful application of tensor recovery technology also shows that low-rank, sparse and other structures in data are a ubiquitous phenomenon, which reflects a certain inherent order or law behind the data. Making full use of these structures can not only reduce computational complexity, but also significantly improve the accuracy of data processing.

[0010] The prior art "Guaranteed Tensor Recovery Fused Low-rankness and Smoothness" discloses an accurate tensor recovery method that combines low-rank and smoothness. This prior art has the following defects: 1. The tensor nuclear norm is not the tightest convex relaxation of the tensor rank, so applying it to the tensor recovery model limits the performance of the model. 2. The model-based method in this prior art is difficult to capture the abstract prior information in the tensor data. 3. The model-based method is not only complex to adjust parameters, but also inferior to the learning-based method in terms of recovery performance and speed.

[0011] Therefore, how to enhance the ability to restore images, reduce the complexity of parameter adjustment, and tap into the deeper data value of tensor data is an issue that technical personnel in this field urgently need to solve. Summary of the invention

[0012] In view of the above problems, the present invention provides a tensor recovery method that integrates non-convex low-rank minimization and deep prior to at least solve some of the technical problems mentioned in the above background technology.

[0013] In order to achieve the above object, the present invention adopts the following technical solution:

[0014] The present invention provides a tensor recovery method integrating non-convex low-rank minimization and deep prior, comprising the following steps:

[0015] Obtaining an observation tensor and an index set, a priori set, and a reversible transformation corresponding to the observation tensor; inputting the acquired data into a constructed tensor recovery model, and outputting an initial recovery tensor;

[0016] The steps of constructing the tensor recovery model include: performing differential processing on multi-order tensors to obtain gradient tensors; constructing TCTV regularization terms according to the tensor non-convex norm corresponding to the gradient tensor; and building a tensor recovery model based on the TCTV regularization terms.

[0017] The initial recovery tensor is input into a convolutional neural network model, and the final recovery tensor is output.

[0018] Furthermore, the TCTV regularization term is expressed as:

[0019]

[0020] Among them, ||X|| TCTV represents the TCTV regularization term; the symbol “:=” represents the definition; m represents the basis of the prior set; Γ represents the prior set; k represents the specific direction of the gradient calculation; ||G k || p Represents the gradient tensor G k The corresponding tensor non-convex norm; p represents a reversible transformation.

[0021] Further, the tensor recovery model includes a tensor completion model and a tensor denoising model;

[0022] The tensor completion model is expressed as:

[0023]

[0024] The tensor denoising model is expressed as:

[0025]

[0026] Among them, X represents a multi-order tensor; Ω represents the index set corresponding to the real tensor X0 to be restored; Ω ⊥ represents the orthogonal complement of the index set Ω; K represents the restriction to Ω ⊥ To fill the missing index value; Ω (K) indicates indicator function; represents the difference operator along each mode in the multi-order tensor X; P(·) represents the projection operator; β represents the trade-off parameter; M represents the observation tensor with sparse noise E; ||E||1 represents the use of 1 norm to characterize sparsity.

[0027] Furthermore, the outputting the initial recovery tensor specifically includes:

[0028] The tensor recovery model is solved using the alternating direction multiplier method. If the relative error between the intermediate recovery tensor of the current round and the observed tensor is less than a preset value, the intermediate recovery tensor of the current round is used as the initial recovery tensor.

[0029] Furthermore, the initial recovery tensor is input into a convolutional neural network model, specifically including:

[0030] For the completion task, the initial restored tensor is randomly covered with 20% pixel values ​​at the missing position, and a fixed random noise of the same size as the initial restored tensor is added, and then input into the convolutional neural network model;

[0031] For the denoising task, a fixed random noise of the same size as the initial restored tensor is added to the initial restored tensor and then input into the convolutional neural network model.

[0032] Furthermore, the convolutional neural network model is integrated into a plug-and-play attention module.

[0033] Furthermore, it also includes:

[0034] Based on the objective function of the completion task or the denoising task, a mean square error loss is calculated according to the final restored tensor and the observed tensor in the current round;

[0035] The mean square error loss is used for back propagation to update the parameters of the convolutional neural network and optimize the convolutional neural network model.

[0036] It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses a tensor recovery method that integrates non-convex low-rank minimization and deep prior, which has the following beneficial effects:

[0037] This invention combines two major types of tensor recovery technologies: tensor recovery model-based and neural network learning-based. It aims to characterize the explicit prior information through non-convex regularization terms, and then capture the implicit prior information through neural networks, thereby improving the recovery performance of the framework. This method enhances the ability to recover images, and the recovery performance is more significant in extreme environments. It plays a key role in dealing with the loss or damage of high-dimensional data; it helps to ensure the accuracy of downstream tasks based on image processing such as face recognition and target tracking.

[0038] The tensor recovery model constructed in the first stage of the present invention covers tensor completion and tensor denoising technologies, which can provide effective solutions to data missing or noise pollution problems. By retaining the high-dimensional structural characteristics of tensor data, this type of method can mine potential global information in incomplete or noise-affected data, thereby achieving more accurate recovery. Its advantages are not only to fill in data gaps and improve data integrity, but also to enhance data accuracy and reliability during the denoising process.

[0039] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0041] Figure 1 A flow chart of a tensor recovery method integrating non-convex low-rank minimization and deep prior provided in an embodiment of the present invention.

[0042] Figure 2 A schematic diagram of the GTTR structure of a two-stage tensor recovery model provided in an embodiment of the present invention.

[0043] Figure 3 A schematic diagram of differences in the first-stage recovery results provided by an embodiment of the present invention.

[0044] Figure 4 A schematic diagram of the convolutional neural network model structure provided for an embodiment of the present invention. DETAILED DESCRIPTION

[0045] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0046] The embodiment of the present invention discloses a tensor recovery method integrating non-convex low-rank minimization and deep prior, see Figure 1 As shown, including:

[0047] Phase 1: Obtain the observed tensor and the index set, prior set and reversible transformation corresponding to the observed tensor; input the acquired data into the constructed tensor recovery model and output the initial recovery tensor; the steps of constructing the tensor recovery model include: performing differential processing on multi-order tensors to obtain gradient tensors; constructing the TCTV regularization term according to the tensor non-convex norm corresponding to the gradient tensor; and building the tensor recovery model based on the TCTV regularization term.

[0048] The second stage: input the initial recovery tensor into the convolutional neural network model and output the final recovery tensor.

[0049] In the field of image processing technology, the above-mentioned observation tensor is the observation image, which refers to a known, partially missing or noise-affected image in the real tensor to be restored, which usually contains some known pixel values ​​and some unknown or damaged pixel values; the above-mentioned index set refers to an index set of known pixel values ​​in the observation image, which specifies which pixel positions have known values; the above-mentioned prior set is a set of predefined information that reflects the structural properties of the image, which usually reflects the smoothness or low rank of the image in different directions; the above-mentioned reversible transformation is used to convert the image to another domain for better processing and restoration.

[0050] The present invention constructs a generalized two-stage tensor recovery model GTTR (such as Figure 2 As shown in Figure 2, it combines two types of tensor recovery technologies: tensor recovery model-based and neural network-based learning. It aims to characterize explicit prior information through non-convex regularization terms, and then capture implicit prior information through neural networks, thereby improving the recovery performance of the framework. This method enhances the ability to recover images, and the recovery performance is more significant in extreme environments. It plays a key role in dealing with high-dimensional data loss or damage; it helps to ensure the accuracy of downstream tasks based on image processing, such as face recognition and target tracking.

[0051] In the embodiment of the present invention, the convolutional neural network model is also updated, that is, based on the objective function of the completion task or the denoising task, the mean square error loss is calculated according to the final restored tensor and the observed tensor in the current round; the mean square error loss is used for back propagation to update the parameters of the convolutional neural network to optimize the convolutional neural network model. When the preset number of iterations is reached, the machine is shut down, and the image is restored as realistically as possible based on the final network parameters, further improving the recovery performance of the two-stage tensor recovery model GTTR. See Figure 2 As shown, the intermediate observation is the initial recovery tensor; θ0 represents the initial parameters of the network; Indicates that the gradient is calculated according to the loss function to perform back propagation and update the network parameters; It represents the new image generated by the parameters when the current network f receives a fixed noise input Z.

[0052] Next, the above contents will be described in detail.

[0053] In the first stage above, the steps for building the tensor recovery model specifically include the following:

[0054] (1) Perform differential processing on the tensor to obtain the gradient tensor:

[0055] For multi-order tensors Perform differential processing on each mode to obtain the gradient tensor G k (k=1,2,...,d); where d represents the dth dimension of the tensor; n d represents the length of the dth dimension; k represents the specific direction of calculating the gradient. For example, when k = d, it means that the gradient is calculated along the dth dimension;

[0056] (2) Design a unified tensor non-convex norm:

[0057] Since the tensor nuclear norm is not the tightest convex relaxation of the tensor rank, a series of non-convex norms (including L p norm, SCAD norm, Logarithm norm, MCP norm, CappedL1 norm, ETP norm, Geman norm, Laplace norm) for further approximation. To this end, for a d-order tensor Under a specific reversible transformation P (such as discrete Fourier transform, discrete cosine transform), the present invention defines a unified tensor non-convex norm, which is expressed as:

[0058]

[0059] in,‖·‖ non represents a certain non-convex norm of the matrix; l refers to the scaling factor corresponding to a specific P transformation; i d is a variable ranging from 1 to n d ;X p Represents a positive slice of a tensor under a particular P transformation.

[0060] (3) According to the non-convex norm of the tensor corresponding to the gradient tensor, the TCTV regularization term is constructed:

[0061] Different from the prior art, the present invention does not characterize the prior information on the original tensor X, but on the basis of the gradient tensor; based on this, the present invention constructs a TCTV regularization term based on the tensor non-convex norm corresponding to the unified gradient tensor, which is used to simultaneously characterize the low rank and smoothness of the gradient tensor; the TCTV regularization term is expressed as:

[0062]

[0063] Among them, ||X|| TCTV represents the TCTV regularization term; the symbol “:=” represents the definition; m represents the basis of the prior set; Γ represents the prior set; k represents the specific direction of the gradient calculation; ||G k || p Represents the gradient tensor G k The corresponding tensor non-convex norm; p represents a reversible transformation.

[0064] Among them, the prior set Γ is specifically set according to different types of data. Taking images as an example, it is usually assumed that images have local smoothness in the spatial direction. The spatial directions here are represented by the numbers 1 and 2, so for images, Γ = {1,2}. In addition to spatial smoothness, hyperspectral images also have smoothness in the spectral direction, so Γ is set to {1,2,3}, where the number 3 represents the spectral direction. In addition to spatial smoothness, color videos also have smoothness in the temporal direction, so Γ can be set to {1,2,4}, where the number 4 represents the temporal direction.

[0065] (4) Based on the TCTV regularization term, a tensor recovery model is constructed; the tensor recovery model in the embodiment of the present invention includes a tensor completion model (TC) and a tensor denoising model (TRPCA); wherein:

[0066] The tensor completion model is expressed as:

[0067]

[0068] The tensor denoising model is expressed as:

[0069]

[0070] Among them, X represents a multi-order tensor; Ω represents the index set corresponding to the real tensor X0 to be restored; Ω ⊥ represents the orthogonal complement of the index set Ω; K represents the restriction to Ω ⊥ To fill the missing index value, the purpose is to fill the missing index position; Ω (K) indicates indicator function; represents the difference operator along each mode in the multi-order tensor X; P(·) represents the projection operator; β represents the trade-off parameter; M represents the observed tensor with sparse noise E; ||E||1 represents the use of 1 norm to characterize sparsity;

[0071] The indicator function δ Ω (K) is defined as:

[0072]

[0073] In the first stage, after the tensor recovery model is constructed, the gradient tensor, augmented Lagrange multiplier and other variables solved by the tensor recovery model are initialized; the observation tensor and the index set, prior set and reversible transformation corresponding to the observation tensor are obtained; the obtained data is input into the constructed tensor recovery model;

[0074] The alternating direction multiplier method (ADMM) is used to alternately control other variables and solve the required variables. If the relative error between the intermediate recovery tensor of the current round and the observation tensor is less than the preset value, the algorithm is considered to have converged, and the intermediate recovery tensor of the current round is used as the initial recovery tensor.

[0075] In the data conversion from the first stage to the second stage, for the completion task, it was found through experiments that about 80% of the pixel values ​​have a small error with the true value, and 20% of the pixel values ​​still have a large error (such as Figure 3 As shown). Therefore, in the embodiment of the present invention, for the initial recovery tensor output in the first stage, 20% of the pixel values ​​are randomly masked again at the missing positions, and are sent together with fixed random noise (the same size as the initial recovery tensor) to the convolutional neural network model in the second stage as the observation tensor for further completion. For the denoising task, the initial recovery tensor is neutralized with fixed random noise (the same size as the initial recovery tensor) and sent together to the convolutional neural network model in the second stage for further denoising. The impact of the two-stage model on the GTTR repair performance can be seen in Table 1 below:

[0076] Table 1 Ablation experiment results of tensor recovery model and convolutional neural network model

[0077] Data Types index Phase 1 Phase II Comprehensive Effect Color images Peak signal-to-noise ratio 24.71 24.97 27.09 Magnetic resonance imaging Peak signal-to-noise ratio 27.21 28.22 29.19 Grayscale Video Peak signal-to-noise ratio 22.65 22.74 23.47

[0078] In the above second stage, an untrained and randomly initialized convolutional neural network (including ResNet, U-Net, skip, etc.) is used, and a fixed random noise of the same size as the initial recovery tensor is used as the input of each iteration; and a plug-and-play attention module (including CBAM, SENET, SKNET, GCB, scSE) is integrated into the convolutional neural network model to enhance the feature extraction ability of the convolutional neural network model. Specifically, the insertion position of the attention module in the convolutional neural network model is as follows: Figure 4 As shown in the figure, the structure of the convolutional neural network model after integrating the attention module includes a residual block (ResBlock) and a U-net downsampling block (UnetDownBlock); where:

[0079] In the residual block, the input data passes through the first batch normalization (Batchnorm) layer, the first 3x3 convolution (3x3 conv) layer, the first ReLU activation function, the second batch normalization (Batchnorm) layer, the second 3x3 convolution (3x3conv) layer and the first attention (Attention) layer in sequence; the output of the first attention layer is added to the input data of the first batch normalization layer and output through the second ReLU activation function; in the U-net downsampling block, the input data passes through the maximum pooling (Maxpooling) layer, the third 3x3 convolution (3x3conv) layer, the fourth 3x3 convolution (3x3conv) layer and the second attention (Attention) layer in sequence;

[0080] The ablation experiment results of the attention module are shown in Table 2 below:

[0081] Table 2 Ablation experiment results of attention module

[0082] Network Architecture No attention mechanism CBAM SENET SKNET GCB SSE U-Net 35.44 35.53 35.52 35.49 35.49 35.55 ResNet18 35.36 35.40 35.49 35.44 35.49 35.42 ResNet34 35.38 35.45 35.44 35.48 35.48 35.48 skip 35.55 35.72 35.66 35.74 35.74 35.74

[0083] Next, the effect of a tensor recovery method integrating non-convex low-rank minimization and deep prior provided by the present invention is verified through a specific embodiment.

[0084] The method provided by the present invention can be applied to multiple fields such as image processing, knowledge graphs, signal processing, etc. Taking the image restoration task as an example, the experiments are completed in MATLAB (R2021a) and PyCharm. The computer configuration CPU is AMD Ryzen75800H with Radeon Graphics (16CPUs) and the running memory is 16GB.

[0085] In the tensor completion task, the experimental data sets used two color image data sets, BSD and USC-SIPI, a medical magnetic resonance imaging (MRI) spine data set, and a gray video data set. Completion was performed under six different missing rate conditions of 70%, 80%, 90%, 95%, 99%, and 99.5%, respectively, and recovery evaluation was performed using three general indicators, PSNR, SSIM, and FSIM. The average experimental numerical results on the color image data set are shown in Table 3. By comparing with other completion methods, it can be seen that the two-stage tensor recovery model GTTR in the present invention achieves the best completion effect. On the color image, MRI, and gray video data sets, the PSNR is improved by approximately 0.68dB, 1.27dB, and 0.65dB, respectively.

[0086] Table 3 Completion results under different missing rate conditions

[0087]

[0088]

[0089] In the tensor denoising task, salt and pepper noise ratios of 0.6 and 0.8 were added respectively, and the specific recovery results are shown in Table 4. By comparing with other denoising methods, it can be seen that the two-stage tensor recovery model GTTR in the present invention has the best denoising performance. In the high noise environment with 0.6 and 0.8 noise ratios, the PSNR is improved by about 4.07dB and 9.37dB respectively.

[0090] Table 4 Denoising results under different noise conditions

[0091]

[0092] In summary, the embodiment of the present invention provides a tensor recovery method that integrates non-convex low-rank minimization and deep prior. In the first stage, a non-convex regularization term based on the gradient tensor is proposed. Since the low-rank and smooth structures are consistent between the original tensor and the gradient tensor, the present invention uses a generalized tensor non-convex norm to characterize the low-rank and smooth prior information of the gradient tensor. The use of gradient tensors helps to improve the spatial smoothness of data, and the non-convex norm provides a more accurate tensor rank approximation. The present invention then inputs the recovery results of the first stage into the neural network model of the second stage. In the structure of the traditional neural network, a variety of plug-and-play attention modules are inserted to improve the feature extraction ability of the network. Through iterative optimization, the neural network in the second stage further improves the image restoration effect. In actual tensor recovery experiments, it is proved that this technology greatly improves the recovery performance, robustness, flexibility and generalization of the model.

[0093] The tensor recovery model constructed in the first stage of the present invention covers tensor completion and tensor denoising technologies, and can provide effective solutions to data missing or noise pollution problems. By retaining the high-dimensional structural characteristics of tensor data, this type of method can mine potential global information in incomplete or noise-affected data, thereby achieving more accurate recovery. Its advantages are not only to fill in data gaps and improve data integrity, but also to enhance data accuracy and reliability during the denoising process. The application of tensor recovery technology helps to enhance the reliability and accuracy of data analysis results, which is particularly important for fields such as image processing, video restoration, and recommendation systems. It helps to significantly improve the application performance in these fields, facilitates the mining of deeper data value of tensor data, and provides a more solid foundation for decision-making. The tensor recovery model can also effectively respond to the challenges of high-dimensional data, improve the efficiency of data processing, and reduce the consumption of computing resources, thereby achieving optimal resource allocation while ensuring data quality.

[0094] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0095] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A tensor recovery method integrating non-convex low-rank minimization and deep prior, characterized in that: The steps include: Obtaining an observation tensor and an index set, a priori set, and a reversible transformation corresponding to the observation tensor; inputting the acquired data into a constructed tensor recovery model, and outputting an initial recovery tensor; The steps of constructing the tensor recovery model include: performing differential processing on multi-order tensors to obtain gradient tensors; constructing TCTV regularization terms according to the tensor non-convex norm corresponding to the gradient tensor; and building a tensor recovery model based on the TCTV regularization terms. The initial recovery tensor is input into a convolutional neural network model, and the final recovery tensor is output.

2. A tensor recovery method integrating non-convex low-rank minimization and deep prior according to claim 1, characterized in that: The TCTV regularization term is expressed as: Among them, ||X|| TCTV represents the TCTV regularization term; m represents the basis of the prior set; Γ represents the prior set; k represents the specific direction of the gradient calculation; ||G k || p Represents the gradient tensor G k The corresponding tensor non-convex norm; p represents a reversible transformation.

3. A tensor recovery method integrating non-convex low-rank minimization and deep prior according to claim 2, characterized in that: The tensor recovery model includes a tensor completion model and a tensor denoising model; The tensor completion model is expressed as: The tensor denoising model is expressed as: Among them, X represents a multi-order tensor; Ω represents the index set corresponding to the real tensor X0 to be restored; Ω ⊥ represents the orthogonal complement of the index set Ω; K represents the restriction to Ω ⊥ To fill the missing index value; Ω (K) indicates indicator function; represents the difference operator along each mode in the multi-order tensor X; P(·) represents the projection operator; β represents the trade-off parameter; M represents the observation tensor with sparse noise E; ||E||1 represents the use of 1 norm to characterize sparsity.

4. The tensor recovery method integrating non-convex low-rank minimization and deep prior according to claim 1, characterized in that: The output initial recovery tensor specifically includes: The tensor recovery model is solved using the alternating direction multiplier method. If the relative error between the intermediate recovery tensor of the current round and the observed tensor is less than a preset value, the intermediate recovery tensor of the current round is used as the initial recovery tensor.

5. The tensor recovery method integrating non-convex low-rank minimization and deep prior according to claim 1, characterized in that: Inputting the initial recovery tensor into the convolutional neural network model specifically includes: For the completion task, the initial restored tensor is randomly covered with 20% pixel values ​​at the missing position, and a fixed random noise of the same size as the initial restored tensor is added, and then input into the convolutional neural network model; For the denoising task, a fixed random noise of the same size as the initial restored tensor is added to the initial restored tensor and then input into the convolutional neural network model.

6. A tensor recovery method integrating non-convex low-rank minimization and deep prior according to claim 1, characterized in that: The convolutional neural network model incorporates a plug-and-play attention module.

7. The tensor recovery method integrating non-convex low-rank minimization and deep prior according to claim 1, characterized in that: Also includes: Based on the objective function of the completion task or the denoising task, a mean square error loss is calculated according to the final restored tensor and the observed tensor in the current round; The mean square error loss is used for back propagation to update the parameters of the convolutional neural network and optimize the convolutional neural network model.

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