信号过完备稀疏表示的唯一解及其边界条件

Uniqueness and Boundary for Overcomplete Sparse Representations of Signals

在探讨应用冗余字典寻找信号稀疏表示算法的基础上,简介信号过完备表示产生的背景和发展过程,认为信号表示的稀疏性与冗余字典的非相干性存在某种必然联系;结合正在进行的信号过完备稀疏表示理论与应用研究的专项课题,理论上讨论了满足基追踪算法和匹配追踪算法精确重构条件以及多个正交基级联字典的非相干系数与精确重构条件的某些研究进展,并提出对于非正交基联合而成的级联字典有待进一步研究的相关问题。

Based on the study of the occurrence background and development process of the signal sparse representation algorithms with redundant dictionaries, it was proposed that the sparsity of overcomplete representations has certain relations with the incoherence of dictionaries. Connected with the on going research project of the theory and application research of overcomplete sparse representation of signals, some advances in research of the exact recovery conditions of Base Pursuit and Matching Pursuit and concatenate dictionaries composed of orthonormal bases are reviewed; further researches of the concatenate dictionaries composed of non-orthonormal bases were proposed in this paper.