基于压缩感知的混合光谱解析算法

RESEARCH ON HYBRID SPECTRUM DECOMPOSITION ALGORITHM BASED ON COMPRESSED SENSING

压缩感知利用信号的稀疏性通过求解欠定线性系统的解来有效地重建信号,其稀疏性要求信号在某个域中是稀疏的。压缩感知理论认为一般情况下,信号的相关性越小,恢复算法的性能越好。求解压缩感知问题的方法有贪婪追踪、凸松弛方法、迭代收缩等算法,以及贝叶斯框架、置信传播等。从欠定线性矩阵方程角度讨论压缩感知问题,通过两种不同量测矩阵(谱库)的具体数值实验,重点研究了OMP、LARS和StOMP三个稀疏恢复算法在混合光谱解析时的性能和存在的问题,并给出相应的优化建议。

Compressed sensing takes advantage of the sparsity of the signal and reconstructs the signal by solving the solution of an underdetermined linear system.Sparsity requires signals to be sparse in a certain domain.Compressed sensing theory holds that in general,the smaller the correlation of the signal,the better the performance of the recovery algorithm.Methods to solve the compressed sensing problem include greedy tracking,convex relaxation method,iterative shrinkage algorithm,Bayesian framework and belief propagation algorithm,etc.This article started with underdetermined linear matrix equations and introduced the basics of compressive sensing.Through the specific numerical experiments of two different spectral libraries,the performance and existing problems of the three sparse recovery algorithms of OMP,LARS,and StOMP in mixed spectral analysis were discussed,and corresponding optimization suggestions were given.