一种剪切波域的稀疏分量分析方法

Method for sparse component analysis in the shearlet domain

在图像盲源分离应用中,传统独立分量分析(ICA)方法直接使用图像混合源作为输入求得解混矩阵,没有利用图像在变换域的稀疏特性,无法获得较好的解混效果.针对这一问题,笔者在分析剪切波具有良好稀疏表示能力的基础上,提出了一种剪切波域的稀疏分量分析方法.该方法首先将图像混合源变换到剪切波域,得到剪切波系数,接着使用峭度选择最稀疏系数,最后将稀疏系数作为ICA方法的输入实现图像分离.由于选择较少的稀疏系数,问题的求解复杂度有了显著的降低.实验结果表明,与传统ICA方法相比,该方法获得了更好的分离效果,且缩短了算法的运行时间.

In applications of the image blind source separation, the traditional method of Independent Component Analysis（ICA） computes the mixed matrix by using source image directly, without using the prior knowledge that images can be represented sparsely in the transform domain, and it can not lead to a better effect. Based on the capacity of image sparse representation by shearlet, a method of sparse component analysis in the shearlet domain is presented. The image mixed source is first transformed to the shearlet domain and obtains a shearlet coefficient, then the sparsest coefficient is selected by computing kurtosis, and finally the sparse coefficient is used as the input of the ICA method to realize image separation. The complexity of the solving procedure represents a significant decrease since it chooses a less sparse coefficient. Experimental results show that, compared with the traditional ICA method, the method in this paper leads to a better separation effect and shortens the operation time of the algorithm.