CN102622729B

CN102622729B - Spatial self-adaptive block-matching image denoising method based on fuzzy set theory

Info

Publication number: CN102622729B
Application number: CN201210059658.0A
Authority: CN
Inventors: 杨波; 赵放; 门爱东; 邸金红; 韩睿; 叶锋; 张鑫明; 肖贺; 姜竹青; 林立翔
Original assignee: Beijing University of Posts and Telecommunications
Current assignee: Beijing University of Posts and Telecommunications
Priority date: 2012-03-08
Filing date: 2012-03-08
Publication date: 2015-04-08
Anticipated expiration: 2032-03-08
Also published as: CN102622729A

Abstract

The invention relates to a method for denoising an image based on fuzzy set theory for space adaptive block matching, comprising the following steps: (1) setting the size of the initial similar block search window Δi _,1 ; (2) calculating the image of pixel i to be processed The variance-normalized symmetric distance between block y(N _i ) and the image block y(N _j ) of pixel j within the search window Δ _i,1 ; (3) According to the distance between image blocks, use fuzzy clustering analysis Calculate the similarity of image blocks And the weighted average of the pixel values in the search window is obtained to obtain the estimated value of the pixel i to be processed (4) Correct the residual noise pixel value; (5) Increase the size of the similar block search window Δi _,n , and repeat steps (2) to (4) until the iteration termination condition is satisfied. The invention has a reasonable design, ensures the effectiveness of pixel similarity division, improves the accuracy of estimation, and effectively improves the performance of the block-based image denoising method.

Description

A Spatial Adaptive Block Matching Image Denoising Method Based on Fuzzy Set Theory

技术领域technical field

本发明涉及图像处理领域，特别是一种基于模糊集合理论的空间自适应块匹配图像去噪方法。The invention relates to the field of image processing, in particular to a space adaptive block matching image denoising method based on fuzzy set theory.

背景技术Background technique

在图像处理中，局部邻域平滑滤波器虽然能够很好地抑制噪声并且重构出图像的主要结构信息，但是却不能有效地保留图像中的细节信息，例如边缘、纹理等信息，这是因为这些方法假设原始图像满足正则性条件，在这种假设下，边缘与纹理等细节被理解为噪声而被光滑。为了克服这一缺陷，A.Buades，B.Coll等人提出了非局部均值滤波(Nonlocal means，NLM)算法，该算法利用了自然图像中高度的信息冗余性，即对于一幅自然图像中的每一个小图像块，在整个图像中存在许多与之相似的图像块。正像局部邻域滤波那样，可以定义“像素i的邻域”为图像中与像素i有着相似块的像素的集合。在这个邻域中的所有像素都可以用来预测像素i的值。从这个意义上，NLM算法相当于扩展了局部邻域滤波，图像的自相似性可以看作是一种更加一般化更加精确的正则性假设。In image processing, although the local neighborhood smoothing filter can suppress the noise well and reconstruct the main structural information of the image, it cannot effectively retain the detailed information in the image, such as edge, texture and other information, because These methods assume that the original image satisfies the regularity condition, and under this assumption, details such as edges and textures are understood as noise and smoothed. In order to overcome this defect, A.Buades, B.Coll et al. proposed the Nonlocal means (NLM) algorithm, which takes advantage of the high degree of information redundancy in natural images, that is, for a natural image For each small image block of , there are many similar image blocks in the whole image. Just like local neighborhood filtering, the "neighborhood of pixel i" can be defined as the set of pixels in the image that have a similar block to pixel i. All pixels in this neighborhood can be used to predict the value of pixel i. In this sense, the NLM algorithm is equivalent to extending the local neighborhood filter, and the self-similarity of the image can be regarded as a more general and precise regularity assumption.

虽然NLM算法有效地对图像的正则性做出了非局部假设，但是并没有考虑到估计值的近似精确度和随机误差之间的关系。当用于加权平均的像素增多时，估值的随机误差虽然减小，但是对真值的近似精确度也会随之降低。这类似于信号处理里的不确定性原理，即信号的时域分辨率与频域分辨率不能同时无限小。这里可表述为估值的随机误差与相对真值的偏差不能同时无限小，那么当估值的随机误差为多小时能保证对真值的近似精确度在可接受的范围内，或者说怎样才能达到二者的最适关系，并且对于不同的空间位置，这二者的最适关系会不会变化，如果会变的话，该如何改变。为了解决这些问题，Kervrann等人通过引入逐点自适应估计的思想，提出了一种最优空间自适应(OptimalSpatial Adaption，OSA)算法来对NLM进行改进，给出了随机误差与近似精确度之间关系的定量分析。与通常的利用图像块数据库学习来泛化图像的先验知识不同，这里所利用的是非局部的图像特征和自回归技术，是一种无监督算法。While the NLM algorithm effectively makes a non-local assumption on the regularity of the image, it does not take into account the relationship between the approximate accuracy of the estimate and the random error. When the number of pixels used for weighted average increases, the random error of estimation decreases, but the approximate accuracy of the true value also decreases. This is similar to the uncertainty principle in signal processing, that is, the time-domain resolution and frequency-domain resolution of a signal cannot be infinitely small at the same time. It can be expressed here that the random error of the estimate and the deviation from the true value cannot be infinitely small at the same time, so when the random error of the estimate is small, the approximate accuracy of the true value can be guaranteed to be within an acceptable range, or how can it be To achieve the optimal relationship between the two, and for different spatial positions, will the optimal relationship between the two change, and if so, how to change it. In order to solve these problems, Kervrann et al. proposed an Optimal Spatial Adaptation (OSA) algorithm to improve NLM by introducing the idea of point-by-point adaptive estimation. Quantitative analysis of the relationship between them. Different from the usual use of image block database learning to generalize the prior knowledge of the image, what is used here is a non-local image feature and autoregressive technology, which is an unsupervised algorithm.

最优空间自适应滤波使用的归一化指数权值函数可以看成一种软高斯阈值函数。对于不相关的像素点，这种权值函数所分配给该点的权值小但并不为零，当待估值像素的搜索窗口内存在大量的不相关点时，对该像素进行加权平均时所引入的估值偏差是不可忽略的，因而使去噪效果变差。此外，在最优空间自适应滤波中，权值函数的控制参数被设为常数，使权值的分配不能很好的适应不同迭代步骤中用于计算权值的图像块估值的统计特性。The normalized exponential weight function used in optimal spatial adaptive filtering can be regarded as a soft Gaussian threshold function. For irrelevant pixels, the weight assigned to the point by this weight function is small but not zero. When there are a large number of irrelevant points in the search window of the pixel to be evaluated, the pixel is weighted and averaged The estimation bias introduced when is not negligible, thus making the denoising effect worse. In addition, in the optimal spatial adaptive filtering, the control parameters of the weight function are set as constants, so that the distribution of weights cannot be well adapted to the statistical characteristics of the image block estimates used to calculate the weights in different iteration steps.

发明内容Contents of the invention

本发明的目的在于克服现有技术的不足，提供一种在不增加算法复杂度的情况下能够有效提高图像去噪性能的基于模糊集合理论的空间自适应块匹配图像去噪方法。The purpose of the present invention is to overcome the deficiencies of the prior art and provide a space adaptive block matching image denoising method based on fuzzy set theory that can effectively improve the performance of image denoising without increasing the complexity of the algorithm.

本发明解决其技术问题是采取以下技术方案实现的：The present invention solves its technical problem and realizes by taking the following technical solutions:

一种基于模糊集合理论的空间自适应块匹配图像去噪方法，包括以下步骤：A method of image denoising based on space adaptive block matching based on fuzzy set theory, comprising the following steps:

⑴设置初始相似块搜索窗口Δ_i,1的大小；(1) Set the size of the initial similar block search window Δi _,1 ;

⑵计算待处理像素i的图像块y(N_i)与搜索窗口Δ_i,n内像素j的图像块y(N_j)之间的方差归一化的对称距离；(2) Calculate the variance-normalized symmetric distance between the image block y(N _i ) of pixel i to be processed and the image block y(N _j ) of pixel j within the search window Δ _i,n ;

⑶根据图像块之间的距离利用模糊聚类分析计算图像块的相似程度并对搜索窗口内的像素值进行加权平均得到待处理像素i的估计值 (3) Calculate the similarity of image blocks by using fuzzy cluster analysis according to the distance between image blocks And weighted average the pixel values in the search window to get the estimated value of the pixel i to be processed

所述的图像块间的相似程度是通过对图像块进行模糊2-均值聚类得到，该相似程度的计算公式如下：The degree of similarity between the image blocks It is obtained by fuzzy 2-means clustering of image blocks, the similarity The calculation formula is as follows:

${d d}_{11,, j j}^{* *} = = \{\begin{matrix} 00,, dist dist ((y the y (({N N}_{i i})),, y the y (({N N}_{j j})))) &GreaterEqual; &Greater Equal; T T \\ 11,, dist dist ((y the y (({N N}_{i i})),, y the y (({N N}_{j j})))) = = 00 \\ \frac{11}{11 + + \frac{{dist dist}^{22} ((y the y (({N N}_{i i})),, y the y (({N N}_{j j}))))}{{((T T - - dist dist ((y the y (({N N}_{i i})),, y the y (({N N}_{j j}))))))}^{22}}} \end{matrix},, 00 < < dist dist ((y the y (({N N}_{i i})),, y the y (({N N}_{j j})))) < < T T$

式中，T为自适应阈值，dist(y(N_i),y(N_j))为待处理像素i的图像块y(N_i)与搜索窗口Δ_i,n内像素j的图像块y(N_j)之间的方差归一化的对称距离；In the formula, T is the adaptive threshold, dist(y(N _i ), y(N _j )) is the image block y(N _i ) of pixel i to be processed and the image block y of pixel j in the search window Δ _i,n The variance-normalized symmetric distance between (N _j );

所述的自适应阈值T随着迭代次数n的增加而增大以适应估值偏差的变化，该自适应阈值T按如下公式计算得到：The adaptive threshold T increases as the number of iterations n increases to adapt to changes in the estimation deviation, and the adaptive threshold T is calculated according to the following formula:

$T T = = \sqrt{{λ λ}_{α α}} + + \sqrt{22} p p ((C C {| | {Δ Δ}_{i i,, n no} | |}^{\frac{11 + + {γ γ}^{22}}{22}}))$

式中，λ_α是卡方分布的分位点，p表示图像块的大小，C₁是一个实常数，σ是噪声图像中高斯噪声的标准差，γ是一个接近于1的常数，|Δ_i,n|表示第n次迭代时相似块搜索窗口的大小；In the formula, λ _α is the chi-square distribution The quantile point, p represents the size of the image block, C ₁ is a real constant, σ is the standard deviation of Gaussian noise in the noisy image, γ is a constant close to 1, |Δi _,n | represents the size of the similar block search window at the nth iteration;

⑷对残余噪声像素值进行修正；(4) Correct the residual noise pixel value;

⑸增加迭代次数n，并增加相似块搜索窗口Δ_i,n的大小，重复步骤⑵至步骤⑷直至满足迭代终止条件。(5) Increase the number of iterations n, and increase the size of the similar block search window Δi _,n , repeat steps (2) to (4) until the iteration termination condition is met.

而且，步骤⑵所述的方差归一化的对称距离是采用如下公式计算得到的：Moreover, the variance-normalized symmetric distance described in step (2) is calculated using the following formula:

$\begin{matrix} {dist dist}^{22} ((y the y (({N N}_{i i})),, y the y (({N N}_{j j})))) = = \frac{11}{22} [[((y the y (({N N}_{i i})) - - y the y {(({N N}_{j j}))}^{T T})) {\overset{^^}{V V}}_{i i}^{- - 11} ((y the y (({N N}_{i i})) - - y the y (({N N}_{j j})))) \\ + + ((y the y (({N N}_{j j})) - - y the y {(({N N}_{i i}))}^{T T})) {\overset{^^}{V V}}_{j j}^{- - 11} ((y the y (({N N}_{j j})) - - y the y (({N N}_{i i}))))]] \end{matrix}$

式中，为一个p²×p²的对角矩阵，该对角矩阵为：In the formula, is a p ² ×p ² diagonal matrix, the diagonal matrix is:

$\overset{^^}{V V} . . = = [\begin{matrix} {(({\overset{^^}{v v} . .}^{((11))}))}^{22} & 00 & . . . . . . & 00 \\ 00 & {(({\overset{^^}{v v} . .}^{((22))}))}^{22} & . . . . . . & 00 \\ . . & . . & . . & . . \\ . . & . . & . . & . . \\ . . & . . & . . & . . \\ 00 & . . . . . . & 00 & {(({\overset{^^}{v v} . .}^{(({p p}^{22}))}))}^{22} \end{matrix}]$

这里l＝1,2,…,p²表示估计值的标准差，指数l用于表示图像块y(N.)中的空间位置。here l=1,2,...,p ² represents the estimated value The standard deviation of , the exponent l is used to represent the spatial position in the image patch y(N.).

而且，步骤⑷所述的对残余噪声像素值进行修正的公式和修正项c分别按如下公式计算得到：Moreover, the formula for correcting the residual noise pixel value described in step (4) and the correction term c are calculated according to the following formula respectively:

$\overset{^^}{x x} ((i i)) = = {y the y}_{res res} ((i i)) + + c c,, c c = = \frac{L L}{88} \underset{D D. &Element; &Element; dir dir}{Σ Σ} (({C C}_{D D.}^{+ +} - - {C C}_{D D.}^{- -}))$

式中，y_res(i)表示第i个像素点的残余噪声像素值，表示其修正后的像素值，L表示图像的灰度级数，和分别为正修正项和负修正项。In the formula, y _res (i) represents the residual noise pixel value of the i-th pixel, Indicates the corrected pixel value, L indicates the gray level of the image, and are positive and negative correction terms, respectively.

而且，所述的正修正项和负修正项采用如下步骤获得：Moreover, the positive modifier term and a negative modifier Obtained by the following steps:

首先，采用如下模糊控制法则来计算模糊梯度值 First, use the following fuzzy control law to calculate the fuzzy gradient value

分别取▽_NW(i)和▽_NW(SW_i)二者对small属性模糊程度中的最大值，▽_NW(i)和▽_NW(NE_i)二者对small属性模糊程度中的最大值，▽_NW(SW_i)和▽_NW(NE_i)二者对small属性模糊程度中的最大值，然后取这三个最大值中的最小值为像素点i沿西北方向的模糊梯度 Take the maximum value of ▽ _NW (i) and ▽ _NW (SW _i ) for the fuzziness of the small attribute, and the maximum value of the two of ▽ _NW (i) and ▽ _NW (NE _i ) for the fuzziness of the small attribute, ▽ _NW (SW _i ) and ▽ _NW (NE _i ) are the maximum value of the blurring degree of the small attribute, and then take the minimum of these three maximum values as the blur gradient of pixel i along the northwest direction

这里，▽_NW(i)表示像素点i沿西北方向的梯度，▽_NW(SW_i)表示像素点i的西南方向的像素点沿西北方向的梯度，同理，▽_NW(NE_i)表示像素点i的东北方向的像素点沿西北方向的梯度；Here, ▽ _NW (i) represents the gradient of pixel i along the northwest direction, ▽ _NW (SW _i ) represents the gradient of the pixel point in the southwest direction of pixel i along the northwest direction, similarly, ▽ _NW (NE _i ) represents the pixel The gradient of the pixel point in the northeast direction of point i along the northwest direction;

然后，采用如下两个模糊控制法则计算相邻点在修正项中的正修正项和负修正项：Then, use the following two fuzzy control rules to calculate the positive and negative correction terms of the adjacent points in the correction term:

(1)取对small属性模糊程度和▽_D(i)对positive属性模糊程度中的最大值为正修正项 (1) take The maximum value of the fuzzy degree of the small attribute and ▽ _D (i) is the positive correction item for the fuzzy degree of the positive attribute

(2)取对small属性模糊程度和▽_D(i)对negative属性模糊程度中的最大值为负修正项 (2) take The maximum value of the fuzzy degree of the small attribute and ▽ _D (i) is the negative correction term for the fuzzy degree of the negative attribute

这里，表示像素点i沿方向D的模糊梯度，▽_D(i)表示像素点i沿方向D的梯度。here, Represents the blur gradient of pixel i along direction D, and ▽ _D (i) represents the gradient of pixel i along direction D.

而且，所述步骤⑸按如下公式增加相似块搜索窗口Δ_i,n的大小：Moreover, the step (5) increases the size of the similar block search window Δi _,n according to the following formula:

|Δ_i,n|＝(2ⁿ+1)×(2ⁿ+1),n＝1,...,N|Δ _i,n |=(2 ⁿ +1)×(2 ⁿ +1),n=1,...,N

式中，n表示迭代次数，N表示所允许的最大迭代次数。In the formula, n represents the number of iterations, and N represents the maximum number of iterations allowed.

而且，步骤⑸所述的终止条件为：Moreover, the termination condition described in step (5) is:

${Δ Δ}_{i i}^{* *} = = arg arg \underset{{Δ Δ}_{i i,, n no} &Element; &Element; {N N}_{Δ Δ}}{max max} {{| | {Δ Δ}_{i i,, n no} | | : : | | {\overset{^^}{x x}}_{i i,, n no} - - {\overset{^^}{x x}}_{i i,, {n no}^{' '}} | | \leq \leq ρv ρv (({\overset{^^}{x x}}_{i i,, {n no}^{' '}})),, 11 \leq \leq {n no}^{' '} < < n no}}$

式中，N_Δ表示所允许的搜索窗口的集合，n表示迭代次数，表示最优相似块搜索窗口，ρ为一正常数。In the formula, N _Δ represents the set of allowed search windows, n represents the number of iterations, Represents the optimal similar block search window, ρ is a normal constant.

本发明的优点和积极效果是：Advantage and positive effect of the present invention are:

本发明通过模糊聚类分析对像素点之间的相似程度进行划分来确定权值函数，并给出一种调整权值函数控制参数的策略以适应不同迭代步骤中估计值的估值偏差，确保像素相似程度划分的有效性，提高估值的准确性。这种模糊权值函数相当于一种半软阈值函数，实现了像素点相似度的最优模糊划分，并且将不相关像素点的权值分配为零来避免不相关点对估值的干扰。通过模糊控制法则来使用相邻像素点对模糊加权平均中残余的噪声像素的值进行修正，能够避免不破坏图像原有的结构信息。本发明能在不增加算法复杂度的情况下有效地提高现有的基于块的图像去噪方法的性能。The present invention divides the similarity between pixels through fuzzy clustering analysis to determine the weight function, and provides a strategy for adjusting the control parameters of the weight function to adapt to the estimation deviation of the estimated value in different iteration steps, so as to ensure The effectiveness of pixel similarity division can improve the accuracy of estimation. This fuzzy weight function is equivalent to a semi-soft threshold function, which realizes the optimal fuzzy division of pixel similarity, and assigns the weight of irrelevant pixels to zero to avoid the interference of irrelevant points on the estimation. Using the fuzzy control law to use adjacent pixels to correct the value of the residual noise pixels in the fuzzy weighted average can avoid destroying the original structure information of the image. The invention can effectively improve the performance of the existing block-based image denoising method without increasing the complexity of the algorithm.

附图说明Description of drawings

图1为本发明所提出的模糊权值函数(半软阈值函数)曲线图；Fig. 1 is the fuzzy weight function (semi-soft threshold function) curve figure that the present invention proposes;

图2为图像像素i的3×3邻域示意图；FIG. 2 is a schematic diagram of a 3×3 neighborhood of an image pixel i;

图3为模糊梯度值的计算示意图；Fig. 3 is the calculation schematic diagram of fuzzy gradient value;

图4为属性small的隶属计算示意图；Fig. 4 is a schematic diagram of the membership calculation of the attribute small;

图5为属性positive和negative的隶属关系示意图；Fig. 5 is a schematic diagram of the affiliation relationship of attributes positive and negative;

图6为Barbara(σ＝20)局部去噪对比效果图；Fig. 6 is Barbara (σ=20) local denoising comparison effect diagram;

图7为Lena(σ＝20)局部去噪对比效果图；Fig. 7 is a comparison effect diagram of local denoising of Lena (σ=20);

图8为Boats(σ＝20)局部去噪对比效果图。Figure 8 is a comparison effect diagram of local denoising of Boats (σ=20).

具体实施方式Detailed ways

以下结合附图对本发明实施例做进一步详述：Embodiments of the present invention are described in further detail below in conjunction with the accompanying drawings:

一种基于模糊集合理论的空间自适应块匹配图像去噪方法，采用相似图像块匹配、模糊加权平均和残余噪声像素值修正的方法来实现。通过模糊聚类分析对图像块的相似程度实现最优模糊划分，根据模糊划分矩阵进一步确定权值分配函数，引入变化的阈值参数使权值在不同的迭代步骤中的分配具有自适应性；对于那些在图像中缺乏相似点的噪声像素，利用模糊控制法则对其残余的噪声值进行修正。本发明通过模糊聚类分析和模糊控制法则可以有效地提高基于块的去噪方法性能。下面详细说明本发明的方法：A space-adaptive block-matching image denoising method based on fuzzy set theory is realized by using similar image block matching, fuzzy weighted average and residual noise pixel value correction. The optimal fuzzy division of the similarity of image blocks is realized through fuzzy clustering analysis, the weight distribution function is further determined according to the fuzzy partition matrix, and the variable threshold parameter is introduced to make the distribution of weights in different iteration steps adaptive; for For those noisy pixels lacking similarities in the image, the residual noise value is corrected using the fuzzy control law. The invention can effectively improve the performance of the block-based denoising method through fuzzy cluster analysis and fuzzy control rules. The method of the present invention is described in detail below:

步骤1：设置初始相似块搜索窗口Δ_i,1的大小。Step 1: Set the size of the initial similar block search window Δi _,1 .

设像素点的p×p图像块值y(N.)为p²维向量空间中的向量元素，那么所有属于搜索窗口Δ_i的像素点j∈Δ_i的向量y(N_j)形成了一个向量集合Y_i。集合Y_i划分为两类，即c＝2，一类由与像素i的图像块y(N_i)相似的向量组成，聚类原型y₁＝y(N_i)；另一类由非相似向量组成，聚类原型y₂为与像素i不相关的像素点的向量 Let the p×p image block value y(N.) of the pixel be p ^2- dimensional vector space , then all the vector y(N _j ₎ of pixel j∈Δ i belonging to the search window Δ _i forms a vector set Y _i . The set Y _i is divided into two types, namely c=2, one type is composed of vectors similar to the image block y(N _i ) of pixel i, and the clustering prototype y ₁ =y(N _i ); the other type is composed of non-similar The clustering prototype y ₂ is a vector of pixels not related to pixel i

步骤2：按如下公式计算待处理像素i的图像块y(N_i)与搜索窗口Δ_i,1内像素j的图像块y(N_j)之间的方差归一化的对称距离：Step 2: Calculate the variance-normalized symmetric distance between the image block y(N _i ) of pixel i to be processed and the image block y(N _j ) of pixel j within the search window Δ _i,1 according to the following formula:

式中为一个p²×p²的对角矩阵(“.”表示图像的像素位置)，该对角矩阵为：In the formula is a p ² ×p ² diagonal matrix ("." indicates the pixel position of the image), the diagonal matrix is:

这里l＝1,2,…,p2表示估计值的标准差，指数l用于表示图像块N.中的空间位置。here l=1,2,...,p2 represents the estimated value The standard deviation of , the index l is used to denote the spatial position in the image patch N.

步骤3：根据图像块之间的距离利用模糊聚类分析计算图像块的相似程度并对搜索窗内的像素值进行加权平均得到待处理像素i的估计值 Step 3: Calculate the similarity of image blocks using fuzzy clustering analysis based on the distance between image blocks And the weighted average of the pixel values in the search window is obtained to obtain the estimated value of the pixel i to be processed

在本步骤中，对像素值进行加权平均计算能够得到待处理像素i的估计值该估计值和权值函数是通过数学模型计算得到：In this step, the weighted average calculation of the pixel values can obtain the estimated value of the pixel i to be processed the estimate And the weight function is calculated by the mathematical model:

${\overset{^^}{x x}}_{i i} = = \underset{j j &Element; &Element; {Δ Δ}_{i i,, n no}}{Σ Σ} {w w}_{i i ~ ~ j j} {y the y}_{j j},, {w w}_{i i ~ ~ j j} = = \frac{{d d}_{11,, j j}^{* *}}{{Σ Σ}_{k k = = 11}^{| | {Δ Δ}_{i i} | |} {d d}_{11,, k k}^{* *}},, j j &Element; &Element; {Δ Δ}_{i i}$

式中y_j表示噪声像素值，表示图像块y(N_i)与y(N_j)(j∈Δ_i)的相似程度。where y _j represents the noise pixel value, Indicates the degree of similarity between image block y(N _i ) and y(N _j )(j∈Δ _i ).

图像块间的相似程度是通过对图像块进行模糊2-均值聚类得到，计算公式如下：The degree of similarity between image blocks is obtained by fuzzy 2-means clustering of image blocks, Calculated as follows:

式中，T为自适应阈值，当图像块之间的距离大于阈值T时则认为这两个图像块显著不同。In the formula, T is an adaptive threshold, and when the distance between image blocks is greater than the threshold T, the two image blocks are considered to be significantly different.

图1给出了计算模型的曲线图，从图中可以看到模糊权值函数是一种半软阈值函数，阈值为T。与原先的软高斯阈值函数相比，计算模型将不相关像素点，即像素点j∈{j|dist(y(N_i),y(N_j))≥T,j∈Δ_i}的权值设为零，从而避免不相关点的干扰，并且实现相似像素点的最优模糊划分。Figure 1 gives the Calculate the graph of the model. From the graph, we can see that the fuzzy weight function is a semi-soft threshold function, and the threshold is T. Compared with the original soft Gaussian threshold function, The calculation model sets the weight of irrelevant pixels, that is, pixel j∈{j|dist(y(N _i ),y(N _j ))≥T, j∈Δ _i } to zero, so as to avoid irrelevant points interference, and achieve the optimal fuzzy division of similar pixels.

随着迭代次数n的增加，图像中参与估值的像素点越来越多，因而搜索窗口Δ_i,n内用于计算像素间相似程度的估计值的估值偏差是不断增大的，这要求模糊权值函数的控制参数T随着迭代次数的增加而变化。随着迭代次数的增加，搜索窗口增大，图像块和之间距离的可能取值范围由于第二项的存在也随之增加。这样对于原本相似的像素点，额外距离偏差的引入导致分配给该点的权值变小，从而降低了估值的有效性。自适应阈值T随着迭代次数n的增加而增大以适应估值偏差的变化，以确保像素相似程度划分的有效性。自适应阈值T按如下公式计算得到：As the number of iterations n increases, more and more pixels participate in the evaluation in the image, so the estimated value used to calculate the similarity between pixels in the search window Δi _,n Valuation bias is increasing, which requires the control parameter T of the fuzzy weight function to change as the number of iterations increases. As the number of iterations increases, the search window increases, and the image block and The possible value range of the distance between them also increases due to the existence of the second term. In this way, for the originally similar pixel points, the introduction of additional distance deviation causes the weight assigned to the point to become smaller, thereby reducing the effectiveness of the estimation. The adaptive threshold T increases with the increase of the number of iterations n to adapt to the change of the estimation deviation, so as to ensure the effectiveness of the pixel similarity division. The adaptive threshold T is calculated according to the following formula:

式中，λ_α是卡方分布的分位点，p表示图像块的大小，C₁是一个实常数，γ是一个接近于1的常数。In the formula, λ _α is the chi-square distribution The quantile point, p represents the size of the image block, C ₁ is a real constant, and γ is a constant close to 1.

步骤4：对残余噪声像素值进行修正，修正公式和修正项c计算如下：Step 4: Correct the residual noise pixel value, the correction formula and the correction item c are calculated as follows:

式中L表示图像的灰度级数，和分别为正修正项和负修正项。In the formula, L represents the gray level of the image, and are positive and negative correction terms, respectively.

由于在自然图像中往往存在一些像素没有与之相似的像素点，或者相似的像素点很少，例如拐角点，在这种情况下，上述的模糊权值函数会产生过多的零权值，导致参与加权平均的实际像素个数过少，从而噪声不能被有效的去除。这些残留下来的噪声像素点类似于脉冲噪声，为了平滑这些噪声点同时又能够尽可能的不破坏图像原有的结构信息，本发明利用模糊控制法则来对噪声点进行修正。其基本原理是利用噪声像素点的8邻域的加权平均值来替换该像素点的值，每一个邻域点的权值根据其与中心点的模糊梯度值的大小而定。模糊梯度值可以由给定的模糊控制法则计算得出，其值如果越小，表明该方向上的邻域点与中心点越相似，邻域点的权值就越大；反之，如果模糊梯度值越大，则说明该方向上的邻域点可能位于边缘之上，其权值就小。通过这种方法避免对图像边缘的模糊。Since there are often some pixels in natural images that have no similar pixels, or few similar pixels, such as corner points, in this case, the above fuzzy weight function will generate too many zero weights, As a result, the number of actual pixels participating in the weighted average is too small, so that the noise cannot be effectively removed. These remaining noise pixels are similar to impulse noise. In order to smooth these noise points without destroying the original structure information of the image as much as possible, the present invention uses fuzzy control law to correct the noise points. The basic principle is to use the weighted average of the 8 neighbors of the noise pixel to replace the value of the pixel, and the weight of each neighbor is determined according to the size of the fuzzy gradient value between it and the center point. The fuzzy gradient value can be calculated by a given fuzzy control law. If the value is smaller, it indicates that the neighborhood points in this direction are more similar to the center point, and the weight of the neighborhood points is greater; on the contrary, if the fuzzy gradient The larger the value, it means that the neighbor points in this direction may be located on the edge, and its weight is smaller. This method avoids blurring the edges of the image.

考虑像素i的一个3×3邻域，如图2所示。定义像素i在方向D(D∈dir＝{NW,W,SW,S,SE,E,NE,N})上的梯度值为像素i的值与其在该方向上的相邻点的值之差。例如，Consider a 3×3 neighborhood of pixel i, as shown in Figure 2. Define the gradient value of pixel i in the direction D (D ∈ dir = {NW, W, SW, S, SE, E, NE, N}) between the value of pixel i and the value of the adjacent point in this direction Difference. For example,

▽_NW(i)＝x(NW_i)-x(i)▽ _NW (i)＝x(NW _i )-x(i)

式中▽_NW(i)表示像素i在方向NW上的梯度值。where ▽ _NW (i) represents the gradient value of pixel i in direction NW.

这里以相邻点NWi为例来讨论如何利用模糊控制技术计算像素i的每一个相邻点在像素i修正值中的权重比例。首先考虑如果在方向SW-NE上有边缘存在，如图3所示，那么像素i的梯度值▽_NW(i)将会很大，同样像素i在方向SW-NE上的邻点的NW方向梯度值，即▽_NW(NE_i)和▽_NW(SW_i)也应该很大。因此，如果像素i，SWi和NEi在NW方向上的梯度值中有两个值很小，那么认为像素NWi与像素i属于同一性质的光滑区域这一假设就是合理的。Here we take the neighboring point NWi as an example to discuss how to use the fuzzy control technology to calculate the weight ratio of each neighboring point of pixel i in the correction value of pixel i. First consider that if there is an edge in the direction SW-NE, as shown in Figure 3, then the gradient value ▽ _NW (i) of pixel i will be very large, and the NW direction of the neighbor point of pixel i in the direction SW-NE The gradient values, i.e. ▽ _NW (NE _i ) and ▽ _NW (SW _i ) should also be large. Therefore, if two of the gradient values of pixel i, SWi and NEi in the NW direction are small, it is reasonable to assume that pixel NWi belongs to the smooth region of the same nature as pixel i.

基于上述说明，为了对残余噪声像素值修正，应该获取正修正项和负修正项正修正项和负修正项采用如下步骤获得：Based on the above description, in order to correct the residual noise pixel value, the positive correction term should be obtained and a negative modifier Positive correction term and a negative modifier Obtained by the following steps:

这里AND运算表示取两个值中的最大者，OR运算表示取两个值中的最小者。对于属性small，定义其隶属函数m_K(▽_D(·))为：Here, the AND operation means to take the largest of the two values, and the OR operation means to take the smallest of the two values. For the attribute small, define its membership function m _K (▽ _D ( )) as:

${m m}_{K K} (({&dtri; &dtri;}_{D D.} ((\cdot &Center Dot;)))) = = \{\begin{matrix} 11 - - \frac{| | {&dtri; &dtri;}_{D D.} ((\cdot &Center Dot;)) | |}{K K},, 00 \leq \leq | | {&dtri; &dtri;}_{D D.} ((\cdot &Center Dot;)) | | \leq \leq K K \\ 00,, | | {&dtri; &dtri;}_{D D.} ((\cdot &Center Dot;)) | | > > K K \end{matrix}$

式中K是一个与噪声方差σ²有关的自适应参数，函数曲线图如图4所示。In the formula, K is an adaptive parameter related to the noise variance ^σ2 , and the function curve is shown in Fig. 4.

然后，采用如下两个模糊控制法则计算相邻点在修正项中的正修正项和负修正项：Then, the following two fuzzy control rules are used to calculate the positive and negative correction terms of the adjacent points in the correction term:

$\begin{matrix} {C C}_{D D.}^{+ +} : : IF IF {&dtri; &dtri;}_{D D.}^{F f} ((i i)) is small AND is small AND {&dtri; &dtri;}_{D D.} ((i i)) is positive THEN is positive THEN {C C}_{D D.}^{+ +} is positive is positive;; \\ {C C}_{D D.}^{- -} : : IF IF {&dtri; &dtri;}_{D D.}^{F f} ((i i)) is small AND is small AND {&dtri; &dtri;}_{D D.} ((i i)) is negative THEN is negative THEN {C C}_{D D.}^{- -} is negative is negative . . \end{matrix}$

图5给出了属性positive和negative的隶属函数，图中L表示图像的灰度级数。Figure 5 shows the membership functions of the attributes positive and negative, and L in the figure represents the gray level of the image.

步骤5：按如下公式增加相似块搜索窗口Δ_i,n的大小：Step 5: Increase the size of the similar block search window Δi _,n according to the following formula:

|Δ_i,n|＝(2ⁿ+1)×(2ⁿ+1),n＝1,...,N_Δ |Δ _i,n |=(2 ⁿ +1)×(2 ⁿ +1),n=1,...,N _Δ

并且重复步骤2至步骤4直至满足如下迭代终止条件：And repeat steps 2 to 4 until the following iteration termination conditions are met:

式中，n表示迭代次数，ρ为一正常数。In the formula, n represents the number of iterations, and ρ is a normal constant.

通过以上步骤，可以有效地提高现有基于块的去噪方法的性能，在不增加算法复杂度的情况下有效的去除了噪声，并且保留了更多的图像细节信息，去噪结果在PSNR值和主观质量上均有改善。Through the above steps, the performance of the existing block-based denoising method can be effectively improved, and the noise can be effectively removed without increasing the complexity of the algorithm, and more image detail information can be retained. The denoising result is in PSNR value There was an improvement in both subjective and subjective quality.

下面以一个仿真实例验证本发明的效果。在仿真实例验证中采用的仿真环境为Visual Studio2008，仿真实验分别选用标准测试图像中的Barbara、Lena和Boats进行测试。所有的测试图像所加噪声均为加性高斯白噪声，并且均值为零，方差为σ²(σ＝10,20,30)。在保证算法的性能的同时，考虑到计算的效率，取图像块的大小为9×9，即p＝9。分位数λ_α取隶属函数参数K＝3σ²。搜索窗口Δ_i,n的最佳选择应使估值偏差恰好不大于这里根据经验假设当迭代次数n＝3时，估值偏差恰好不大于并且设γ＝0.7，因此可以得到：The effects of the present invention are verified below with a simulation example. The simulation environment used in the simulation example verification is Visual Studio2008, and the simulation experiment uses Barbara, Lena and Boats in the standard test image for testing. The noise added to all test images is additive Gaussian white noise with a mean value of zero and a variance of σ ² (σ=10,20,30). While ensuring the performance of the algorithm, considering the efficiency of calculation, the size of the image block is taken as 9×9, that is, p=9. Quantile λ _α takes Membership function parameter K=3σ ² . The optimal choice of the search window Δi _,n should bias the estimates exactly no greater than Here it is empirically assumed that when the number of iterations n=3, the estimation deviation exactly no greater than And set γ=0.7, so we can get:

$b b (({\overset{^^}{x x}}_{i i,, n no})) / / v v (({\overset{^^}{x x}}_{i i,, n no})) = = C C {| | {Δ Δ}_{i i,, 33} | |}^{\frac{11 + + {0.7 0.7}^{22}}{22}} = = 0.7 0.7$

计算上式可以得到C＝0.0265。Calculating the above formula can get C=0.0265.

为了对图像质量进行客观比较，表1给出了本发明所述方法与原始的最优空间自适应滤波(OSA)以及非局部均值去噪滤波(NLM)的去噪结果的峰值信噪比(PSNR)的比较。In order to carry out objective comparison to image quality, table 1 has provided the peak signal-to-noise ratio (PSNR) of the denoising result ( PSNR) comparison.

表1为本发明所述方法与其他算法去噪结果PSNR值比较Table 1 compares the method for the present invention with other algorithm denoising results PSNR values

从表中可以看到，在不同的噪声方差下，对于不同的测试图像，所述方法去噪结果的PSNR值均要高于其它两种算法，并且随着噪声方差的增加，所述方法具有更好的稳定性。It can be seen from the table that under different noise variances, for different test images, the PSNR values of the denoising results of the method are higher than those of the other two algorithms, and as the noise variance increases, the method has better stability.

为了从主观上对去噪性能进行评价，图6、图7和图8分别给出了对测试图像Barbara(σ＝20)、Lena(σ＝20)和Boats(σ＝20)的去噪效果图。为了便于图像细节的比较，对图中的局部区域进行了放大。In order to evaluate the denoising performance subjectively, Figure 6, Figure 7 and Figure 8 show the denoising effects on the test images Barbara (σ=20), Lena (σ=20) and Boats (σ=20) respectively picture. In order to facilitate the comparison of image details, local areas in the figure are enlarged.

在图6中，(a)表示噪声图像(22.18dB)，(b)表示使用NLM算法的去噪效果图(29.88dB)；(c)表示使用OSA算法的去噪效果图(30.37dB)，(d)表示使用本方法的去噪效果图(31.16dB)，从图6给出的对比效果图中可以看出：本发明所提出的方法很好地保留了图像中桌布的纹理信息，而OSA算法对原有的纹理结构造成了模糊，NLM算法虽然也较好的保留了纹理结构，但是并没有很好的去除噪声。In Figure 6, (a) represents the noise image (22.18dB), (b) represents the denoising effect map using the NLM algorithm (29.88dB); (c) represents the denoising effect map using the OSA algorithm (30.37dB), (d) represents the denoising effect figure (31.16dB) using this method, as can be seen from the comparison effect figure provided in Figure 6: the method proposed by the present invention well retains the texture information of the tablecloth in the image, and The OSA algorithm blurs the original texture structure. Although the NLM algorithm also preserves the texture structure well, it does not remove the noise very well.

在图7中，(a)表示噪声图像(22.13dB)，(b)表示使用NLM算法的去噪效果图(31.23dB)，(c)表示使用OSA算法的去噪效果图(32.64dB)，(d)表示使用FW-OSA算法的去噪效果图(32.72dB)，从图7给出的对比效果图中可以看出：本发明所提出的方法较好地保留了Lena帽子上的细节信息，而OSA算法则丢失了这些细节使图像过于平滑，NLM算法在一定程度上保留了一些细节但是没有很好的抑制噪声，使图像看起来很“糙”。In Figure 7, (a) represents the noise image (22.13dB), (b) represents the denoising effect map using the NLM algorithm (31.23dB), (c) represents the denoising effect map using the OSA algorithm (32.64dB), (d) represents the denoising effect diagram (32.72dB) using the FW-OSA algorithm. It can be seen from the comparison effect diagram given in Fig. 7 that the method proposed by the present invention better retains the detailed information on the Lena hat , while the OSA algorithm loses these details and makes the image too smooth, and the NLM algorithm retains some details to a certain extent but does not suppress noise well, making the image look "rough".

在图8中，(a)表示噪声图像(22.17dB)，(b)表示使用NLM算法的去噪效果图(29.64dB)，(c)表示使用OSA算法的去噪效果图(30.12dB)，(d)表示使用FW-OSA算法的去噪效果图(30.35dB)，从图8给出的对比效果图中可以看出：本发明所提出的方法相对于其它两种算法较好的保留了细节并且有效的去除了噪声。In Figure 8, (a) represents the noise image (22.17dB), (b) represents the denoising effect map using the NLM algorithm (29.64dB), (c) represents the denoising effect map using the OSA algorithm (30.12dB), (d) represents the denoising effect diagram (30.35dB) using the FW-OSA algorithm. It can be seen from the comparison effect diagram given in Fig. 8 that the method proposed by the present invention better retains the Details and effectively remove noise.

需要强调的是，本发明所述的实施例是说明性的，而不是限定性的，因此本发明并不限于具体实施方式中所述的实施例，凡是由本领域技术人员根据本发明的技术方案得出的其他实施方式，同样属于本发明保护的范围。It should be emphasized that the embodiments described in the present invention are illustrative rather than restrictive, so the present invention is not limited to the embodiments described in the specific implementation, and those skilled in the art according to the technical solutions of the present invention Other obtained implementation modes also belong to the protection scope of the present invention.

Claims

1. a kind of space adaptive block matching image denoising method based on fuzzy set theory, it is characterized in that: comprise the following steps:

(1) Set the size of the initial similar block search window Δi _,1 ;

(2) Calculate the variance-normalized symmetric distance between the image block y(N _i ) of pixel i to be processed and the image block y(N _j ) of pixel j within the search window Δ _i,n ;

(3) Calculate the similarity of image blocks by using fuzzy cluster analysis according to the distance between image blocks And weighted average the pixel values in the search window to get the estimated value of the pixel i to be processed

The degree of similarity between the image blocks It is obtained by fuzzy 2-means clustering of image blocks, the similarity The calculation formula is as follows:

{d d}_{11,, j j}^{* *} = = \{\begin{matrix} 00,, dist dist ((y the y (({N N}_{i i})),, y the y (({N N}_{j j})))) &GreaterEqual; &Greater Equal; T T \\ 11,, dist dist ((y the y (({N N}_{i i})),, y the y (({N N}_{j j})))) = = 00 \\ \frac{11}{11 + + \frac{{dist dist}^{22} ((y the y (({N N}_{i i})),, y the y (({N N}_{j j}))))}{{((T T - - dist dist ((y the y (({N N}_{i i})),, y the y (({N N}_{j j}))))))}^{22}}} \end{matrix},, 00 < < dist dist ((y the y (({N N}_{i i})),, y the y (({N N}_{j j})))) < < T T

In the formula, T is the adaptive threshold, dist(y(N _i ), y(N _j )) is the image block y(N _i ) of pixel i to be processed and the image block y of pixel j in the search window Δ _i,n The variance-normalized symmetric distance between (N _j );

The adaptive threshold T increases as the number of iterations n increases to adapt to changes in the estimation deviation, and the adaptive threshold T is calculated according to the following formula:

T T = = \sqrt{{λ λ}_{α α}} + + \sqrt{22} p p ((C C {| | {Δ Δ}_{i i,, n no} | |}^{\frac{11 + + {γ γ}^{22}}{22}}))

In the formula, λ _α is the chi-square distribution The quantile point, p represents the size of the image block, C ₁ is a real constant, σ is the standard deviation of Gaussian noise in the noisy image, γ is a constant close to 1, |Δi _,n | represents the size of the similar block search window at the nth iteration;

(4) Correct the residual noise pixel value;

(5) Increase the number of iterations n, and increase the size of the similar block search window Δi _,n , repeat steps (2) to (4) until the iteration termination condition is met.

2. the space adaptive block matching image denoising method based on fuzzy set theory according to claim 1, is characterized in that: the symmetric distance of variance normalization described in step (2) is to adopt following formula to calculate and obtain:

\begin{matrix} {dist dist}^{22} ((y the y (({N N}_{i i})),, y the y (({N N}_{j j})))) = = \frac{11}{22} [[((y the y (({N N}_{i i})) - - y the y {(({N N}_{j j}))}^{T T})) {\overset{^^}{V V}}_{i i}^{- - 11} ((y the y (({N N}_{i i})) - - y the y (({N N}_{j j})))) \\ + + ((y the y (({N N}_{j j})) - - y the y {(({N N}_{i i}))}^{T T})) {\overset{^^}{V V}}_{j j}^{- - 11} ((y the y (({N N}_{j j})) - - y the y (({N N}_{i i}))))]] \end{matrix}

In the formula, is a p ² ×p ² diagonal matrix, the diagonal matrix is:

\overset{^^}{V V . .} = = [\begin{matrix} {(({\overset{^^}{v v . .}}^{(({p p}^{22}))}))}^{22} & 00 & . . . . . . & 00 \\ 00 & {(({\overset{^^}{v v}}^{((22))}))}^{22} & . . . . . . & 00 \\ . . & . . & . . & . . \\ . . & . . & . . & . . \\ . . & . . & . . & . . \\ 00 & . . . . . . & 00 & {(({\overset{^^}{v v . .}}^{(({p p}^{22}))}))}^{22} \end{matrix}]

here l=1,2,...,p ² represents the estimated value The standard deviation of , the exponent l is used to represent the spatial position in the image patch y(N.).

3. the space-adaptive block-matching image denoising method based on fuzzy set theory according to claim 1, is characterized in that: the formula and correction term c that the described residual noise pixel value of step (4) is revised are according to following formula respectively Calculated to get:

\overset{^^}{x x} ((i i)) = = {y the y}_{res res} ((i i)) + + c c,, c c = = \frac{L L}{88} \underset{D D. &Element; &Element; dir dir}{Σ Σ} (({C C}_{D D.}^{+ +} - - {C C}_{D D.}^{- -}))

In the formula, y _res (i) represents the residual noise pixel value of the i-th pixel, Indicates the corrected pixel value, L indicates the gray level of the image, and are positive and negative correction terms, respectively.

4. The space adaptive block matching image denoising method based on fuzzy set theory according to claim 3, characterized in that: the positive correction term and a negative modifier Obtained by the following steps:

First, use the following fuzzy control law to calculate the fuzzy gradient value

Take the maximum value of ▽ _NW (i) and ▽ _NW (SW _i ) for the fuzziness of the small attribute, and the maximum value of the two of ▽ _NW (i) and ▽ _NW (NE _i ) for the fuzziness of the small attribute, ▽ _NW (SW _i ) and ▽ _NW (NE _i ) are the maximum value of the blurring degree of the small attribute, and then take the minimum of these three maximum values as the blur gradient of pixel i along the northwest direction

Here, ▽ _NW (i) represents the gradient of pixel i along the northwest direction, ▽ _NW (SW _i ) represents the gradient of the pixel point in the southwest direction of pixel i along the northwest direction, similarly, ▽ _NW (NE _i ) represents the pixel The gradient of the pixel point in the northeast direction of point i along the northwest direction;

Then, the following two fuzzy control rules are used to calculate the positive and negative correction terms of the adjacent points in the correction term:

(1) take The maximum value of the fuzzy degree of the small attribute and ▽ _D (i) is the positive correction item for the fuzzy degree of the positive attribute

(2) take The maximum value of the fuzzy degree of the small attribute and ▽ _D (i) is the negative correction term for the fuzzy degree of the negative attribute

here, Represents the blur gradient of pixel i along direction D, and ▽ _D (i) represents the gradient of pixel i along direction D.

5. the space adaptive block matching image denoising method based on fuzzy set theory according to claim 1, is characterized in that: said step (5) increases the size of similar block search window Δi _,n by the following formula:

|Δ _i,n |=(2 ⁿ +1)×(2 ⁿ +1),n=1,...,N

In the formula, n represents the number of iterations, and N represents the maximum number of iterations allowed.

6. The space adaptive block matching image denoising method based on fuzzy set theory according to claim 1, characterized in that: the termination condition described in step (5) is:

{Δ Δ}_{i i}^{* *} = = arg arg \underset{{Δ Δ}_{i i,, n no} &Element; &Element; {N N}_{Δ Δ}}{max max} {{| | {Δ Δ}_{i i,, n no} | | : : | | {\overset{^^}{x x}}_{i i,, n no} - - {\overset{^^}{x x}}_{i i,, {n no}^{' '}} | | \leq \leq ρv ρv (({\overset{^^}{x x}}_{i i,, {n no}^{' '}})),, 11 \leq \leq {n no}^{' '} < < n no}}

In the formula, N _Δ represents the set of allowed search windows, n represents the number of iterations, Represents the optimal similar block search window, ρ is a normal constant.