关键词: 压缩感知, 稀疏优化, 活动集方法, 投影算子法, 经典凸规划法

Abstract: Compressed Sensing（CS） is a new theoretical frame about information acquisition and processing developed in recent years. This paper gives an introduction to the basic theory of CS, focused on sparse optimization algorithms, which are divided into three classes in this paper：active set methods, projection operator methods and classical convex programming methods. The basic idea, main research progresses, and adaptive optimization problems of each method are discussed. Finally, some open problems and research directions in sparse optimization of CS are pointed out.

Key words: compressed sensing, sparse optimization, active set methods, projection operator methods, classical convex programming methods