曲波域图像噪声的估计
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摘要
本文对图像噪声估计的研究背景、现实意义、研究现状进行了综述性的介绍。并在综合分析现有方法的的基础上，提出了一种在曲波域上噪声估计的方法。在本文中我们考虑估计被一个均值为零的加性高斯白噪声污染图像的噪声的方差，如下式描述，g(x,y)=f(x,y)=η(x,y)(1)
这里f(x,y)真实图像，η(x,y)是方差为a~2的高斯白噪声信号，g(x,y)为被噪声污染的图像，f(x,y)和η(x,y)在统计上是独立的,这是一个在数字图像处理中最简单并且应用最广泛的模型，需要我们估计的参数只有方差α~2。
图像中的噪声是作为图像中的高频信息来表达的，然而图像中的高频信息却不都是噪声，如图像中的边缘、纹理都作为图像中的高频信息来表达，这些都会给图像中的噪声估计带来严重的影响，如何在图像中尽量区别这两种高频特征，克服边缘、纹理这些高频信息的影响，准确地估计噪声参数是一项很有意义的工作，本文的主要工作就是围绕这个中心展幵的。
本文通过以下四个方面的创新，来提高噪音的估计精度：在图像的曲波变换域估计图像的噪声；
1.由于曲波变换的性质，使得在图像的曲波变换域，不同方向上的曲波系数体现了原图像中相应方向特征的信息，所以我们可以在曲波域中找到最佳的噪声方向，从方向选择角度提高噪声估计精度。
2，通过构造MVO(最大模值方向矩阵)与MVOCM(最大模值方向连通度矩阵)，有效地在曲波变换域区分了图像的噪声结构与线结构这两种高频结构，从点集选择角度提高噪声的估计精度；
3.证明了，在给定估计精度时，噪声水平和点集规模之间的必须满足的关系，给出了在不同噪声水平下噪声估计的理论指导；
4.提出了一种自适应邻域扩张技巧用于噪声估计点集的选择，提高点集选择的可操作性。
实验结果显示，我们的方法无论对不同的噪声水平估计上都获得了很好的精度！
In this paper we study the variance estimation problem for noisyimage, which is corrupted by the zero mean additive white Gaussnoise. Assuming that image and noise are uncorrelated, the noisyimage g(x，y) can be represented asg(x, y)=f(x, y)+η(x, y)
Where f(x，y) is the clean image, and η(x,y) is the additive white Gaussnoise with variance. This is one of the simplest and widely usedmodel in the digital image processing. The only parameter that need toestimate is the variance a~2.
The noise signal corresponds to the high rfequency information ofthe image, but the main energy of high frequency information is not allprovided by the noise signal. For example, edges and textures alsocorrespond to the high frequency information of the image. Theseedges and textures will birng seirous effect to the noise estimation of theimage. How to distinguish these two kinds of high frequencycharacteirstics as far as possible in the image, overcome the influence ofother high frequency information such as edges and textures, andestimate the noise parameters accurately, is a very meaningfulproblem, which is also the center of this thesis.
In this thesis, the estimation precision of the noise model isimproved by the following four aspects:
1. Estimation of image noise in the domain of Curvelet transform;Curvelet transform is a multiscale pyramid with many direction andposition at each scale and needle shaped element at fine scale.Curvelet transform can sparsely characteirze the images which have line, curve or hyperplane singularities and the approximation eiffciency.The Curvelet coeiffcients of different directions reflect the differentdirection information of the original image. So，from the point ofdirection selecting, we can find the best direction in the curveletdomain for improving the accuracy of noise estimation.
2. We construct the MVO (Maximum modulus value oirentationmatrix) and MVOCM (Maximum modulus value direction connectivitymatirx)，distinguishe the two kinds of high frequency structure: noisestructure and line structure of original image in the curvelet transformdomain effectively. Improve the accuracy of noise estimation from thepoint of set selecting;
3. We prove the relation between the noise level and the size ofpoint sets when the estimation accuracy is given，as the theoreticalguidance for the noise estimation under different noise levels.
4. We propose an adaptive neighborhood expansion technique toimprove the operability of point set selection for noise estimation.
The experimental results show that our method works well forestimating noise at different levels.
这里f(x,y)真实图像，η(x,y)是方差为a~2的高斯白噪声信号，g(x,y)为被噪声污染的图像，f(x,y)和η(x,y)在统计上是独立的,这是一个在数字图像处理中最简单并且应用最广泛的模型，需要我们估计的参数只有方差α~2。
图像中的噪声是作为图像中的高频信息来表达的，然而图像中的高频信息却不都是噪声，如图像中的边缘、纹理都作为图像中的高频信息来表达，这些都会给图像中的噪声估计带来严重的影响，如何在图像中尽量区别这两种高频特征，克服边缘、纹理这些高频信息的影响，准确地估计噪声参数是一项很有意义的工作，本文的主要工作就是围绕这个中心展幵的。
本文通过以下四个方面的创新，来提高噪音的估计精度：在图像的曲波变换域估计图像的噪声；
1.由于曲波变换的性质，使得在图像的曲波变换域，不同方向上的曲波系数体现了原图像中相应方向特征的信息，所以我们可以在曲波域中找到最佳的噪声方向，从方向选择角度提高噪声估计精度。
2，通过构造MVO(最大模值方向矩阵)与MVOCM(最大模值方向连通度矩阵)，有效地在曲波变换域区分了图像的噪声结构与线结构这两种高频结构，从点集选择角度提高噪声的估计精度；
3.证明了，在给定估计精度时，噪声水平和点集规模之间的必须满足的关系，给出了在不同噪声水平下噪声估计的理论指导；
4.提出了一种自适应邻域扩张技巧用于噪声估计点集的选择，提高点集选择的可操作性。
实验结果显示，我们的方法无论对不同的噪声水平估计上都获得了很好的精度！
In this paper we study the variance estimation problem for noisyimage, which is corrupted by the zero mean additive white Gaussnoise. Assuming that image and noise are uncorrelated, the noisyimage g(x，y) can be represented asg(x, y)=f(x, y)+η(x, y)
Where f(x，y) is the clean image, and η(x,y) is the additive white Gaussnoise with variance. This is one of the simplest and widely usedmodel in the digital image processing. The only parameter that need toestimate is the variance a~2.
The noise signal corresponds to the high rfequency information ofthe image, but the main energy of high frequency information is not allprovided by the noise signal. For example, edges and textures alsocorrespond to the high frequency information of the image. Theseedges and textures will birng seirous effect to the noise estimation of theimage. How to distinguish these two kinds of high frequencycharacteirstics as far as possible in the image, overcome the influence ofother high frequency information such as edges and textures, andestimate the noise parameters accurately, is a very meaningfulproblem, which is also the center of this thesis.
In this thesis, the estimation precision of the noise model isimproved by the following four aspects:
1. Estimation of image noise in the domain of Curvelet transform;Curvelet transform is a multiscale pyramid with many direction andposition at each scale and needle shaped element at fine scale.Curvelet transform can sparsely characteirze the images which have line, curve or hyperplane singularities and the approximation eiffciency.The Curvelet coeiffcients of different directions reflect the differentdirection information of the original image. So，from the point ofdirection selecting, we can find the best direction in the curveletdomain for improving the accuracy of noise estimation.
2. We construct the MVO (Maximum modulus value oirentationmatrix) and MVOCM (Maximum modulus value direction connectivitymatirx)，distinguishe the two kinds of high frequency structure: noisestructure and line structure of original image in the curvelet transformdomain effectively. Improve the accuracy of noise estimation from thepoint of set selecting;
3. We prove the relation between the noise level and the size ofpoint sets when the estimation accuracy is given，as the theoreticalguidance for the noise estimation under different noise levels.
4. We propose an adaptive neighborhood expansion technique toimprove the operability of point set selection for noise estimation.
The experimental results show that our method works well forestimating noise at different levels.
引文
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[5] M.Uss,B.Vozel,V.Lukin,I.Baryshev,K.Chehdi,0Image Noise-Information MapFor Noise Standard Deviation Estimation0,IEEE,ICASSP2011.
[6] Tian Yi Li,Ming Hui Wang,0Estimating Noise Parameter Based on the WaveletCoe cients Estimation of Original Image0,International Conferenges on Chal-lenges in Environmental Science and Computer Engineering,2010.
[7] Dong-Hyuk Shin, Rae-Hong Park, Senior Member,Seungoon Yang and Jae-HanJung/,Block-Based Noise Estimation Using Adaptive Gaussian Filtering0, IEEETransactions on Consumer Electronis,Vol.51,NO.1,, pp.218226,2005.
[8] Aram Danielyan and Alessandro Foi,0Noise Variance Estimation in NonlocalTransform Domain0, Proc. Int. Workshop on Local and Non-Local Approx. inImage Process, pp.41-45, August2009.
[9] K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian,/Image denoisingwidth block-mathing and3-D filtering0, IEEE Transactions on Image Process-ing,VOL.6064,2006.
[10] Stanislav Pyatykh,Jurgen Hesser and Lei Zheng,0Image Noise Level Es-timation by Principal Component Analysis0,IEEE Transactions on IamgeProcessing,VOL.22,NO.2,pp.687-698,2013.
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