CN115936136A - Data recovery method and system based on low-rank structure - Google Patents

Abstract

The present application relates to a data restoration method and system based on a low-rank structure. The method includes: collecting an image data set, analyzing the impact of target occlusion in different regions and positions in the image data set on the quality and signal-to-noise ratio of the target data; , build a low-rank matrix data restoration model based on semi-quadratic minimization; through the low-rank matrix data restoration model, and according to the semi-quadratic minimization theory, data is performed on the missing part of the target data of the image dataset recovery. In the embodiment of the present invention, aiming at the problem of lack of occluded target data, by introducing a robust factor into the loss function, a low-rank matrix data restoration method based on semi-quadratic minimization is designed, and optimized with the help of semi-quadratic minimization theory Solve to realize the restoration of the occluded target data matrix, while effectively reducing the interference of missing data and noise sample points.

Description

A data restoration method and system based on low-rank structure

Technical Field

The present application relates to the field of data restoration, and in particular to a data restoration method and system based on a low-rank structure.

Background Art

Object occlusion is the missing of data features, which is one of the typical scenarios of incomplete data analysis in the fields of machine learning and signal processing. Learning methods for incomplete data have been widely used in several fields such as recommendation systems, medical data analysis, image restoration and image super-resolution.

In order to solve the problem of incomplete label information, methods such as semi-supervised learning and weakly supervised learning are often used to enhance label information. For example, the semi-supervised classification method based on generative models is a relatively early learning method. Its core idea is to adopt clustering assumptions, integrate labeled data and unlabeled data, establish a joint probability distribution model of data, and obtain the posterior probability that the data belongs to a certain class by assuming the probability distribution model of data. The disadvantage of this type of method is that the probability distribution of data needs to be assumed before the model is established. However, in practice, due to the sparsity of data, the assumed probability distribution is often inaccurate. In addition, the core idea of the graph-based semi-supervised classification method is label information propagation. By constructing a weighted undirected graph to express the relationship between data, the label information is propagated from labeled data to unlabeled data according to the weighted connection information on the graph. When the quality of the graph matrix construction is high, this type of method can achieve good results. Its disadvantage is that this method is a direct induction model and needs to be retrained when processing new data. The discriminant semi-supervised classification method maximizes the distance from the classification hyperplane to the nearest sample through learning. The self-training semi-supervised classification method first constructs a classifier with labeled samples to predict unlabeled samples, and adds the more credible unlabeled samples and their predicted labels as labeled data to the training set. This method requires continuous addition of new data to iteratively train the classifier, so it takes a long time. In addition, if the initial classifier is biased, the error will continue to accumulate, resulting in an inaccurate final model.

Summary of the invention

Based on this, it is necessary to provide a data recovery method and system based on a low-rank structure to address the above technical problems.

In a first aspect, an embodiment of the present invention provides a data recovery method based on a low-rank structure, the method comprising:

Collecting an image data set, and analyzing the impact of target occlusions in different areas and positions in the image data set on the quality and signal-to-noise ratio of the target data;

According to the analysis results, a low-rank matrix data restoration model based on semi-quadratic minimization is constructed for missing occluded target data in the image data set;

The low-rank matrix data recovery model is used to recover the missing parts of the target data of the image data set according to the semi-quadratic minimization theory.

Furthermore, the collecting of the image data set and analyzing the influence of target occlusion in different areas and positions in the image data set on the quality and signal-to-noise ratio of the target data include:

Convert the missing data in the image data set into a high-dimensional missing data matrix X, where the high-dimensional missing data matrix X is generated by mixing a real data matrix Z and noise E;

The real data matrix Z is decomposed into the product of two low-rank matrices, that is, Z = UW, where W∈R ^k×n is the low-dimensional representation matrix and U∈R ^d×k is the low-dimensional representation subspace basis matrix.

Furthermore, according to the analysis results, for the missing occluded target data in the image data set, a low-rank matrix data restoration model based on semi-quadratic minimization is constructed, including:

The low-rank matrix data restoration model constructed is:

是加在低维表示子空间基矩阵U和低维表示矩阵W的正则项，λ和γ是大于零的超参数。Among them, f(Z, U, W) represents the loss function of low-rank approximation, φ(U) and

It is a regular term added to the low-dimensional representation subspace basis matrix U and the low-dimensional representation matrix W, and λ and γ are hyperparameters greater than zero.

Furthermore, according to the analysis result, for the missing occluded target data in the image data set, a low-rank matrix data restoration model based on semi-quadratic minimization is constructed, which also includes:

The robustness of the learning model is enhanced by minimizing the robust estimation function through semi-quadratic minimization, and the loss function is expressed as:

A robust estimator with robust factors l ₁ -l ₂ is introduced to assign smaller weights to missing samples and outliers in the loss function, and the loss function is converted again to:

等价转化为The potential function ρ(t) is introduced into the loss function, and the potential function

Equivalent conversion to

Where s is an auxiliary variable, ψ(s) is the dual function of the robust factor; then the loss function is further converted to:

On the other hand, an embodiment of the present invention further provides a data recovery system based on a low-rank structure, comprising:

An image missing analysis module is used to collect an image data set and analyze the impact of target occlusions in different areas and positions in the image data set on the quality and signal-to-noise ratio of the target data;

A data restoration model module is used to construct a low-rank matrix data restoration model based on semi-quadratic minimization according to the analysis results and for missing occluded target data in the image data set;

The image restoration module is used to restore the missing part of the target data of the image data set through the low-rank matrix data restoration model and according to the semi-quadratic minimization theory.

Furthermore, the image missing analysis module includes a low-rank representation unit, and the low-rank representation unit is used to:

Convert the missing data in the image data set into a high-dimensional missing data matrix X, where the high-dimensional missing data matrix X is generated by mixing a real data matrix Z and noise E;

The real data matrix Z is decomposed into the product of two low-rank matrices, that is, Z = UW, where W∈R ^k×n is the low-dimensional representation matrix and U∈R ^d×k is the low-dimensional representation subspace basis matrix.

Furthermore, the data recovery model module includes an objective function unit, and the objective function unit is used to:

The low-rank matrix data restoration model constructed is:

是加在低维表示子空间基矩阵U和低维表示矩阵W的正则项，λ和γ是大于零的超参数。Among them, f(Z, U, W) represents the loss function of low-rank approximation, φ(U) and

It is a regular term added to the low-dimensional representation subspace basis matrix U and the low-dimensional representation matrix W, and λ and γ are hyperparameters greater than zero.

Furthermore, the data restoration model module also includes a loss function unit, and the loss function unit is used to:

The robustness of the learning model is enhanced by minimizing the robust estimation function through semi-quadratic minimization, and the loss function is expressed as:

A robust estimator with robust factors l ₁ -l ₂ is introduced to assign smaller weights to missing samples and outliers in the loss function, and the loss function is converted again to:

等价转化为The potential function ρ(t) is introduced into the loss function, and the potential function

Equivalent conversion to

Where s is an auxiliary variable, ψ(s) is the dual function of the robust factor; then the loss function is further converted to:

Furthermore, the data recovery model module also includes a model solving unit, and the model solving unit is used to:

在低维表示矩阵W上加入核范数的正则项，即

Add a smoothing term to the low-dimensional representation subspace basis matrix U, that is,

Add the regular term of the nuclear norm to the low-dimensional representation matrix W, that is,

The constructed low-rank matrix data recovery model is converted into:

将所述低秩矩阵数据复原模型再次转换为：By reducing the impact of abnormal samples or missing samples on the model, according to the robustness factor

The low-rank matrix data restoration model is converted again into:

An alternating minimization strategy is used to solve the problem, other variables are regarded as known variables and fixed, one set of variables is updated, and the solution result of the low-rank matrix data restoration model is obtained.

The above-mentioned data restoration method and system based on low-rank structure, the method includes: collecting image data sets, analyzing the impact of target occlusion in different areas and positions in the image data sets on the quality and signal-to-noise ratio of target data; according to the analysis results, for the missing target data with occlusion in the image data sets, constructing a low-rank matrix data restoration model based on semi-quadratic minimization; through the low-rank matrix data restoration model, and according to the semi-quadratic minimization theory, the missing part of the target data in the image data sets is restored. In this embodiment of the present invention, for the problem of missing target data with occlusion, a low-rank matrix data restoration method based on semi-quadratic minimization is designed by introducing a robust factor in the loss function, and the optimization solution is performed with the help of the semi-quadratic minimization theory to realize the recovery of the occluded target data matrix, while effectively reducing the interference of data missing and noise sample points. Finally, compared with the traditional method, the numerical experiment verifies the effectiveness of the proposed method, which has a significant effect on improving the target data quality and target intelligent recognition performance under occlusion.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic diagram of a process of a data recovery method based on a low-rank structure in one embodiment;

FIG2 is a schematic diagram of a process of performing low-rank representation on missing data in one embodiment;

FIG3 is a structural block diagram of a data recovery system based on a low-rank structure in one embodiment.

DETAILED DESCRIPTION

In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

Due to the influence of factors such as bait interference or occlusion during data collection, data feature collection is incomplete, which is the phenomenon of missing data features. Missing data features lead to incomplete target information, which will greatly affect the subsequent target recognition performance. Analysis shows that common visible light images themselves have a low-rank prior structure. To this end, it is necessary to model the low-rank structure of the data, integrate the prior structure information to complete the missing features, and make up for and enhance the target data information.

In one embodiment, as shown in FIG1 , a data recovery method based on a low-rank structure is provided, the method comprising:

Step 101, collecting an image data set, and analyzing the impact of target occlusion in different areas and positions in the image data set on the quality and signal-to-noise ratio of the target data;

Step 102, according to the analysis result, for the missing target data with occlusion in the image data set, construct a low-rank matrix data restoration model based on semi-quadratic minimization;

Step 103 , using the low-rank matrix data restoration model and according to the semi-quadratic minimization theory, restore the missing part of the target data of the image data set.

Specifically, we first focus on the data loss problem caused by target occlusion. We analyze the impact of target occlusion in different regions and locations on the quality and signal-to-noise ratio of target data through simulation experiments, and deeply analyze the signal characteristics and impact of different types of target occlusion locations. At the same time, we verify the rationality of the low-rank assumption of occluded target data through experimental analysis, providing support for the construction of occluded data feature restoration models and methods based on low-rank structures.

This embodiment aims at the problem of missing target data under occlusion. By introducing a robust factor into the loss function, a low-rank matrix data recovery method based on semi-quadratic minimization is designed, and the semi-quadratic minimization theory is used to optimize and solve the problem, thereby realizing the recovery of the occluded target data matrix and effectively reducing the interference of missing data and noise sample points. Finally, the proposed method is compared with the traditional method, and the numerical experiment verifies the effectiveness of the proposed method, which has a significant effect on improving the target data quality and target intelligent recognition performance under occlusion.

In one embodiment, as shown in FIG2 , the process of performing low-rank representation on missing data includes the following steps:

Step 201, converting the missing data in the image data set into a high-dimensional missing data matrix X, wherein the high-dimensional missing data matrix X is generated by mixing a real data matrix Z and noise E;

Step 202, decompose the real data matrix Z into the product of two low-rank matrices, that is, Z = UW, where W∈R ^k×n is a low-dimensional representation matrix, and U∈R ^d×k is a low-dimensional representation subspace basis matrix.

In one embodiment, according to the analysis result, for the missing occluded target data in the image data set, a low-rank matrix data restoration model based on semi-quadratic minimization is constructed, including:

The low-rank matrix data restoration model constructed is:

是加在低维表示子空间基矩阵U和低维表示矩阵W的正则项，λ和γ是大于零的超参数。Among them, f(Z, U, W) represents the loss function of low-rank approximation, φ(U) and

It is a regular term added to the low-dimensional representation subspace basis matrix U and the low-dimensional representation matrix W, and λ and γ are hyperparameters greater than zero.

Specifically, in order to improve the robustness of the missing method, a low-rank matrix recovery method based on semi-quadratic minimization (IMLHM) is designed based on the semi-quadratic minimization theory. Specifically, given a high-dimensional missing data matrix X, X can usually be generated by mixing Z and noise E. Based on the assumption of low rank of data, the real data matrix Z is decomposed into the product of two low-rank matrices, that is, Z = UW, where W∈R ^k×n is the low-dimensional representation matrix, and U∈R ^d×k is the low-dimensional representation subspace basis matrix. Then the low-rank matrix recovery framework based on semi-quadratic minimization can be described as

In one embodiment, according to the analysis result, for the missing occluded target data in the image data set, constructing a low-rank matrix data restoration model based on semi-quadratic minimization further includes:

The robustness of the learning model is enhanced by minimizing the robust estimation function through semi-quadratic minimization, and the loss function is expressed as:

A robust estimator with robust factors l ₁ -l ₂ is introduced to assign smaller weights to missing samples and outliers in the loss function, and the loss function is converted again to:

等价转化为The potential function ρ(t) is introduced into the loss function, and the potential function

Equivalent conversion to

Where s is an auxiliary variable, ψ(s) is the dual function of the robust factor; then the loss function is further converted to:

范数度量拟合误差值，然而该损失对数据噪声、数据缺失和异常点等影响十分敏感，进而使得传统方法对数据缺失敏感。为了增强学习模型的鲁棒性，半二次最小化稳健估计函数是一种常用的方法，因此，可以对损失函数进行转换。Specifically, many traditional learning methods are special cases of this framework, that is, they use different loss functions or regularization terms based on this framework.

The norm measures the fitting error value, but the loss is very sensitive to data noise, data missing and outliers, which makes the traditional method sensitive to data missing. In order to enhance the robustness of the learning model, semi-quadratic minimization of the robust estimation function is a common method, so the loss function can be transformed.

In addition, the introduction of the robust estimator is equivalent to assigning smaller weights to missing samples and outliers, and assigning larger weights to important points. Specifically, the weight assigned to each sample x _i is θ(||z _i -Uwi _{|| F} ). Among the above robust estimation functions, because the l ₁ -l ₂ robust factor has the simplest form and good effect, l ₁ -l ₂ is selected as part of the loss function of this method.

In one embodiment, according to the analysis result, for the missing occluded target data in the image data set, constructing a low-rank matrix data restoration model based on semi-quadratic minimization further includes:

在低维表示矩阵W上加入核范数的正则项，即

Add a smoothing term to the low-dimensional representation subspace basis matrix U, that is,

Add the regular term of the nuclear norm to the low-dimensional representation matrix W, that is,

The constructed low-rank matrix data recovery model is converted into:

将所述低秩矩阵数据复原模型再次转换为：By reducing the impact of abnormal samples or missing samples on the model, according to the robustness factor

The low-rank matrix data restoration model is converted again into:

An alternating minimization strategy is used to solve the problem, other variables are regarded as known variables and fixed, one set of variables is updated, and the solution result of the low-rank matrix data restoration model is obtained.

在W上加入核范数的正则项，即

因此，提出的基于半二次最小化的低秩矩阵复原方法的目标函数。Specifically, in order to make the low-dimensional representation have a low-rank clustering structure and avoid model overfitting, a smoothing term is added to U:

Add the regularization term of the nuclear norm to W, that is

Therefore, the objective function of the proposed low-rank matrix restoration method based on semi-quadratic minimization.

可以等价转化为The introduction of robust estimation function increases the difficulty of solving the optimization problem. Therefore, based on the semi-quadratic minimization theory, we know that

can be equivalently converted into

Among them, s is an auxiliary variable, and ψ(s) is the dual function of the robust factor. To this end, the loss function in the formula can be equivalently converted to:

若z_i和Uw_i之间的差异越大，样本权重s_i将越小，进而有效地减少异常样本或者缺失样本对模型的影响。s的取值与更新由极小化函数θ(t)决定，同时ψ(s)的显式形式不知道也不会影响模型参数更新，可以忽略不计。In addition, different robust estimators have different dual functions ψ(s), and different dual functions ψ(s) correspond to different minimization functions θ(t). At the same time, the minimization function θ(t) determines the auxiliary variable s. There are two forms of minimization functions: additive form and multiplicative form. Since the multiplicative form requires fewer iterations to converge than the additive form, the multiplicative form is generally used. For the robust factor of the l ₁ -l ₂ function

The larger the difference between z _i and U w _i , the smaller the sample weight _si will be, which effectively reduces the impact of abnormal samples or missing samples on the model. The value and update of s are determined by the minimization function θ(t). At the same time, the explicit form of ψ(s) is unknown and will not affect the update of model parameters, so it can be ignored.

记In the solution process,

remember

The matrix form of the problem is:

An alternating minimization strategy is used to solve the problem, other variables are regarded as known variables and fixed, one set of variables is updated, and the solution result of the low-rank matrix data restoration model is obtained.

The specific iterative steps are shown in the algorithm.

It should be understood that, although the various steps in the above-mentioned flow chart are displayed in sequence according to the indication of the arrows, these steps are not necessarily executed in sequence in the order indicated by the arrows. Unless there is a clear explanation in this article, the execution of these steps is not strictly limited in order, and these steps can be executed in other orders. Moreover, at least a part of the steps in the above-mentioned flow chart may include a plurality of sub-steps or a plurality of stages, and these sub-steps or stages are not necessarily executed at the same time, but can be executed at different times, and the execution order of these sub-steps or stages is not necessarily to be carried out in sequence, but can be executed in turn or alternately with other steps or at least a part of the sub-steps or stages of other steps.

In one embodiment, as shown in FIG3 , a data recovery system based on a low-rank structure is provided, comprising:

An image missing analysis module 301 is used to collect an image data set and analyze the impact of target occlusions in different regions and positions in the image data set on the quality and signal-to-noise ratio of the target data;

A data restoration model module 302 is used to construct a low-rank matrix data restoration model based on semi-quadratic minimization according to the analysis results and for missing occluded target data in the image data set;

The image restoration module 303 is used to restore the missing part of the target data of the image data set through the low-rank matrix data restoration model and according to the semi-quadratic minimization theory.

In one embodiment, as shown in FIG3 , the image missing analysis module 301 includes a low-rank representation unit 3011, and the low-rank representation unit 3011 is used to:

Convert the missing data in the image data set into a high-dimensional missing data matrix X, where the high-dimensional missing data matrix X is generated by mixing a real data matrix Z and noise E;

The real data matrix Z is decomposed into the product of two low-rank matrices, that is, Z = UW, where W∈R ^k×n is the low-dimensional representation matrix and U∈R ^d×k is the low-dimensional representation subspace basis matrix.

In one embodiment, as shown in FIG. 3 , the data recovery model module 302 includes an objective function unit 3021, and the objective function unit 3021 is used to:

The low-rank matrix data restoration model constructed is:

是加在低维表示子空间基矩阵U和低维表示矩阵W的正则项，λ和γ是大于零的超参数。Among them, f(Z, U, W) represents the loss function of low-rank approximation, φ(U) and

It is a regular term added to the low-dimensional representation subspace basis matrix U and the low-dimensional representation matrix W, and λ and γ are hyperparameters greater than zero.

In one embodiment, as shown in FIG. 3 , the data recovery model module 302 further includes a loss function unit 3022, and the loss function unit 3022 is used to:

The robustness of the learning model is enhanced by minimizing the robust estimation function through semi-quadratic minimization, and the loss function is expressed as:

A robust estimator with robust factors l ₁ -l ₂ is introduced to assign smaller weights to missing samples and outliers in the loss function, and the loss function is converted again to:

等价转化为The potential function ρ(t) is introduced into the loss function, and the potential function

Equivalent conversion to

Where s is an auxiliary variable, ψ(s) is the dual function of the robust factor; then the loss function is further converted to:

In one embodiment, as shown in FIG. 3 , the data recovery model module 302 further includes a model solving unit 3023, and the model solving unit 3023 is used to:

在低维表示矩阵W上加入核范数的正则项，即

Add a smoothing term to the low-dimensional representation subspace basis matrix U, that is,

Add the regular term of the nuclear norm to the low-dimensional representation matrix W, that is,

The constructed low-rank matrix data recovery model is converted into:

将所述低秩矩阵数据复原模型再次转换为：By reducing the impact of abnormal samples or missing samples on the model, according to the robustness factor

The low-rank matrix data restoration model is converted again into:

An alternating minimization strategy is used to solve the problem, other variables are regarded as known variables and fixed, one set of variables is updated, and the solution result of the low-rank matrix data restoration model is obtained.

For the specific limitations of the data recovery system based on the low-rank structure, please refer to the limitations of the data recovery method based on the low-rank structure above, which will not be repeated here. Each module in the above-mentioned data recovery system based on the low-rank structure can be implemented in whole or in part by software, hardware and a combination thereof. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules.

Those skilled in the art will understand that the structure shown in FIG. 3 is merely a block diagram of a partial structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than shown in the figure, or combine certain components, or have a different arrangement of components.

A person of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing related hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods.

The technical features of the above embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

The above-mentioned embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the attached claims.

Claims (10)

1. A method for data recovery based on a low rank structure, the method comprising:

acquiring an image data set, and analyzing the influence of target occlusion in different areas and positions in the image data set on the quality and the signal-to-noise ratio of target data;

according to the analysis result, aiming at the shielded target data missing in the image data set, constructing a low-rank matrix data restoration model based on semiquadratic minimization;

and performing data recovery on the missing part in the target data of the image data set through the low-rank matrix data recovery model according to a half-quadratic minimization theory.

2. The low-rank structure-based data recovery method according to claim 1, wherein the acquiring the image dataset and analyzing the influence of the occlusion of the target in different areas and positions in the image dataset on the quality and the signal-to-noise ratio of the target data comprises:

converting missing data in the image dataset into a high-dimensional missing data matrix X, wherein the high-dimensional missing data matrix X is generated by mixing a real data matrix Z and noise E;

the true data matrix Z is decomposed into the product of two low rank matrices, i.e. Z = UW, where W ∈ R ^k×n For a low-dimensional representation matrix, U ∈ R ^d×k Is a low-dimensional representation subspace base matrix.

3. The method for data recovery based on low rank structure according to claim 1, wherein the constructing a model for recovering low rank matrix data based on semi-quadratic minimization for the missing occluded target data in the image data set according to the analysis result comprises:

the low-rank matrix data recovery model is constructed by the following steps:

where f (Z, U, W) represents a loss function of a low rank approximation, phi (U) and

is a canonical term added to the low-dimensional representation subspace base matrix U and the low-dimensional representation matrix W, λ and γ being hyperparameters greater than zero.

4. The method for data recovery based on low rank structure according to claim 2, wherein the constructing a model for recovering low rank matrix data based on semi-quadratic minimization for the missing occluded target data in the image data set according to the analysis result further comprises:

enhancing the robustness of the learning model by minimizing the robust estimation function semiquadratic, and expressing the loss function as:

introducing a robust factor l ₁ -l ₂ The loss function missing samples and the abnormal points are distributed with smaller de-weightsAnd, converting the loss function again to:

introducing a potential function rho (t) into the loss function and adding the potential function

Conversion to equivalence

Wherein s is an auxiliary variable, and psi(s) is a dual function of the robust factor; the loss function further translates to:

5. the method for data recovery based on low rank structure according to claim 4, wherein the constructing a model for recovering low rank matrix data based on semi-quadratic minimization for the missing occluded target data in the image data set according to the analysis result further comprises:

adding a smoothing term to the low-dimensional representation subspace basis matrix U, i.e.

Adding a regularization term of the nuclear norm to the low-dimensional representation matrix W, i.e. < >>

Converting the constructed low-rank matrix data recovery model into:

by reducing the effect of abnormal or missing samples on the model, according to a robust factor

Reconverting the low-rank matrix data recovery model to:

and solving by adopting an alternative minimization strategy, taking other variables as known variables and fixing, updating one group of variables, and obtaining a solving result of the low-rank matrix data recovery model.

6. A low rank structure based data recovery system, comprising:

the image missing analysis module is used for acquiring an image data set and analyzing the influence of target shielding in different areas and positions in the image data set on the quality and the signal-to-noise ratio of target data;

the data recovery model module is used for constructing a low-rank matrix data recovery model based on semi-quadratic minimization aiming at the shielded target data missing in the image data set according to the analysis result;

and the image restoration module is used for restoring the missing part in the target data of the image data set through the low-rank matrix data restoration model according to a half-quadratic minimization theory.

7. The low-rank structure-based data recovery system according to claim 6, wherein the image missing analysis module comprises a low-rank representation unit for:

converting missing data in the image dataset into a high-dimensional missing data matrix X, wherein the high-dimensional missing data matrix X is generated by mixing a real data matrix Z and noise E;

the true data matrix Z is decomposed into the product of two low rank matrices, i.e. Z = UW, where W ∈ R ^k×n For a low-dimensional representation matrix, U ∈ R ^d×k Is a low-dimensional representation subspace base matrix.

8. The low rank structure based data recovery system of claim 6, wherein the data recovery model module comprises an objective function unit to:

the low-rank matrix data recovery model is constructed by the following steps:

where f (Z, U, W) represents a loss function of a low rank approximation, phi (U) and

are regular terms added to the low-dimensional representation subspace base matrix U and the low-dimensional representation matrix W, λ and γ being hyperparameters greater than zero.

9. The low rank structure based data recovery system of claim 6, wherein the data recovery model module further comprises a loss function unit for:

enhancing the robustness of the learning model by minimizing the robust estimation function by a half-quadratic, the loss function is expressed as:

introducing a robust factor l ₁ -l ₂ The robust estimator of (2) assigns smaller de-weights to the missing samples and outliers of the loss function, and transforms the loss function again into:

introducing a potential function rho (t) into the loss function and adding the potential function

Conversion to equivalence

Wherein s is an auxiliary variable, and psi(s) is a dual function of the robust factor; the loss function further translates to:

10. the low-rank structure based data recovery system according to claim 6, wherein the data recovery model module further comprises a model solving unit for:

adding a smoothing term to the low-dimensional representation subspace basis matrix U, i.e.

Adding a regularization term of the nuclear norm to the low-dimensional representation matrix W, i.e. < >>

Converting the constructed low-rank matrix data recovery model into:

by reducing the influence of abnormal samples or missing samples on the model, according to the robust factor

Reconverting the low-rank matrix data recovery model to:

and solving by adopting an alternative minimization strategy, taking other variables as known variables and fixing, updating one group of variables, and obtaining a solving result of the low-rank matrix data recovery model.

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