The Orthogonal Super Greedy Algorithm and Applications in Compressed Sensing

作者：Entao Liu, Vladimir Nikolaevich Temlyakov · 发表于：IEEE Transactions on Information Theory · 年份：2011 · DOI：10.1109/tit.2011.2177632 · 被引用次数：242 · 研究领域：Sparse and Compressive Sensing Techniques、Blind Source Separation Techniques、Microwave Imaging and Scattering Analysis

The general theory of greedy approximation is well developed. Much less is known about how specific features of a dictionary can be used to our advantage. In this paper, we discuss incoherent dictionaries. We build a new greedy algorithm which is called the orthogonal super greedy algorithm (OSGA). We show that the rates of convergence of OSGA and the orthogonal matching pursuit (OMP) with respect to incoherent dictionaries are the same. Based on the analysis of the number of orthogonal projections and the number of iterations, we observed that OSGA is times simpler (more efficient) than OMP. Greedy approximation is also a fundamental tool for sparse signal recovery. The performance of orthogonal multimatching pursuit, a counterpart of OSGA in the compressed sensing setting, is also analyzed under restricted isometry property conditions.