CN105427249A - Wind power image quality enhancing method based on robustness nuclear norm regular regression - Google Patents

Abstract

The invention discloses a wind power image quality enhancing method based on robustness nuclear norm regular regression. The method comprises steps that firstly, each pixel position of an image is taken as a center, and image blocks of all pixel positions of a low quality test image and a training sample image are acquired; secondly, for all image blocks of the lower quality test image, the robustness nuclear norm regular regression method is utilized to acquire robustness linearity expression of an image block set of all image blocks on the corresponding positions of the lower quality training sample image; thirdly, on the condition that the robustness expression coefficient is not changed, high quality training sample image blocks are utilized to replace low quality training sample image blocks, so the high quality test image blocks corresponding to low quality test image blocks are acquired, non-local self-similarity is utilized to realize further quality enhancement for the high quality test image blocks, and fourthly, the high quality test image blocks after further quality enhancement are connected in series and are integrated, and the high quality test image is acquired.

Description

Wind power image quality enhancement method based on robust kernel norm canonical regression

Technical Field

The invention relates to an image quality enhancement method, in particular to a wind power image quality enhancement method based on robust kernel norm regular regression, and belongs to the technical field of image processing.

Background

Image recognition is generally divided into four steps: image preprocessing, feature extraction, feature expression and classification. In order to better track and identify the operating state of the wind turbine blades, it is often necessary to take some images of the wind turbine. Conventional image recognition algorithms assume that the input image has a better resolution. However, in real life, since the target image is often far away from the image capturing apparatus and is affected by the change of the illumination condition, the motion blur of the target image, the noise of the apparatus itself, and other factors, the acquired image is often small in size, low in resolution, large in noise, and extremely limited in feature detail information. In this case, the recognition effect achieved by the conventional image recognition algorithm is far from the expected result.

The performance of the recognition algorithm can be effectively improved by the image quality enhancement method. The single image quality enhancement technology is one of the research hotspots in digital image processing, and a large number of domestic and foreign researchers have conducted extensive and intensive research on the single image quality enhancement technology. From the perspective of historical development, the image quality enhancement technology roughly goes through three stages of an interpolation method, a reconstruction method and a machine learning method. The conventional super-resolution processing technology based on interpolation generally considers discrete image signals as continuous signals, and estimates the pixel values of unknown sampling points by using the continuity characteristics. However, the natural images in the real world include a large number of singular features such as edges, corners, and high-frequency texture regions. Therefore, interpolation algorithms based on the continuity assumption tend to form obvious ringing and aliasing effects, and the super-resolution processing effect is seriously influenced. The method based on reconstruction simulates the formation process of a digital image, and the final result is solved by modeling the process of acquiring image signals by the digital imaging equipment. This method often requires the assumption of some parameters, such as the Point Spread Function (PSF) of the camera, the environmental noise, etc., but these assumed parameters usually do not match the actual parameters, or even are far away from them, which causes the super-resolution result to be severely biased. In addition, sensitivity to amplification factors is one of the main defects of the reconstruction method, which can seriously affect the application and popularization of the algorithm. In contrast, the machine learning method is more attractive than the former two methods, and is well developed from the perspective of theoretical research and practical application.

The current image quality enhancement methods are classified as follows:

1. neighborhood embedding method (NE)

Chang, d.y.yeung and y.m.xiong in Super-resolution through feature reconstruction (pp.1275-1282, vol.1), published in ieee con ference computer vision and pattern recognition (2004), based on local linear embedding theory, reduce the number of reconstructed samples by assuming that the low-resolution feature space and the high-resolution feature space have similar structures, and replace the low-resolution feature with the high-resolution feature while maintaining the similarity structures, obtain a high-quality image block. The method improves the algorithm execution efficiency and obtains good image quality enhancement performance.

2. Characteristic transformation method (Eigentranformation)

Wang, X.Tang in 2005, Hallucientingfacebyyerentinformation, published by IEEETransactionsonsystems, Man, and Connecteuretics (PartC: applied and reviews, vol.35, No.3, pp.425-434), applied Principal Component Analysis (PCA) to characterize the structural similarity of images. PCA is used to represent the low resolution input images as a linear combination of a low resolution training dictionary. By replacing the low resolution training dictionary with a corresponding high resolution training dictionary, a high resolution image may be obtained.

3. Sparse representation method (SR)

Yang, J.Wright, H.Tang and Y.Ma in 2010, Imagesuper-resolution video registration, published by IEEETransactionon Imageprocessing (vol.19, No.11, pp.2861-2873), propose to calculate the coefficients of representation of test image patches on training image patches using sparse representation. Because the number of neighborhoods is not fixed in the sparse approximation process, but the approximation error is as small as possible, the problem of improper fitting in the coefficient solving process is effectively avoided.

In the above methods, before solving the representation coefficients, the two-dimensional low-resolution image (block) is represented as a column vector in advance. This inevitably loses some structural information of the two-dimensional image (such as the rank of the matrix) so that the solution to represent the coefficients is not very accurate. In the conventional method, model construction in the case of noise is not discussed.

Disclosure of Invention

The invention aims to solve the technical problem of providing a wind power image quality enhancement method based on robust kernel norm regular regression, and the method can meet the requirement of high-quality images in practical application by aiming at the defect that the conventional method is sensitive to noise possibly contained in a test image.

The invention adopts the following technical scheme for solving the technical problems:

the invention provides a wind power image quality enhancement method based on robust kernel norm canonical regression, which comprises the following specific steps of:

step 1, taking each pixel position in an image as a center, and acquiring image blocks of each pixel position of a low-quality test image and a training sample image;

step 2, for each image block in the low-quality test image, a robust kernel norm regular regression method is used for obtaining robust linear representation of an image block set at a corresponding position in the low-quality training sample image;

step 3, under the condition that the robust representation coefficient is kept unchanged, replacing the low-quality training sample image blocks with the high-quality training sample image blocks, so as to obtain high-quality measurement attempt image blocks corresponding to the low-quality measurement attempt image blocks, and further performing quality enhancement on the high-quality measurement attempt image blocks by using non-local self-similarity;

and 4, cascading and integrating the high-quality measurement attempt image blocks with further quality enhancement in the step 3 so as to obtain a high-quality test image.

As a further optimization scheme of the present invention, in step 1, taking each pixel position in the image as a center, obtaining image blocks of each pixel position of the low-quality test image and the training sample image, specifically:

1.1) obtaining a low-quality version of a training image;

1.2) taking each pixel position in the image as a center, and obtaining image blocks of each pixel position of the low-quality test image and the training sample image.

As a further optimization scheme of the present invention, in step 1.1, a low quality version of the training image is obtained by two bicubic interpolations.

As a further optimization scheme of the present invention, in step 2, for each image block in the low-quality test image, a robust kernel norm regular regression method is applied to obtain a robust linear representation of an image block set at a corresponding position in the low-quality training sample image, specifically:

D＝x₁C₁+x₂C₂+…+x_MC_M+e

where D is the low quality measurement attempt block for pixel location (i, j); c_rIs the image block at position (i, j) in the r-th low-quality pixel training sample, r ═ 1,2, …, M is the number of training samples; x is the number of_rTo represent the r-th element in the coefficient vector xA value;

based on the robust regression idea, the robust linear representation coefficient vector x is obtained by solving the following model:

$\underset{x}{\min }\left|\right|x|{|}_q+\mathrm{\λ}|\left|Wo\right(C\left(x\right)-D\left)\right|{|}_{*}$

wherein | x | non-conducting phosphor_qIs a q-norm representing a coefficient vector x,λ is a first regularization parameter; w is a weight matrix, W is the ith row and jth column elementα and β are both preset parameters, Y_i,jIs the value of the ith row and the jth column element of the residual error matrix Y; omicron denotes the Hadamard product of the matrix; c (x) x₁C₁+x₂C₂+…+x_MC_MIs from spaceToA linear mapping of (1), d × d being the size of the image block | | · | | magnetism_*Representing the nuclear norm.

As a further optimization of the invention, based on the modelThe method for solving the robust linear representation coefficient vector x is as follows:

2.1) setting a maximum iteration coefficient, and setting the initial iteration time t to be 0;

2.2) updating the weight matrix W and the representation residual error matrix Y, specifically:

$W_{i,j}=\frac{\exp \left(\mathrm{\α}\mathrm{\β}-\mathrm{\α}{\left(Y_{i,j}\right)}^2\right)}{1+xp\left(\mathrm{\α}\mathrm{\β}-\mathrm{\α}{\left(Y_{i,j}\right)}^2\right)}$

Y＝D-D^(t)

wherein D is^(t)Is the low quality measurement of pixel location (i, j) at the t-th iteration of the block, and D⁽⁰⁾＝D_ini，D_iniIs a mean image of a low quality training sample,

2.3) updating the low-quality measuring image blocks and the low-quality training image blocks, specifically:

A＝WoD

B_r＝WοC_r

where A is the low quality measurement attempt block at the weighted pixel location (i, j) and B is_rIs the image block of pixel position (i, j) in the weighted r-th low-quality training sample; 2.4) updating the modelThe method specifically comprises the following steps:

$\underset{x,z,E}{\min }\left|\right|z|{|}_q+\mathrm{\λ}|\left|E\right|{|}_{*}$

s.t.G(x)-A＝Eandx＝z

its lagrange function is expressed as:

$L_{\mathrm{\μ}}(x,z,E)=\left|\right|z|{|}_q+\mathrm{\λ}|\left|E\right|{|}_{*}+\frac{\mathrm{\μ}}{2}\left(\right||x-z+\frac{1}{\mathrm{\μ}}{y}_1|{|}_F^2+\left|\right|G\left(x\right)-A-E+\frac{1}{\mathrm{\μ}}{Y}_2\left|{|}_F^2\right)-\frac{1}{2\mathrm{\μ}}\left|\right|y_1|{|}_2^2-\frac{1}{2\mathrm{\μ}}|\left|Y_2\right|{|}_F^2$

wherein,y₁、Y₂are lagrange multipliers, mu is a second regularization parameter,is the F norm of the matrix;

2.5) adopting an alternative direction multiplier method ADMM to solve the updated model in the step 2.5 to obtain an expression coefficient x output in the t iteration_r ^(t)Thereby obtaining a representative coefficient vector x output in the t iteration^(t)；

2.6) reconstructing low quality measurement attempt blocks, specifically:

$D^{\left(t\right)}={\Σ}_{r=1}^M{x_r}^{\left(t\right)}{B}_r$

wherein D is^(t)Is a low quality trial block at the t-th iteration;

2.7) if the maximum iteration number or the following termination condition is reached, outputting the expression coefficient vector x^(t)As a final solution result; otherwise, setting t as t +1, and returning to the step 2.2;

||W^(t)-W^(t-1)||₂/||W^(t-1)||₂≤γ

wherein γ is a preset first error tolerance value.

As a further optimization scheme of the invention, the maximum iteration number in the step 2.2 is more than or equal to 2.

As a further optimization scheme of the present invention, in step 2.5, an alternating direction multiplier method ADMM is used to solve the model in step 2.5, specifically:

2.5.1) fixing x and E, updating z, specifically:

a) when q is 1, z is found by the soft threshold method:

$z^{l+1}=\underset{z}{\arg \min }\frac{1}{\mathrm{\μ}}\left|\right|z|{|}_1+\frac{1}{2}||z-\left(x^l+\frac{1}{\mathrm{\μ}}{y}_1^l\right)|{|}_F^2;$

b) when q is 2, the process is repeated,

$z^{l+1}=\frac{\mathrm{\μ}}{\mathrm{\μ}+2}\left(x^l+\frac{1}{\mathrm{\μ}}{y}_1^l\right);$

wherein z is^l+1Updating the value of z, x, for step l +1^l、y₁ ^lRespectively x and y after the first step of updating₁A value of (d);

2.5.2) fixing z and E, updating x, and specifically:

$x^{l+1}=(H^{T}H+I)\backslash \[H^{T}Vec\left(A+E^l-\frac{1}{\mathrm{\μ}}{Y}_2^l\right)+z^{l+1}-\frac{1}{\mathrm{\μ}}{y}_1^l\];$

wherein x is^l+1Updating the value of x after step l +1, H ═ Vec (B)₁),…,Vec(B_M)]Vec (-) denotes vectorization of the matrix, E^l、y₁ ^l、Y₂ ^lE, y after respectively updating for the first step₁、Y₂A value of (d);

2.5.3) fixing x and z, updating E, specifically:

solving for optimal E by singular value thresholding^l+1：

$E^{l+1}=\underset{E}{\arg \min }\frac{\mathrm{\λ}}{\mathrm{\μ}}\left|\right|E|{|}_{*}+\frac{1}{2}||E-(G\left(x^{l+1}\right)-A+\frac{1}{\mathrm{\μ}}{Y}_2^l\left)\right|{|}_F^2;$

Wherein E is^l+1The value of E after the step (l + 1) is updated,

2.5.4) updating Lagrange multipliers, which specifically comprises the following steps:

$y_1^{l+1}=y_1^l+\mathrm{\μ}(x^{l+1}-z^{l+1})$

$Y_2^{l+1}=Y_2^l+\mathrm{\μ}(G\left(x^{l+1}\right)-A-E^{l+1})$

wherein,respectively y after the step l +1₁、Y₂A value of (d);

2.5.5) output x if the following termination condition is reached^l+1As x_r ^(t)(ii) a Otherwise, returning to the step 2.5.1;

$\left|\right|G\left(x\right)-A-E+\frac{1}{\mathrm{\μ}}{Y}_2|{|}_{\mathrm{\∞}}\≤\mathrm{\ϵ}and||x-z|{|}_{\mathrm{\∞}}\≤\mathrm{\ϵ}$

wherein | · | purple sweet_∞Is an infinite norm of the matrix and is a preset second error tolerance value.

As a further optimization scheme of the present invention, in step 3, non-local self-similarity is used to further enhance the quality of the high-quality measurement trial block, specifically:

high quality measurement for pixel location (i, j) is attempted for block X_H ^p(i, j), finding similar image blocks b among the high quality measurement attempt blocks at the remaining pixel positions_nN is {1,2, …, L }, L is the number of similar blocks, and for X_H ^p(i, j) is linearly expressed as follows:

${X_H}^p(i,j)=\underset{{X_H}^p\left(i,j\right)}{\arg \min }{\Σ}_{r=1}^M{x}_r{Y_H}^{rp}(i,j)+\mathrm{\δ}\left|\right|{X_H}^p(i,j)-{\Σ}_{n=1}^L{w}_n{b}_n|{|}_2^2$

wherein,for the high quality image block corresponding to the image block at pixel position (i, j) in the r-th low quality training sample, a third regularization parameter, w_nAre linear combination coefficients.

Compared with the prior art, the invention adopting the technical scheme has the following technical effects: the wind power image quality enhancement method based on the robust kernel norm canonical regression can fully utilize the kernel norm measurement criterion to depict the structural information hidden in a noise image and obtain the representation coefficient of noise robustness, so that the obtained high-quality image is more robust to structural noise, and help is provided for the processing and identification of subsequent images.

Drawings

FIG. 1 is a flow chart of the present invention.

Detailed Description

The technical scheme of the invention is further explained in detail by combining the drawings and the specific embodiments:

the invention provides a wind power image quality enhancement method based on robust kernel norm canonical regression, and a specific flow is shown in fig. 1.

And (I) taking each pixel position in the image as a center, and acquiring image blocks of each pixel position of the low-quality test image and the training sample image.

(1) A low quality version of the training image is acquired.

Assuming that the size of the image is w × h and the sampling factor is q, the image set composed of training samples is represented as a three-dimensional matrixAnd r is {1,2, L, M }), wherein M represents the number of training samples. First, a low resolution training sample image set obtained by bicubic interpolation is represented as a three-dimensional matrixThen, the low-quality training sample image set obtained by bicubic interpolation is represented as a three-dimensional matrix

(2) And taking each pixel position in the image as a center, and acquiring image blocks of each pixel position of the low-quality test image and the training sample image.

Taking image blocks of size d × d, centered at each pixel position in the image (size w × h.) for a low quality test imageWhose set of image blocks can be represented asWherein, (i, j) represents the pixel position of the image block, and N represents the number of the image blocks; for low quality training sample image set Y_LThe set of image blocks of each training sample can be represented asFor high quality training sample image set Y_HThe set of image blocks of each training sample can be represented as

And (II) for each image block in the low-quality test image, a robust kernel norm regular regression method is used for obtaining robust linear representation of the image block set at the corresponding position in the low-quality training sample image.

For low quality test image X_LImage block X of pixel position (i, j) in (b)_L ^p(i, j), linearly representing the image blocks at corresponding positions in the low-quality training sample image set by using the image blocks, specifically:

X_L ^p(i,j)＝x₁(i,j)Y_L ^1p(i,j)+x₂(i,j)Y_L ^2p(i,j)+…+x_M(i,j)Y_L ^Mp(i,j)+e

wherein x is₁(i,j),x₂(i,j),…,x_M(i, j) is a representation coefficient, and e is a residual term.

For simplicity, X is replaced by D in the following solution to represent the coefficients_L ^p(i, j) with C₁,C₂,…,C_MReplacement of Y_L ^1p(i,j),Y_L ^2p(i,j),…,Y_L ^Mp(i, j) with x₁,x₂,…,x_MReplacement of x₁(i,j),x₂(i,j),…,x_M(i, j), then C_rThe image block representing pixel position (i, j) in the r-th low-quality training sample, and D represents the low-quality trial image block of pixel position (i, j). And, defining a slave spaceToA linear mapping of c (x) x₁C₁+x₂C₂+…+x_MC_M。

Thus, the representative coefficients of the test image block can be obtained by the following model solution:

$\underset{x}{\min }\left|\right|x|{|}_q+\mathrm{\λ}||C\left(x\right)-D|{|}_{*}$

wherein | x | Y calculation_qIs a q-norm representing a coefficient vector x,x_ris the value of the r-th element in x; λ is a first regularization parameter; | | C (x) -D | non-woven phosphor_*Is the nuclear norm of the residual C (x) -D (C (x) -D sum of all singular values).

In practical application, due to the influence of factors such as motion blur of a target image and noise of the device, the acquired image is often noisy, and the characteristic detail information is extremely limited. Therefore, the representation coefficients obtained by the above model are not accurate enough. Therefore, with the idea of robust regression, the following model is to be used for solving the representation coefficients:

$\underset{x}{\min }\left|\right|x|{|}_q+\mathrm{\λ}|\left|Wo\right(C\left(x\right)-D\left)\right|{|}_{*}$

wherein W is a weight matrix, and the ith row and the jth column of Wα and β are preset parameters, Y_i,jIs the value of the ith row and the jth column element of the residual error matrix Y; omicron denotes the Hadamard product of the matrix.

The representative coefficient vector x may be solved in the following iterative manner:

(1) and setting the maximum iteration coefficient, and setting the initial iteration time t to be 0.

(2) Updating the weight matrix W and the representation residual error matrix Y, specifically:

$W_{i,j}=\frac{\exp \left(\mathrm{\α}\mathrm{\β}-\mathrm{\α}{\left(Y_{i,j}\right)}^2\right)}{1+xp\left(\mathrm{\α}\mathrm{\β}-\mathrm{\α}{\left(Y_{i,j}\right)}^2\right)}$

Y＝D-D^(t)

wherein D is^(t)Is the low quality measurement of pixel location (i, j) at the t-th iteration of the block, and D⁽⁰⁾＝D_ini，D_iniIs of low qualityAverage images of the samples were trained.

(3) Updating the low-quality trial image blocks and the low-quality training image blocks:

A＝WoD

B_r＝WοC_r

where A is the low quality measurement attempt block at the weighted pixel location (i, j) and B is_rIs the image block of pixel position (i, j) in the weighted r-th low-quality training sample.

(4) The solution model for updating the robust linear representation coefficients is:

$\underset{x}{\min }\left|\right|x|{|}_q+\mathrm{\λ}||G\left(x\right)-A|{|}_{*},$

wherein, $G\left(x\right)={\Σ}_{r=1}^M{x}_r{B}_r.$

the above model may be further expressed as:

$\underset{x,z,E}{\min }\left|\right|z|{|}_q+\mathrm{\λ}|\left|E\right|{|}_{*}$

s.t.G(x)-A＝Eandx＝z

its lagrange function is expressed as:

$L_{\mathrm{\μ}}(x,z,E)=\left|\right|z|{|}_q+\mathrm{\λ}|\left|E\right|{|}_{*}+\frac{\mathrm{\μ}}{2}\left(\right||x-z+\frac{1}{\mathrm{\μ}}{y}_1|{|}_F^2+\left|\right|G\left(x\right)-A-E+\frac{1}{\mathrm{\μ}}{Y}_2\left|{|}_F^2\right)-\frac{1}{2\mathrm{\μ}}\left|\right|y_1|{|}_2^2-\frac{1}{2\mathrm{\μ}}|\left|Y_2\right|{|}_F^2.$

wherein, y₁、Y₂Are lagrange multipliers, mu is a regularization parameter,is the F-norm of the matrix.

Solving the model by adopting an alternative direction multiplier method ADMM, which comprises the following specific processes:

(a) fixing x and E, and updating z;

1) when q is 1, z can be found by a soft threshold method:

$z^{l+1}=\underset{z}{\arg \min }\frac{1}{\mathrm{\μ}}\left|\right|z|{|}_1+\frac{1}{2}||z-\left(x^l+\frac{1}{\mathrm{\μ}}{y}_1^l\right)|{|}_F^2$

2) when q is 2:

$z^{l+1}=\frac{\mathrm{\μ}}{\mathrm{\μ}+2}\left(x^l+\frac{1}{\mathrm{\μ}}{y}_1^l\right)$

wherein z is^l+1Updating the value of z, x, for step l +1^l、y₁ ^lRespectively x and y after the first step of updating₁The value of (c).

(b) Fixing z, E, updating x:

$x^{l+1}=(H^{T}H+I)\backslash \[H^{T}Vec\left(A+E^l-\frac{1}{\mathrm{\μ}}{Y}_2^l\right)+z^{l+1}-\frac{1}{\mathrm{\μ}}{y}_1^l\];$

wherein x is^l+1Updating the value of x after step l +1, H ═ Vec (B)₁),…,Vec(B_M)]Vec (-) denotes vectorization of the matrix, E^l、y₁ ^l、Y₂ ^lE, y after respectively updating for the first step₁、Y₂I is an identity matrix.

(c) Fixing x, z, updating E:

$E^{l+1}=\underset{E}{\arg \min }\frac{\mathrm{\λ}}{\mathrm{\μ}}\left|\right|E|{|}_{*}+\frac{1}{2}||E-(G\left(x^{l+1}\right)-A+\frac{1}{\mathrm{\μ}}{Y}_2^l\left)\right|{|}_F^2;$

optimal E can be solved by singular value thresholding^l+1Wherein E is^l+1The value of E after the step (l + 1) is updated, $G\left(x^{l+1}\right)={\Σ}_{r=1}^M{x_r}^{l+1}{B}_r.$

(d) updating Lagrange multiplier:

$y_1^{l+1}=y_1^l+\mathrm{\μ}(x^{l+1}-z^{l+1})$

$Y_2^{l+1}=Y_2^l+\mathrm{\μ}(G\left(x^{l+1}\right)-A-E^{l+1})$

wherein,respectively y after the step l +1₁、Y₂The value of (c).

(e) If the following termination condition is reached, output x^l+1As x_r ^(t)(ii) a Otherwise, return to (a):

$\left|\right|G\left(x\right)-A-E+\frac{1}{\mathrm{\μ}}{Y}_2|{|}_{\mathrm{\∞}}\≤\mathrm{\ϵ}and||x-z|{|}_{\mathrm{\∞}}\≤\mathrm{\ϵ}$

wherein | · | purple sweet_∞Is an infinite norm of the matrix and is a preset second error tolerance value.

(5) Reconstructing the low quality measurement attempt block:

$D^{\left(t\right)}={\mathrm{\Σ}}_{r=1}^M{x_r}^{\left(t\right)}{B}_r$

wherein D is^(t)Is a low quality trial block at the t-th iteration;

(6) if the maximum iteration number or the following termination condition is reached, outputting the expression coefficient vector x^(t)As a final solution result; otherwise, setting the iteration time t as t +1, and returning to the step 2.2;

||W^(t)-W^(t-1)||₂/||W^(t-1)||₂≤γ

wherein γ is a preset first error tolerance value.

And (III) under the condition that the robust representation coefficient is kept unchanged, replacing the low-quality training sample image blocks with the high-quality training sample image blocks, thereby obtaining high-quality measurement attempt image blocks corresponding to the low-quality measurement attempt image blocks, and further performing quality enhancement on the high-quality measurement attempt image blocks by using non-local self-similarity.

(1) And replacing the low-quality training sample image blocks with the high-quality training sample image blocks under the condition of keeping the robust representation coefficients unchanged.

Low quality measurement of pixel location (i, j) is attempted for block X_L ^p(i, j) the high quality measurement attempt block of pixel location (i, j) may be expressed as:

${X_H}^p(i,j)={\Σ}_{r=1}^M{x}_r(i,j){Y_H}^{rp}(i,j)$

wherein x is_rAnd (i, j) is the robust representation coefficient obtained by the solution in the step (two).

(2) Further quality enhancement is applied to the high quality measurement attempt blocks using non-local self-similarity.

High quality measurement for pixel location (i, j) is attempted for block X_H ^p(i, j), finding similar image blocks b among the high quality measurement attempt blocks at the remaining pixel positions_nN is {1,2, …, L }, L is the number of similar blocks, and for X_H ^p(i, j) is linearly expressed as follows:

${X_H}^p\left(i,j\right)=\underset{{X_H}^p\left(i,j\right)}{\arg \min }{\Σ}_{r=1}^M{x}_r\left(i,j\right){Y_H}^{rp}\left(i,j\right)+\mathrm{\δ}\left|\right|{X_H}^p\left(i,j\right)-{\Σ}_{n=1}^L{w}_n{b}_n|{|}_2^2$

wherein, Y_H ^rp(i, j) is_rThe high-quality image block corresponding to the image block of the pixel position (i, j) in the low-quality training sample is the third regularization parameter, w_nAre linear combination coefficients.

And (IV) connecting and integrating the high-quality measurement image blocks with the further quality enhancement in the step (III) so as to obtain a high-quality test image.

The obtained high quality measurement image is pieced together to obtain a low quality test image X_LCorresponding high quality metrology image X_H. Wherein, for the pixel values of the overlapping area, the average value is taken as the final result.

Here, the number of pixels in the overlap region is two cases:

(1) if the image block size d is odd, the image block X_H ^pThe number of overlapping pixels of (i, j) and its adjacent block is d × [ (d-1)/2%]；

(2) If the image block size d is even, the image block X_H ^pThe number of overlapping pixels between (i, j) and its adjacent block is d × (d/2).

The above description is only an embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can understand that the modifications or substitutions within the technical scope of the present invention are included in the scope of the present invention, and therefore, the scope of the present invention should be subject to the protection scope of the claims.

Claims (8)

1. A wind power image quality enhancement method based on robust kernel norm canonical regression is characterized by comprising the following specific steps:

step 1, taking each pixel position in an image as a center, and acquiring image blocks of each pixel position of a low-quality test image and a training sample image;

step 2, for each image block in the low-quality test image, a robust kernel norm regular regression method is used for obtaining robust linear representation of an image block set at a corresponding position in the low-quality training sample image;

step 3, under the condition that the robust representation coefficient is kept unchanged, replacing the low-quality training sample image blocks with the high-quality training sample image blocks, so as to obtain high-quality measurement attempt image blocks corresponding to the low-quality measurement attempt image blocks, and further performing quality enhancement on the high-quality measurement attempt image blocks by using non-local self-similarity;

and 4, cascading and integrating the high-quality measurement attempt image blocks with further quality enhancement in the step 3 so as to obtain a high-quality test image.

2. The wind power image quality enhancement method based on robust kernel norm canonical regression as claimed in claim 1, wherein in step 1, the image blocks of each pixel position of the low-quality test image and the training sample image are obtained with each pixel position in the image as a center, specifically:

1.1) obtaining a low-quality version of a training image;

1.2) taking each pixel position in the image as a center, and obtaining image blocks of each pixel position of the low-quality test image and the training sample image.

3. The wind power image quality enhancement method based on robust kernel norm canonical regression as claimed in claim 2, wherein in step 1.1, a low quality version of the training image is obtained by two bicubic interpolations.

4. The wind power image quality enhancement method based on robust kernel norm regular regression as claimed in claim 1, wherein in step 2, for each image block in the low-quality test image, a robust kernel norm regular regression method is applied to obtain robust linear representation of an image block set at a corresponding position in the low-quality training sample image, specifically:

D＝x₁C₁+x₂C₂+…+x_MC_M+e

where D is the low quality measurement attempt block for pixel location (i, j); c_rIs the r-th low qualityMeasuring the image block at position (i, j) in the pixel training sample, wherein r is {1,2, …, M }, and M is the number of training samples; x is the number of_rIs the value representing the r-th element in the coefficient vector x;

based on the robust regression idea, the robust linear representation coefficient vector x is obtained by solving the following model:

wherein | x | non-conducting phosphor_qIs a q-norm representing a coefficient vector x,λ is a first regularization parameter; w is a weight matrix, W is the ith row and jth column elementα and β are both preset parameters, Y_i,jIs the value of the ith row and the jth column element of the residual error matrix Y; a Hadamard product representing a matrix; c (x) x₁C₁+x₂C₂+…+x_MC_MIs from spaceToA linear mapping of (1), d × d being the size of the image block | | · | | magnetism_*Representing the nuclear norm.

5. The wind power image quality enhancement method based on robust kernel norm canonical regression as claimed in claim 4, wherein the wind power image quality enhancement method is based on a modelThe method for solving the robust linear representation coefficient vector x is as follows:

2.1) setting a maximum iteration coefficient, and setting the initial iteration time t to be 0;

2.2) updating the weight matrix W and the representation residual error matrix Y, specifically:

Y＝D-D^(t)

wherein D is^(t)Is the low quality measurement of pixel location (i, j) at the t-th iteration of the block, and D⁽⁰⁾＝D_ini，D_iniIs a mean image of a low quality training sample,

2.3) updating the low-quality measuring image blocks and the low-quality training image blocks, specifically:

A＝WоD

B_r＝WоC_r

where A is the low quality measurement attempt block at the weighted pixel location (i, j) and B is_rIs the image block of pixel position (i, j) in the weighted r-th low-quality training sample; 2.4) updating the modelThe method specifically comprises the following steps:

s.t.G(x)-A＝Eandx＝z

its lagrange function is expressed as:

wherein,y₁、Y₂are lagrange multipliers, mu is a second regularization parameter,is the F norm of the matrix;

2.5) adopting an alternative direction multiplier method ADMM to solve the updated model in the step 2.5 to obtain an expression coefficient x output in the t iteration_r ^(t)To obtain the expression coefficient vector x output in the t iteration^(t)；

2.6) reconstructing low quality measurement attempt blocks, specifically:

wherein D is^(t)Is a low quality trial block at the t-th iteration;

2.7) if the maximum iteration number or the following termination condition is reached, outputting the expression coefficient vector x^(t)As a final solution result; otherwise, setting t as t +1, and returning to the step 2.2;

||W^(t)-W^(t-1)||₂/||W^(t-1)||₂≤γ

wherein γ is a preset first error tolerance value.

6. The wind power image quality enhancement method based on robust kernel norm canonical regression as claimed in claim 5, wherein the maximum number of iterations in step 2.2 is greater than or equal to 2.

7. The wind power image quality enhancement method based on robust kernel norm canonical regression as claimed in claim 5, wherein the model in step 2.5 is solved by an Alternative Direction Multiplier Method (ADMM) in step 2.5, specifically:

2.5.1) fixing x and E, updating z, specifically:

a) when q is 1, z is found by the soft threshold method:

b) when q is 2, the process is repeated,

wherein z is^l+1Updating the value of z, x, for step l +1^l、y₁ ^lRespectively x and y after the first step of updating₁A value of (d);

2.5.2) fixing z and E, updating x, and specifically:

wherein x is^l+1Updating the value of x after step l +1, H ═ Vec (B)₁),…,Vec(B_M)]Vec (-) denotes vectorization of the matrix, E^l、y₁ ^l、Y₂ ^lE, y after respectively updating for the first step₁、Y₂A value of (d);

2.5.3) fixing x and z, updating E, specifically:

solving for optimal E by singular value thresholding^l+1：

Wherein E is^l+1The value of E after the step (l + 1) is updated,

2.5.4) updating Lagrange multipliers, which specifically comprises the following steps:

wherein,respectively y after the step l +1₁、Y₂A value of (d);

2.5.5) output x if the following termination condition is reached^l+1AsOtherwise, returning to the step 2.5.1;

wherein | · | purple sweet_∞Is an infinite norm of the matrix and is a preset second error tolerance value.

8. The wind power image quality enhancement method based on robust kernel norm canonical regression as claimed in claim 5, wherein the further quality enhancement is performed on the high quality measurement trial image blocks by applying non-local self-similarity in step 3, specifically:

high quality measurement for pixel location (i, j) is attempted for block X_H ^p(i, j), finding similar image blocks b among the high quality measurement attempt blocks at the remaining pixel positions_nN is {1,2, …, L }, L is the number of similar blocks, and for X_H ^p(i, j) is linearly expressed as follows:

wherein, Y_H ^rp(i, j) is_rThe high-quality image block corresponding to the image block of the pixel position (i, j) in the low-quality training sample is the third regularization parameter, w_nAre linear combination coefficients.