基于稀疏分解和非局部平均的乘性噪声图像滤波

The image denosing methods based on sparse representation and nonlocal mean have been well studied for additive noise reducing, and experiments show that these methods do good job in this case. However, they become invalid when facing multiplicative image noise. So, this study search for filtering algorithms based on sparse representation and nonlocal mean, in order to suppress the multiplicative noise in image such as Synthetic aperature radar (SAR). Firstly, the speckle filter based on nonlocal mean will be studied. We will use the the local coefficient of variation (CV) to correct the euclidean distance (the image patches' similarity measurement). The revised measurement is robust in multiplicative noise model, and it can index both the structural similarity and the heterogeneity between image patches. Secondly, the data fidelity term of "Michael Elad model " will be altered according to multiplicative noise model, then a novel regularization filter model based on sparse representaion will be presented; when being used to process the SAR image, it can effectively reduce the speckle and protect the details in SAR image simultaneously. Lastly, the novel filter based on nonlocal varation denosing model and sparse representaion will be studied for supressing multiplicative noise in image; this method take the advantages of sparse representation and nonlocal mean. The computational complexity of it is reduced. Above all, this method can better recovery the texture and details in aperture areo, which appear when we piece the small image patches together to form a large image. The research result are the supplementary to image denosing algorithm based on sparse representation and nonlocal mean.

以稀疏分解和非局部均值为代表的图像去噪方法在含有加性噪声的图像中取得了很好的效果，但这两类方法对含有乘性噪声图像的处理却不尽如人意。本项目以SAR图像相干斑抑制为载体，分别研究这两类方法在含有乘性噪声图像中的应用。首先，研究基于非局部平均的斑点噪声抑制方法，利用SAR图像的变差系数修正欧式距离（相似性度量）。修正后的度量方式在乘性噪声模型中稳健性好，能在度量图像块之间的结构相似性的同时刻画两个图像块的异质性。其次，根据乘性噪声模型修改"Michael Elad模型"的数据保持项，提出基于稀疏分解的正则化乘性噪声抑制模型；应用于斑点噪声抑制，提高图像的细节信息保持度。最后，结合稀疏分解和非局部思想的优点，设计基于稀疏分解和非局部变分的去噪模型。该方法既能减少计算复杂度，又能更好地恢复小图像块在拼接过程形成的缝隙区域的纹理、细节等信息。研究成果将会补充以稀疏分解和非局部均值为基础的图像去噪方法

目前，针对加性噪声模型（特别是高斯白噪声）的图像滤波算法研究得比较多；但是针对乘性噪声模型的图像滤波算法研究得相对比较少。乘性噪声与图像像素点的灰度（或色度）的相关性，使得乘性噪声的滤波成为一个难点问题。本项目以SAR图像相干斑抑制为应用目标，重点研究了基于非局部和稀疏表达的乘性噪声图像滤波算法。针对传统的欧式距离不能鲁棒地度量含有相干斑噪声的SAR图像之间的相似性这一问题，将SAR图像的异质性测量方法与传统的欧式距离结合，提出了一种新的用于斑点噪声抑制的非局部平均滤波算法；仿真实验验证了该算法的有效性和快速性。将非局部谱先验模型的思想应用于斑点噪声抑制中，在WNNM（Weighted Nuclear Norm Minimization）方法的框架下，提出了一种基于低秩和异质性测量的相干斑滤波方法；仿真实验表明该方法在去除斑点噪声的同时能有效保持图像的纹理信息。针对传统的“Michael Elad”去噪模型不能直接应用于抑制相干斑噪声的问题，将乘性噪声模型通过对数变换转化为加性噪声模型，并考虑相干斑噪声经过对数变换后的分布与标准正态分布之间的距离，提出了一种基于稀疏分解的斑点噪声抑制方法；仿真实验显示该方法能有效去除斑点噪声，保持图像的细节信息。针对基于小波变换（典型的稀疏变换）的斑点噪声抑制算法存在过平滑的现象，以多尺度局部变差系数作为异质性测度，将含斑SAR图像的小波系数分为四类区域，对各区域采取不同的处理策略；仿真实验表明该分类方法在抑制斑点噪声的同时能有效减少过平滑现象。提出一种基于非局部稀疏的变分模型，应用于斑点噪声抑制；利用交替方法乘子法迭代求解该模型。课题组基本上按照项目计划书进行了课题的研究，取得了一定的成果，达到了预定的目标。截止目前，课题组在国内外期刊发表论文7篇，申请2项国家发明专利。