A multi-degraded image restoration method based on degradation pattern decoupling learning

Abstract

The present invention discloses a method for restoring multiple degraded images based on degradation pattern decoupling learning, comprising the following steps: transmitting the degraded image to a trained image restoration model to output a restored image; the image restoration model comprises a backbone network and a decoupling optimization operator, the decoupling optimization operator comprising a singular vector optimization operator and a singular value optimization operator; the singular vector optimization operator optimizes the degradation representation singular vectors of the degraded image by utilizing the characteristic that orthogonal matrix multiplication does not change the singular values ​​but only changes the singular vectors; the singular value optimization operator optimizes the degradation representation singular values ​​of the degraded image by utilizing the fast Fourier transform based on the signal formation principle similar to singular value decomposition and Fourier transform; the method for restoring multiple degraded images realizes joint optimization among multiple degraded image restoration tasks, thereby achieving better performance with fewer model parameters and computational complexity.

Description

Technical Field

[0001] The present invention relates to the field of image processing technology, and in particular to a multi-degraded image restoration method based on degradation pattern decoupling learning. Background Art

[0002] Image restoration aims to recover potentially high-quality images from degraded observations. Common image restoration tasks include image deraining, image dehazing, image denoising, image deblurring, and low-light image enhancement. In addition to achieving satisfactory visual results in classic photo restoration, image restoration is also widely used in other real-world scenarios such as autonomous driving and road monitoring to assist with high-level visual tasks such as target recognition and tracking. Currently, most image restoration methods only address one type of degradation, making it difficult to adapt to the variability and unpredictability of degradation types in complex scenes. Therefore, deployments often require switching between multiple degradation restoration models, resulting in significant consumption of storage and computing resources.

[0003] To address this issue, work in the era of deep learning has begun to focus on multi-degraded image restoration. This approach utilizes a single network model to handle different image restoration tasks. These approaches can be categorized into general multi-degraded image restoration methods and joint multi-degraded image restoration methods. The former uses the same network architecture but employs different network parameters for different image restoration tasks. The latter uses a single set of network parameters to handle different types of degradation.

[0004] Most current joint multi-degraded image restoration methods adopt a mutually exclusive degradation paradigm for learning. This emphasizes the differences between different degradation types to achieve specialized processing within the network, while the correlation between different degradation types is not effectively considered. For example, in addition to a shared backbone network, different head and tail networks are used for different degradation types, or different queries are set for different degradation types in the Transformer architecture for discriminative query, and contrastive learning is used to provide degradation representations of different degradation types to guide the model for restoration. As a result, existing multi-degraded image restoration methods often require large model sizes and heavy computational complexity to achieve good performance.

[0005] Although a small amount of work has begun to explore joint optimization between two degradation types, such as leveraging the complementarity of blurred and noisy image pairs during the imaging process for joint restoration, using a low-light enhancement encoder and a deblurring decoder to achieve hybrid degradation restoration, and using a method to quantify the relationship between any two image restoration tasks and using an auxiliary restoration task to improve the performance of the main restoration task, these methods are often highly degradation-specific or difficult to apply to joint optimization across a wider range of degradation types. Summary of the Invention

[0006] Based on the technical problems existing in the background technology, the present invention proposes a multi-degraded image restoration method based on degradation pattern decoupling learning, which realizes the joint optimization between multiple degraded image restoration tasks, thereby achieving better performance with fewer model parameters and computational complexity.

[0007] The present invention proposes a method for restoring multiple degraded images based on degradation pattern decoupling learning, comprising the following steps:

[0008] Feed the degraded image into the trained image restoration model to output the restored image;

[0009] The image restoration model includes a backbone network and a decoupling optimization operator, the decoupling optimization operator replaces the basic building blocks in the backbone network, and the decoupling optimization operator includes a singular vector optimization operator and a singular value optimization operator;

[0010] The singular vector optimization operator optimizes the degradation representation singular vectors of the degraded image by taking advantage of the fact that orthogonal matrix multiplication does not change the singular values ​​but only changes the singular vectors.

[0011] The singular value optimization operator is based on the signal formation principle similar to singular value decomposition and Fourier transform, and uses fast Fourier transform to optimize the degradation representation singular values ​​of the degraded image.

[0012] Furthermore, the decoupling optimization operator embedded in the bottleneck layer of the backbone network only has a singular value optimization operator, and the decoupling optimization operators in the remaining embedded positions have a singular vector optimization operator and a singular value optimization operator.

[0013] Furthermore, the specific process of decoupling optimization in the singular vector optimization operator is as follows:

[0014] Define the input feature of the i-th decoupling optimization operator embedded in the image restoration model as X, and calculate the inverse pixel reconstruction representation X′ of the input feature X;

[0015] Apply convolution with orthogonality constraint to the inverse pixel reconstructed representation X′ to obtain feature Y′ vec , calculate the feature Y′ vec The pixel reorganization representation Y vec , pixel reorganization represents Y vec Output features of the optimization operator for singular vectors.

[0016] Furthermore, the characteristics Where h and w represent the height and width of the input feature X, respectively, c represents the dimension of the input feature X, and r represents the scaling factor;

[0017] Feature Y′ vec The calculation formula is as follows:

[0018] Y′ vec =conv(X′)

[0019] Orthogonality constraints for convolution Expressed as:

[0020]

[0021] in, W represents the weight matrix of 1×1 convolution, 1 represents a matrix with all elements set to 1, I represents the identity matrix, ⊙ represents element-by-element multiplication, ‖·‖ F represents the Frobenius norm of the matrix, and T represents the matrix transpose.

[0022] Furthermore, the specific process of decoupling optimization of the singular value optimization operator is as follows:

[0023] Define the input feature X of the singular value optimization operator in the i-th decoupling optimization operator embedded in the image restoration model val , input feature X val The output feature Y of the singular vector optimization operator vec ;

[0024] For the input feature X val Perform Fourier transform to obtain features Pair Features Perform convolution operation to output features

[0025] calculate The inverse Fourier transform Y val ; Feature Y val Serves as the output features of the singular value optimization operator.

[0026] Furthermore, the singular vector optimization operator and the singular value optimization operator are encapsulated into a decoupled optimization operator to achieve decoupled learning of the image restoration model. The encapsulation process is as follows: define the singular vector optimization operator as vec(·), define the singular value optimization operator as val(·), and then the decoupled optimization operator is calculated according to the following formula:

[0027] Y=conv([val(vec(X)),vec(X)])

[0028] Where X is the input feature of the i-th decoupling optimization operator embedded in the image restoration model, Y is the output feature of the i-th decoupling optimization operator embedded in the image restoration model, [·] represents the inter-channel cascade, and conv(·) represents a 3×3 convolution.

[0029] Furthermore, the training process of the image restoration model is as follows:

[0030] An image restoration model is constructed using a universal image restoration network with arbitrary convolutional architecture as the backbone network, and the decoupled optimization operator is embedded into the image restoration model.

[0031] Constructing a training set, wherein the training set includes images of multiple degradation types;

[0032] Constructing a target loss function of the image restoration model, the target loss function includes the original loss function of the backbone network and the reconstruction loss function after the decoupling optimization operator is embedded;

[0033] The training set is input into the image restoration model for training to obtain the pre-trained image restoration model.

[0034] Furthermore, the objective loss function of the image restoration model is as follows:

[0035]

[0036]

[0037]

[0038] in, represents the original loss function of the backbone network, λ oryh and λ frv represents the balance weight of the loss function, represents the orthogonality constraint of convolution, represents the reconstruction loss function, I clean Represents the original undegraded image corresponding to the input degraded image, I rec represents the restored image output by the image restoration model after the input degraded image, ‖.‖1 represents the L1 norm, and U rec , Represents the restored image I rec The singular vector matrix, Σ rec Represents the restored image I rec The singular value matrix of U clean , Represents the original undegraded image I clean The singular vector matrix, Σ clean Represents the original undegraded image I clean The singular value matrix of , j represents the red, green and blue channels, and β represents the balance weight.

[0039] The advantage of the multi-degraded image restoration method based on degradation pattern decoupling learning provided by the present invention is that it can be combined with an image restoration backbone network of any convolutional architecture to achieve better multi-degraded image restoration performance. Specifically, two optimization operators are proposed to support the decoupled optimization of the singular values ​​and singular vectors of degradation representations. The singular vector optimization operator utilizes the characteristic that orthogonal matrix multiplication does not change the singular values ​​but only the singular vectors, thereby focusing on the optimization of the singular vectors of degradation representations. The singular value optimization operator utilizes the signal formation principle similar to singular value decomposition and Fourier transform, that is, the signal can be regarded as the weighted sum of a set of bases, and thus uses the fast Fourier transform to focus on optimizing the singular values ​​of the degradation representation; focusing on optimizing the singular values ​​and singular vectors of each degradation representation, it implicitly utilizes the correlation between different degradation types within the same degradation mode, and avoids interference conflicts between degradation types between different degradation modes, thereby realizing joint optimization between multiple degraded image restoration tasks, thereby achieving better performance with fewer model parameters and computational complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a structural schematic diagram of the present invention;

[0041] Figure 2 Schematic diagram of the decoupling optimization operator structure;

[0042] Figure 3 Schematic diagram of the paradigm for embedding decoupled optimization operators into the backbone network;

[0043] Figure 4 Optimization diagram for the singular vector optimization operator;

[0044] Figure 5 Optimization diagram for the singular value optimization operator. DETAILED DESCRIPTION

[0045] The technical solutions of the present invention are described in detail below through specific embodiments. Numerous specific details are set forth in the following description to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways than those described herein, and those skilled in the art may make similar modifications without departing from the scope of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0046] like Figures 1 to 5 As shown, the present invention proposes a multi-degraded image restoration method based on degradation mode decoupling learning, which includes the following steps:

[0047] The degraded image is fed into a trained image restoration model to output a restored image. The image restoration model includes a backbone network and a decoupling optimization operator, which replaces the basic building blocks of the backbone network. The decoupling optimization operator includes a singular vector optimization operator and a singular value optimization operator.

[0048] This embodiment aims to optimize the degradation type hierarchy in the multi-degraded image restoration method by using a set of network parameters to handle different degradation types, and proposes to re-examine the degradation modes of various degradation types from the perspective of singular value decomposition. The degradation types involved include image deraining, image defogging, image denoising, image deblurring, and low-light image enhancement. It is found that the decomposed singular vectors and singular values ​​respectively bear the degradation information of different degradation types, thereby dividing different image restoration tasks into two categories, namely, the degradation mode dominated by singular vectors and the degradation mode dominated by singular values, such as Figure 1 As shown. Therefore, the present invention provides a more unified perspective of degradation modes on top of degradation types, and realizes optimization of degradation mode levels, wherein rain removal, denoising, and deblurring are degradation modes dominated by singular vectors, and defogging and low-light enhancement are degradation modes dominated by singular values. This helps to achieve a more unified joint optimization of multiple degradations. Specifically, by focusing on optimizing the singular values ​​and singular vectors of each degradation representation and implicitly utilizing the correlation between different degradation types within the same degradation mode, and avoiding interference conflicts between degradation types between different degradation modes, the joint optimization of multiple degraded image restoration tasks is realized, thereby achieving better performance with fewer model parameters and computational complexity.

[0049] The multi-degraded image restoration method proposed in this embodiment can be combined with an image restoration backbone network of any convolutional architecture to obtain better multi-degraded image restoration performance. Specifically, two optimization operators are proposed to support the decoupled optimization of the singular values ​​and singular vectors of degradation representations. Among them, the singular vector optimization operator uses the characteristic that orthogonal matrix multiplication does not change the singular values ​​but only changes the singular vectors, thereby focusing on the optimization of the singular vectors of degradation representations. The singular value optimization operator uses the signal formation principle similar to the singular value decomposition and Fourier transform, that is, the signal can be regarded as the weighted sum of a set of bases, thereby using the fast Fourier transform to focus on the optimization of the singular values ​​of degradation representations.

[0050] The decoupling optimization operator is embedded in the backbone network in the following way: the basic building blocks in the image restoration model are replaced by the decoupling optimization operator, where the basic building blocks can be shallow small networks, such as Figure 3 As shown in the first paradigm; or a single layer of convolution, such as Figure 3This is shown in the second paradigm. Specifically, considering that singular vectors correspond to image content information and spatial details, while singular values ​​correspond to the image's global statistical properties, the decoupled optimization operator embedded only in the bottleneck layer of the backbone network contains a singular value optimization operator, while the decoupled optimization operator at all other locations contains both a singular vector optimization operator and a singular value optimization operator. This approach takes into account the non-negligible computational complexity introduced by the fast Fourier transform in the singular value optimization operator.

[0051] The singular vector optimization operator and the singular value optimization operator are described in detail below.

[0052] (A) If Figure 4 As shown in Figure 2, the specific process of decoupling optimization in the singular vector optimization operator is shown.

[0053] (A1) Define the input features of the i-th decoupling optimization operator embedded in the image restoration model as (The subscript i is omitted for simplicity), where h and w represent the height and width of the input feature X, respectively, and c represents the dimension of the input feature X. The unpixel shuffle of the input feature X is calculated to represent X′; to transfer the spatial information of the input feature X to the channel dimension, where the scaling factor is r, then

[0054] (A2) Apply convolution with orthogonality constraint to the inverse pixel reconstructed representation X′ to obtain the feature Y′ vec =conv(X′),Y′ vec The convolution kernel size is 1×1, which is equivalent to performing orthogonal matrix multiplication on X′ along the channel dimension, that is, only the singular vectors of X′ are changed without changing the singular values ​​of X′, thus achieving decoupling optimization of the singular vectors of X′. Orthogonal constraints of convolution Expressed as:

[0055]

[0056] Among them, W represents the weight matrix of 1×1 convolution, 1 represents a matrix with all elements set to 1, I represents the identity matrix, ⊙ represents element-by-element multiplication, ‖·‖ F represents the Frobenius norm of the matrix, and T represents the matrix transpose.

[0057] (A3) Calculate feature Y′ vec Pixelshuffle represents Y vec , Pixelshuffle means Output features of the optimization operator for singular vectors.

[0058] (B) Figure 5As shown in Figure 2, the specific process of decoupling optimization of the singular value optimization operator is shown.

[0059] (B1) Define the input feature X of the singular value optimization operator in the i-th decoupling optimization operator embedded in the image restoration model val , input feature X val The output feature Y of the singular vector optimization operator vec ;

[0060] Considering that the SVD (Singular Value Decomposition) configuration of the signal is similar to the IDFT (Inverse Discrete Fourier Transform) configuration of the signal, that is, both are weighted sums on a set of bases. Specifically, the input feature A two-dimensional slice of For example (the three-dimensional signal form can be simply generalized by repetition between channels), the SVD configuration of the signal is:

[0061]

[0062] in, Represents the signal X′ val The singular vector matrix after performing singular value decomposition, Represents the signal X′ val The singular value matrix after performing singular value decomposition, k = min (h, w) is X' val rank. represents the i-th column of the singular vector matrix U,V, σ i represents the i-th diagonal element of the singular value matrix, and T represents the matrix transpose.

[0063] Then the signal X′ val It can be viewed as a weighted sum of a set of bases, the base components are The weighting coefficient is The DFT configuration of the signal is:

[0064]

[0065] Among them, G(u,v) represents the signal X′ val The coefficients at the frequency domain coordinates (u,v) after performing the discrete Fourier transform, and Represents the two-dimensional spatial coordinates, represents a two-dimensional complex wave. Then the signal X′ val It can be viewed as a weighted sum of a set of bases, the base components are The weighting coefficient is

[0066] From this, we can deduce the similarity between the SVD configuration of the signal and the DFT configuration of the signal, and the singular value σ of the signal iIt has the same function as the discrete Fourier transform coefficients G(u,v) of the signal. Therefore, the optimization of singular values ​​can be converted into the optimization of Fourier transform coefficients.

[0067] (B2) Input feature X val Perform Fourier transform to obtain features Features Perform convolution operation to output features Output features The convolution kernel size is 1×1. That is, the optimization of the Fourier transform coefficients of the input features is similar to the optimization of the singular values ​​of the input features, that is, to achieve X val Singular value decoupling optimization.

[0068] (B3) Calculation The inverse Fourier transform of Feature Y val Serves as the output features of the singular value optimization operator.

[0069] (C) Figure 2 and 3 As shown in Figure 2, the specific process of decoupling optimization operator.

[0070] The singular vector optimization operator and the singular value optimization operator are encapsulated into a decoupled optimization operator to achieve decoupled learning of the image restoration model. The encapsulation process is as follows: define the singular vector optimization operator as vec(·), as shown in step (A), define the singular value optimization operator as val(·), as shown in step (B), and then calculate the decoupled optimization operator according to the following formula:

[0071] X=conv([val(vec(X)),vec(X)])

[0072] Where X is the input feature of the i-th decoupled optimization operator embedded in the image restoration model, Y is the output feature of the i-th decoupled optimization operator embedded in the image restoration model (the subscript i is omitted for simplicity), [·] represents inter-channel cascade, and conv(·) represents 3×3 convolution.

[0073] (D) Objective loss function of image restoration model as follows:

[0074]

[0075]

[0076]

[0077] in, represents the original loss function of the backbone network, λ orth and λdec represents the balance weight of the loss function, represents the orthogonality constraint of convolution, represents the reconstruction loss function, I clean Represents the original undegraded image corresponding to the input degraded image, I rec represents the restored image output by the image restoration model after the input degraded image, ‖.‖1 represents the L1 norm, and U rec , Represents the restored image I rec The singular vector matrix, Σ rec Represents the restored image I rec The singular value matrix of U clean , Represents the original undegraded image I clean The singular vector matrix, Σ clean Represents the original undegraded image I clean The singular value matrix, j represents the red, green and blue channels, β represents the balance weight, β is 0.1, λ orth Take 0.01, λ dec Take 0.1.

[0078] (E) The training process of the image restoration model is as follows:

[0079] (E1) An image restoration model is constructed using a universal image restoration network with arbitrary convolutional architecture as the backbone network, and the decoupled optimization operator is embedded into the image restoration model;

[0080] (E2) constructing a training set, wherein the training set includes images of multiple degradation types;

[0081] Prepare a batch of images containing different degradation types. Here, we use five degradation types as examples: rain removal, dehazing, denoising, deblurring, and low-light. Use the degraded images as training images for the image restoration model. Simultaneously, save the original, undegraded images corresponding to the degraded images to serve as the target loss function in the image restoration model. The images are preprocessed, including data augmentation such as random horizontal and vertical flips and random rotations, and then cropped into 128×128 image blocks for training.

[0082] (E3) constructing a target loss function of the image restoration model, wherein the target loss function includes the original loss function of the backbone network and the reconstruction loss function after the decoupling optimization operator is embedded;

[0083] (E4) inputting the training set into the image restoration model for training to obtain the pre-trained image restoration model;

[0084] Train the image restoration model according to the target loss function until the preset training completion criteria are met. Here, 1200 epochs can be used as the training completion criteria. Optimize the entire network using the Adam optimizer, using cosine annealing as the learning strategy, an initial learning rate of 1e-4, and a batch size of 8.

[0085] In order to quantitatively evaluate the effectiveness of the present invention, this invention was quantitatively evaluated on the Rain100L, SOTS-Outdoor, BSD68, Urban100, Kodak24, GoPro, and LOL datasets together with methods such as NAFNet, Restormer, and AirNet. Three performance indicators, namely, Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Metric (SSIM), and Learned Perceptual Image Patch Similarity (LPIPS), were selected as numerical evaluation indicators. In the quantitative analysis, the present invention achieved the best average performance on a total of seven test datasets with five degradation types, and achieved smaller model parameters and computational complexity compared to the baseline model.

[0086] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solution and inventive concept of the present invention, should be covered by the scope of protection of the present invention.

Claims

1. A method for restoring multiple degraded images based on degradation pattern decoupling learning, characterized in that: The steps include: Feed the degraded image into the trained image restoration model to output the restored image; The image restoration model includes a backbone network and a decoupling optimization operator, the decoupling optimization operator replaces the basic building blocks in the backbone network, and the decoupling optimization operator includes a singular vector optimization operator and a singular value optimization operator; The singular vector optimization operator optimizes the degradation representation singular vectors of the degraded image by taking advantage of the fact that orthogonal matrix multiplication does not change the singular values ​​but only changes the singular vectors. The singular value optimization operator is based on the signal formation principle similar to singular value decomposition and Fourier transform, and uses fast Fourier transform to optimize the degradation representation singular values ​​of the degraded image.

2. The method for restoring multiple degraded images based on degradation pattern decoupling learning according to claim 1, characterized in that: The decoupling optimization operator embedded in the bottleneck layer of the backbone network only has a singular value optimization operator, and the decoupling optimization operators in the other embedded positions have a singular vector optimization operator and a singular value optimization operator.

3. The method for restoring multiple degraded images based on degradation pattern decoupling learning according to claim 1, characterized in that: The specific process of decoupling optimization in the singular vector optimization operator is as follows: Define the input feature of the i-th decoupling optimization operator embedded in the image restoration model as X, and calculate the inverse pixel reconstruction representation X′ of the input feature X; Apply convolution with orthogonality constraint to the inverse pixel reconstructed representation X′ to obtain feature Y′ vec , calculate the feature Y′ vec The pixel reorganization representation Y vec , pixel reorganization represents Y vec Output features of the optimization operator for singular vectors.

4. The method for restoring multiple degraded images based on degradation pattern decoupling learning according to claim 3, characterized in that: feature Where h and w represent the height and width of the input feature X, respectively, c represents the dimension of the input feature X, and r represents the scaling factor; Feature Y′ vec The calculation formula is as follows: Y′ vec =conv(X′) Orthogonality constraints for convolution Expressed as: in, W represents the weight matrix of 1×1 convolution, 1 represents a matrix with all elements set to 1, I represents the identity matrix, ⊙ represents element-by-element multiplication, ‖·‖ F represents the Frobenius norm of the matrix, and T represents the matrix transpose.

5. The method for restoring multiple degraded images based on degradation pattern decoupling learning according to claim 3, characterized in that: The specific process of decoupling optimization of the singular value optimization operator is as follows: Define the input feature X of the singular value optimization operator in the i-th decoupling optimization operator embedded in the image restoration model val , input feature X val The output feature Y of the singular vector optimization operator vec ; For the input feature X val Perform Fourier transform to obtain features Pair Features Perform convolution operation to output features calculate The inverse Fourier transform Y val ; Feature Y val Serves as the output features of the singular value optimization operator.

6. The method for restoring multiple degraded images based on degradation pattern decoupling learning according to claim 5, characterized in that: The singular vector optimization operator and the singular value optimization operator are encapsulated into a decoupled optimization operator to achieve decoupled learning of the image restoration model. The encapsulation process is as follows: define the singular vector optimization operator as vec(·), define the singular value optimization operator as val(·), and then the decoupled optimization operator is calculated according to the following formula: X=conv([val(vec(X)),vec(X)]) Where X is the input feature of the i-th decoupling optimization operator embedded in the image restoration model, Y is the output feature of the i-th decoupling optimization operator embedded in the image restoration model, [·] represents the inter-channel cascade, and conv(·) represents a 3×3 convolution.

7. The method for restoring multiple degraded images based on degradation pattern decoupling learning according to claim 4, characterized in that: The training process of the image restoration model is as follows: An image restoration model is constructed using a universal image restoration network with arbitrary convolutional architecture as the backbone network, and the decoupled optimization operator is embedded into the image restoration model. Constructing a training set, wherein the training set includes images of multiple degradation types; Constructing a target loss function of the image restoration model, the target loss function includes the original loss function of the backbone network and the reconstruction loss function after the decoupling optimization operator is embedded; The training set is input into the image restoration model for training to obtain the pre-trained image restoration model.

8. The method for restoring multiple degraded images based on degradation pattern decoupling learning according to claim 7, characterized in that: The objective loss function of the image restoration model as follows: in, represents the original loss function of the backbone network, λ orth and λ dec represents the balance weight of the loss function, represents the orthogonality constraint of convolution, represents the reconstruction loss function, I clean Represents the original undegraded image corresponding to the input degraded image, I rec represents the restored image output by the image restoration model after the input degraded image, ‖.‖1 represents the L1 norm, Represents the restored image I rec The singular vector matrix, Σ rec Represents the restored image I rec The singular value matrix of ; Represents the original undegraded image I clean The singular vector matrix, Σ clean Represents the original undegraded image I clean The singular value matrix of , j represents the red, green and blue channels, and β represents the balance weight.

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