图像稀疏表示的结构自适应子空间匹配追踪算法研究

A Structure-Adaptive Matching Pursuit Subspace Search Algorithm for Effective Image Sparse Representation

如何设计高效的图像稀疏表示模型及其分解算法是稀疏表示领域的研究热点.文中首先构建了图像的结构自适应多成分稀疏表示模型,该模型采用相对阈值标准对图像进行结构自适应的四叉树区域剖分,并将其分类为平滑、边缘和纹理结构的同性区域,构建与其结构形态相一致的多成分字典进行表示.进一步提出了一种结构自适应的子空间匹配追踪图像稀疏分解算法,将每一区域只在与其结构类型相一致的单一结构类型子成分字典中进行低维子空间搜索,降低了图像维数与字典搜索复杂度,提高了稀疏分解效率.实验结果验证了文中算法的有效性.

It is hot research topics that how to design a proper image sparse representation model and a fast numerical algorithm for effective sparse decomposition of images. At first structure adaptive multi-component sparse representation model of image is constructed. This model adaptively segments an image into quad-tree block in terms of geometrical structure character and rela- tive threshold, and each homogenous block is classified as one of plain, edge or texture structure. At the same time, a multi-component dictionary is construed to represent each block. Furthermore, a structure adaptive matching pursuit subspace search algorithm is proposed to obtain effective image sparse representation. When seeking for sparse decomposition of every quad-tree block, it is only to search in subspace of single component sub-dictionary with the same structure type as current block. Due to the reduction of dimension of image and complexity of searching in the dictionary, our algorithm for sparse representation is effective and fast. The experimental results confirm the efficiency of our algorithm.