压缩感知和稀疏优化简介

介绍压缩感知和稀疏优化的基本概念、理论基础和算法概要. 压缩感知利用原始信号的稀疏性，从远少于信号元素个数的测量出发，通过求解稀疏优化问题来恢复完整的原始稀疏信号. 通过一个小例子展示这一过程，并以此说明压缩感知和稀疏优化的基本理念. 接着简要介绍用以保证l₁凸优化恢复稀疏信号的零空间性质和RIP条件. 最后介绍求解稀疏优化的几个经典算法.

Introduction to compressive sensing and sparse optimization

We briefly introduce the basic principle and theory of compressive sensing and sparse optimization.Compressive sensing is a new paradigm of signal acquisition, which senses a sparse signal by taking a set of incomplete measurements and recovers the signal by solving an optimization problem.This article first illustrates the compressive sensing paradigm through a synthetic example.Then we describe two sufficient conditions, the null space property and restricted isometry principle,for l₁ convex minimization to give the sparsest solution.Finally,we summarize a few typical algorithms for solving the optimization models arising from compressive sensing.