Color image noise separation method based on smoothed low-rank tensor multi-view clustering

Abstract

The present invention discloses a method for color image noise separation based on smooth low-rank tensor multi-view clustering, which relates to the field of color image processing and includes the following steps: S1: constructing a noisy image model of a three-dimensional color image; S2: constructing a noise-free image model based on smooth low-rank tensor multi-view clustering; S3: combining the noisy image model and the noise-free image model to construct a noise separation model based on smooth low-rank tensor multi-view clustering; S4: solving the noise separation model using an ADMM optimization framework, and after solving the noise separation model, outputting a noise-free image in combination with a feature dictionary of X in a basis space, thereby completing noise separation of the three-dimensional color image. The present invention utilizes the multi-view structural prior of the color image in the tensor subspace and has excellent noise separation performance under different noise intensities and different data.

Description

Technical Field

[0001] The present invention relates to the field of color image processing, and in particular to a color image noise separation method based on smooth low-rank tensor multi-view clustering. Background Art

[0002] With the rapid development of optoelectronic information science, color image processing technology has achieved significant application progress in various fields. For example, in traffic monitoring, the unique spectral information of color images enables rapid license plate identification and tracking of vehicles violating regulations. In remote sensing, the rich spatial information of color images facilitates geometric feature mining of ground objects. However, due to hardware limitations, the imaging environment of acquisition equipment is often unpredictable, making it difficult to acquire high-quality images in harsh environments, and the acquired data is noisy. Generally, improvements to imaging equipment can be made to increase the number of photons captured by the photosensitive device. While this can suppress noise to some extent, it also increases the size and power consumption of the imaging device. To obtain noise-free images, the most popular approach is to combine imaging technology with digital tools, leveraging mathematical algorithms to overcome the shortcomings of physical optics in imaging hardware. Therefore, studying the problem of noise separation in color images not only reduces the hardware requirements of imaging equipment and overcomes the limitations of the imaging environment on image acquisition, but also has important implications for scientific exploration, production, and daily life in harsh environments.

[0003] Although color image noise separation technology has achieved certain results in multiple application scenarios, denoising technology still has significant deficiencies in utilizing the high-dimensional structure and subspace information of images, resulting in reduced restoration performance. For example, traditional noise separation methods based on matrix low-rank regularization process each channel, ignoring the low-rank correlation of data in different channels, resulting in reduced data reconstruction capabilities. Although tensor-based noise separation methods overcome the problems caused by the matrix framework, the model has defects in expressing low-dimensional subspaces, reducing the ability to express low-rank features and causing distortion of information in the image. In recent years, artificial intelligence methods represented by deep learning have become increasingly popular in image processing due to their big data-driven advantages, but the underlying mathematical mechanism is still unclear, and the large scale of parameters in the model reduces the stability and transferability of the model, affecting the algorithm's generalization ability and image restoration accuracy.

[0004] Therefore, a new method for color image noise separation is needed. Summary of the Invention

[0005] The purpose of the present invention is to provide a color image noise separation method based on smooth low-rank tensor multi-view clustering to address the above-mentioned problems. It utilizes the multi-view structure prior of color images in tensor subspace and has good noise separation performance under different noise intensities and different data.

[0006] The technical solution adopted by the present invention is as follows: a color image noise separation method based on smoothed low-rank tensor multi-view clustering, comprising the following steps:

[0007] S1: Construct a noisy image model of a 3D color image;

[0008] S2: Construct a noise-free image model based on multi-view clustering of smoothed low-rank tensors;

[0009] S3: Combine the noisy image model and the noise-free image model to build a noise separation model based on smooth low-rank tensor multi-view clustering;

[0010] S4: The noise separation model is solved with the help of the ADMM optimization framework. After the solution, the feature dictionary of X in the basis space is combined to output a noise-free image, completing the noise separation of the 3D color image.

[0011] Furthermore, in step S11, the noisy image model is Equation 1:

[0012]

[0013] in: 、 、 They represent the noisy color image, the color image to be restored, and the noise component respectively; R is a set of real numbers, H is the number of pixels in the horizontal direction of the image, W is the number of pixels in the vertical direction of the image, and "3" is the number of channels.

[0014] Furthermore, by introducing the prior information of image and noise into Equation 1, the following objective function is obtained as Equation 2:

[0015]

[0016] in: and They represent the prior information of the image to be restored X and the noise component E respectively, and λ is the regularization parameter between the image and noise constraint terms;

[0017] Solve Equation 2 to estimate X.

[0018] Furthermore, in step S2, the low-dimensional structure of the data and the smooth low-rank tensor multi-view clustering are used to characterize the subspace information to construct a noise-free image model. The noise-free image model is Equation 3:

[0019]

[0020] Where * represents the tensor product between two tensors; D is the feature dictionary of X in the basis space; Z is the expression coefficient corresponding to the dictionary D; Representing a low-rank prior for the gradient domain tensor.

[0021] Furthermore, in formula 3 The expression is formula 4:

[0022]

[0023] in, represents the gradient operator along the k-th dimension, is the tensor nuclear norm, Represents a collection of tensors in different directions.

[0024] Further, in step S3, the The sparse constraint of the norm is combined with Equation 1, Equation 2, Equation 3 and Equation 4 to construct a noise separation model based on smooth low-rank tensor multi-view clustering. The noise separation model is Equation 5:

[0025]

[0026] in, express norm.

[0027] Furthermore, we introduce auxiliary variables and The noise separation model is equivalently optimized. After equivalent optimization, it is equivalently converted into a Lagrangian function according to the optimization strategy of ADMM. The Lagrangian function is formula 6:

[0028]

[0029] in, is a parameter, 、 and It is a multiplier;

[0030] Based on the ADMM solution framework, the iterative optimization process based on Equation 6 is as follows:

[0031] S41: Optimization :Fix other variables and iteratively optimize through TNN singular value threshold method ;

[0032] S42: Optimize Z: fix other variables and iteratively optimize Z;

[0033] S43: Optimize G: fix other variables and iteratively optimize G;

[0034] S44: Optimize E: fix other variables, solve through soft threshold operator, and iteratively optimize E;

[0035] S45: Update Lagrange multipliers 、 and

[0036] S46: Update parameters , , .

[0037] Furthermore, during the iterative optimization process of Equation 6, the stopping criterion is to check whether the convergence condition is satisfied. If satisfied, stop iterative optimization; otherwise, continue iterative optimization.

[0038] Furthermore, in step S4, the feature dictionary of X in the base space The acquisition is to restore the color image based on the tensor robust principal component analysis method. , and then use the tensor singular value decomposition get ,in, The algorithm is the abbreviation of the tensor singular value decomposition algorithm, U and V are the left and right singular value matrices respectively, and S is the diagonal matrix; the feature dictionary of X in the basis space is obtained by the tensor product of U and V .

[0039] Furthermore, in step S4, the output noise-free image is .

[0040] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0041] The present invention first learns a relatively high-quality expression dictionary from the denoising results of the noise separation method based on the tensor nuclear norm; then, by leveraging the representation advantage of the expression dictionary on subspace information, the smoothness and low-rank features of the coefficients are jointly mined, and a subspace expression framework of a smooth low-rank tensor is formed; subsequently, combined with the sparse distribution characteristics of noise, a color image noise separation algorithm based on multi-view clustering of smooth low-rank tensor subspaces is derived; finally, an optimization framework based on the alternating direction multiplier method is used to solve the proposed denoising algorithm; thus, good noise separation performance is achieved under different noise intensities and different data. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] The present invention will now be described by way of example with reference to the accompanying drawings, in which:

[0043] Figure 1is a flow chart of the present invention;

[0044] Figure 2 The results of quantitative analysis of multiple images;

[0045] Figure 3 Visual comparison of the noise separation results of Image 1 under three different noise intensities;

[0046] Figure 4 Visual comparison of noise separation results of images 2, 3, 4, and 5 at noise intensity 0.1. DETAILED DESCRIPTION

[0047] The multiple data used in the present invention are from a public color data set. During the experiment, the noise separation performance of the multiple data was tested when there was noise in the image pixels at a ratio of 0.10, 0.15, and 0.20. The comparison methods include the Robust Principal Component Analysis (RPCA) method, the tensor singular value decomposition (t-SVD)-based method, and the tensor robust principal component analysis (TRPCA) method. In terms of quantitative performance evaluation, the classic peak signal-to-noise ratio (PSNR (dB)) was introduced as a measurement indicator.

[0048] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art of the present invention. The terms used in the specification of the present invention herein are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0049] like Figure 1 As shown, a color image noise separation method based on smoothed low-rank tensor multi-view clustering proposed in the present invention is used to perform noise separation experiments on color images with noise pixel ratios of 0.10, 0.15, and 0.20, including the following steps:

[0050] S1: Construct a noisy image model of a three-dimensional color image; the details are as follows.

[0051] By expanding the noise separation model of traditional images, the noise separation problem of constructed three-dimensional color images can be modeled as a noisy image model. The noisy image model is Equation 1:

[0052]

[0053] in, 、 、 They represent the noisy color image, the color image to be restored, and the noise component respectively; R is a set of real numbers, H is the number of pixels in the horizontal direction of the image, W is the number of pixels in the vertical direction of the image, and "3" is the number of channels.

[0054] Due to the lack of accurate modeling of noise components, the high-quality image X cannot be directly solved from Equation 1. Therefore, by introducing prior information of the image and noise into Equation 1, the following objective function is obtained as Equation 2:

[0055]

[0056] in: and They represent the prior information of the image to be restored X and the noise component E respectively, and λ is the regularization parameter between the image and noise constraint terms;

[0057] X is estimated by solving Equation 2.

[0058] S2: Construct a noise-free image model based on smooth low-rank tensor multi-view clustering; the details are as follows.

[0059] For high-dimensional color images, it is necessary to model the identification features of the data based on multi-view clustering technology. Therefore, in this embodiment, subspace information is used to represent the low-dimensional structure of the data. At the same time, in order to characterize local smoothness, the noise-free image X is modeled using smooth low-rank tensor multi-view clustering. Specifically, the noise-free image model is constructed by using subspace information to represent the low-dimensional structure of the data and smooth low-rank tensor multi-view clustering. The noise-free image model is Equation 3:

[0060]

[0061] Where * represents the tensor product between two tensors; D is the feature dictionary of X in the basis space; Z is the expression coefficient corresponding to the dictionary D; Representing a low-rank prior for the gradient domain tensor.

[0062] for The expression is formula 4:

[0063]

[0064] in, represents the gradient operator along the k-th dimension, is the tensor nuclear norm, Represents a collection of tensors in different directions.

[0065] S3: Combine the noisy image model and the noise-free image model to construct a noise separation model based on smooth low-rank tensor multi-view clustering; the details are as follows.

[0066] In the process of noise modeling, noise usually meets sparse distribution. Therefore, this embodiment introduces The sparse constraint of the norm is combined with Equation 1, Equation 2, Equation 3 and Equation 4 to construct a noise separation model based on smooth low-rank tensor multi-view clustering. The noise separation model is Equation 5:

[0067]

[0068] in, express norm.

[0069] It is difficult to directly solve Equation 5, so this embodiment introduces an auxiliary variable and By performing equivalent optimization on the noise separation model, we can obtain an equivalent optimization expression, which is Equation 5-1:

[0070] .

[0071] S4: The noise separation model is solved using the ADMM optimization framework. After the solution, the feature dictionary of X in the basis space is combined to output a noise-free image, completing the noise separation of the 3D color image. The details are as follows.

[0072] According to the optimization strategy of ADMM, Equation 5-1 can be equivalently transformed into the Lagrangian function, which is Equation 6:

[0073]

[0074] in, is a parameter, 、 and It is a multiplier;

[0075] Based on the ADMM solution framework, the iterative optimization process based on Equation 6 is as follows:

[0076] S41: Optimization :Fix other variables and iterate optimization The objective function is Equation 6-1:

[0077]

[0078] Equation 6-1 is a standard tensor kernel norm optimization problem, which is solved by the TNN singular value threshold method and iterative optimization. .

[0079] S42: Optimize Z: Fix other variables and iteratively optimize the objective function of Z as Equation 6-2:

[0080]

[0081] Equation 6-2 is a typical least squares problem. It can be solved by taking the first-order partial derivative of the variable Z and setting it to zero. The closed-form solution of Z is Equation 6-3:

[0082]

[0083] in: represents the inverse of D, is the identity matrix.

[0084] S43: Optimize G: Fix other variables and iteratively optimize the objective function of G to be Equation 6-4:

[0085]

[0086] Derivative Equation 6-4 and then further obtain the closed-form solution of G as Equation 6-5:

[0087]

[0088] in: for The transpose of is the identity matrix.

[0089] S44: Optimize E: Fix other variables and iteratively optimize the objective function of E to be Equation 6-6:

[0090]

[0091] Equation 6-6 can be solved by the soft threshold operator, that is, Equation 6-7:

[0092]

[0093] have:

[0094] in: ,and >0, is the threshold.

[0095] S45: Update Lagrange multipliers 、 and

[0096] Specifically, update the Lagrange multiplier according to equation 6-8 、 and ; Formula 6-8 is:

[0097]

[0098] S46: Update parameters , , .

[0099] Furthermore, during the iterative optimization process of Equation 6, the stopping criterion is to check whether the convergence condition is satisfied. If satisfied, stop iterative optimization; otherwise, continue iterative optimization.

[0100] Furthermore, the color image is restored based on the tensor robust principal component analysis method. , and then use the tensor singular value decomposition get ,in, The algorithm is the abbreviation of the tensor singular value decomposition algorithm, U and V are the left and right singular value matrices respectively, and S is a diagonal matrix; and the feature dictionary of X in the basis space is obtained by the tensor product of U and V .

[0101] Furthermore, the output noise-free image is .

[0102] In summary, the color image noise separation method based on smooth low-rank tensor multi-view clustering can be summarized using the following algorithm:

[0103] Input: noise image Y, feature dictionary D of X in base space, and .

[0104] initialization: , K=0, , , .

[0105] ①:for n=1:N do;

[0106] ②: Fix other variables and update using formula 6-1 ;

[0107] ③: Fix other variables and update using formula 6-1 ;

[0108] ④: Fix other variables and update using formula 6-1 ;

[0109] ⑤: Fix other variables and update using formula 6-1 ;

[0110] ⑥: Fix other variables and update using formula 6-1 ;

[0111] ⑦: Update ;

[0112] ⑧:while ;

[0113] ⑨:end for;

[0114] Output: The noise-free image is .

[0115] In this embodiment, in order to quantitatively and qualitatively evaluate the noise reduction effect, the present invention selects three benchmark noise separation algorithms RPCA, t-SVD and TRPCA as comparison methods, and uses these comparison methods to compare the noise image noise reduction results with the results of the present invention. The PSNR (dB) quality evaluation index is used to quantitatively analyze the results. Figure 2 As shown; the visual comparison results are as follows Figure 3 and Figure 4 shown.

[0116] according to Figure 2 It can be seen that the PSNR obtained by the present invention is higher than that of the comparison methods RPCA, t-SVD, and TRPCA under different data and different noise intensities. For example, on Image 1, when the noise intensity is 0.2, the PSNR of the present invention is 7.21dB higher than that of the suboptimal method TRPCA. When the noise intensity is 0.1, this value is further amplified to 2.7dB. Similar performance is also seen in other data. Therefore, the noise reduction results of the present invention have obvious advantages, and also demonstrate the superior performance of multi-view clustering constraints based on smooth low-rank tensors in suppressing feature distortion.

[0117] Figure 3 The visual comparison of noise separation of Image 1 at noise intensities of 0.10, 0.15, and 0.20 is shown. It can be observed that all methods have a certain degree of noise suppression effect, but from the sub-image blocks of the methods (see the green magnified box), the present invention has the best performance in reconstructing detailed features, which verifies the effectiveness of the present invention in noise separation. In addition, Figure 4 The noise reduction performance of the image on multiple data when the noise intensity is 0.10 is given. It is easy to see that the present invention has the best visual results on all data, which also shows the robustness of the present invention on different data.

[0118] The present invention is not limited to the aforementioned specific embodiments, but extends to any new features or any new combination disclosed in this specification, as well as any new method or process steps or any new combination disclosed.

Claims

1. A color image noise separation method based on smoothed low-rank tensor multi-view clustering, characterized by: The following steps are involved: S1: Construct a noisy image model of a 3D color image; In step S1, the noisy image model is Equation 1: in: 、 、 represent the noisy color image, the color image to be restored, and the noise component respectively; R is a real number set, H is the number of pixels in the horizontal direction of the image, W is the number of pixels in the vertical direction of the image, and "3" is the number of channels; Introducing the prior information of image and noise into Equation 1, the following objective function is obtained as Equation 2: in: and They represent the prior information of the image to be restored X and the noise component E respectively, and λ is the regularization parameter between the image and noise constraint terms; Solve equation 2 to estimate X; S2: Construct a noise-free image model based on multi-view clustering of smoothed low-rank tensors; In step S2, the low-dimensional structure of the data and the smooth low-rank tensor multi-view clustering are used to characterize the subspace information to construct a noise-free image model. The noise-free image model is Equation 3: Where * represents the tensor product between two tensors; D is the feature dictionary of X in the basis space; Z is the expression coefficient corresponding to the dictionary D; Representing a low-rank prior for the gradient domain tensor; In formula 3 The expression is formula 4: in, represents the gradient operator along the k-th dimension, is the tensor nuclear norm, Represents a set of components along different directions of the tensor; S3: Combine the noisy image model and the noise-free image model to build a noise separation model based on smooth low-rank tensor multi-view clustering; In step S3, the The sparse constraint of the norm is combined with Equation 1, Equation 2, Equation 3 and Equation 4 to construct a noise separation model based on smooth low-rank tensor multi-view clustering. The noise separation model is Equation 5: in, express norm; S4: The noise separation model is solved using the ADMM optimization framework. After the solution, the feature dictionary of X in the basis space is combined to output a noise-free image, completing the noise separation of the 3D color image. Introducing auxiliary variables and The noise separation model is equivalently optimized. After equivalent optimization, it is equivalently converted into a Lagrangian function according to the optimization strategy of ADMM. The Lagrangian function is formula 6: in, is a parameter, 、 and It is a multiplier; Based on the ADMM solution framework, the iterative optimization process based on Equation 6 is as follows: Steps S41 to S46: S41: Optimization :Fix other variables and iteratively optimize through TNN singular value threshold method ; S42: Optimize Z: fix other variables and iteratively optimize Z; S43: Optimize G: fix other variables and iteratively optimize G; S44: Optimize E: fix other variables, solve through soft threshold operator, and iteratively optimize E; S45: Update Lagrange multipliers 、 and S46: Update parameters , , ; During the iterative optimization process of Equation 6, the stopping criterion is to check whether the convergence condition is satisfied. , if satisfied, stop iterative optimization; otherwise, continue iterative optimization; In step S4, the feature dictionary of X in the base space The acquisition is to restore the color image based on the tensor robust principal component analysis method. , and then use the tensor singular value decomposition get ,in, The algorithm is the abbreviation of the tensor singular value decomposition algorithm, U and V are the left and right singular value matrices respectively, and S is a diagonal matrix; and the feature dictionary of X in the basis space is obtained by the tensor product of U and V ; In step S4, the output noise-free image is .

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