从稀疏到结构化稀疏:贝叶斯方法

From Sparsity to Structured Sparsity: Bayesian Perspective

稀疏分解算法是稀疏表达理论和压缩感知理论中的核心问题,也是当前信号处理领域的一个热门话题。近年来,研究人员发现除了稀疏以外,如果引入稀疏系数之间的相关性先验信息,可以大大提高稀疏分解算法的精度,这种方法称为"结构化稀疏分解算法"。本文归纳和总结了从稀疏到结构化稀疏的信号模型,并且介绍了两种不同的贝叶斯稀疏(或者结构化稀疏)算法,以及从稀疏到结构化稀疏贝叶斯稀疏分解算法的扩展。同时,本文还介绍了结构化稀疏分解算法在医学信号处理和语音信号处理中的应用。

Sparse decomposition algorithm is one of the hottest research topic in signal processing field and plays an important role in sparse representation and Compressive Sensing（CS）.Recently,beside sparsity,the structures that describes the dependencies of sparse coefficients has been exploited to improve the accuracy of sparse decomposition algorithms.It is called structured sparse decomposition algorithms.This paper will review the sparse signal model and structured sparse signal model.After that,two sparse decomposition algorithms based on Bayesian framework are introduced and their extensions to structured sparse signals are addressed.At last,the applications of structured sparsity in medical signal processing and audio signal processing are respectively demonstrated.