改进的基于拉普拉斯先验的贝叶斯压缩感知算法  

Improved Bayesian compressive sensing algorithm with Laplace priors

作　　者：章坚武[1] 颜欢[1] 包建荣[1] 

机构地区：[1]杭州电子科技大学通信工程学院,浙江杭州310018

出　　处：《电路与系统学报》2012年第1期34-40,共7页Journal of Circuits and Systems

基　　金：国家自然科学基金资助课题(61001133)

摘　　要：贝叶斯压缩感知(Bayesian Compressed Sensing,BCS)通过稀疏贝叶斯回归模型中相关向量机(Relevance Vector Machine,RVM)的学习来解决压缩感知(Compressed Sensing,CS)中的信号重构问题。本文通过修正基于拉普拉斯先验BCS的噪声模型,较好地实现了含噪CS信号的重构。它主要利用稳健型相关向量机(Robust RVM,RRVM),改进了基于拉普拉斯先验的BCS算法。它通过对每个观测噪声方差系数进行最优化估计,来消除内外部噪声对信号重构的影响。相关的仿真验证了在外部脉冲噪声以及内部高斯白噪声共同干扰条件下,相比原始BCS算法,改进算法具有更好的重构性能和稳定性。Bayesian Compressed Sensing （BCS） utilizes the learning of the Relevance Vector Machine （RVM） of the sparse Bayesian model to solve the problem of Compressed Sensing （CS） signal＇s reconstruction. In this paper, by modifying the noise model in BCS based on the Laplace prior probability, our algorithm realizes the reconstruction of the noise-contained CS signal very well. In our algorithm, the Robust RVM is mainly .adopted to improve the performance of BCS algorithm with Laplace priors. It eliminates the influence of the inner and outer noise in signal＇s reconstruction through optimal estimation of every measurement of the noise variance coefficients. Under the interference of both outer impulse noises and inner additive white Gaussian noises, the proposed algorithm has better performance and stability compared with the original BCS algorithm.

关 键 词：贝叶斯压缩感知 拉普拉斯先验 稳健型相关向量机 重构信号 

分 类 号：TN958[电子电信—信号与信息处理]