Structured Bayesian Compressive Sensing

With the continuous development of signal processing technology and the arrival of the era of big data,the requirements for signal processing technology is significantly increasing.Tra-ditional sampling technology can no longer meet people's requirements for data.Compressive Sensing(CS)theory provides a new sampling idea,which carrys out sampling and compression simultaneous.And this method greatly reduces the required storage and transmission space of the device.In this theory,only a small amount of observation data is used to accurately reconstruct the original sparse signal.Compressed sensing theory mainly includes three aspects,the sparse representation of the signal,the design of the sensing matrix and the reconstruction algorithm.Among them,the reconstruction algorithm is the key research content of compressive sensing and this article.In fact,the reconstruction algorithm directly determines the performance of compressive sensing.Bayesian Compressive Sensing combines Bayesian theory with compressive sensing,assuming that the original signal follows a certain prior probability distribution,and then estimates the parameters of the prior distribution through the Bayesian estimation method.In many practical applications,the signal often has some structures other than sparse characteristics.If the struc-tural information of the signal can be fully utilized,the algorithm reconstruction performance will be greatly improved.This article focuses on structured Bayesian compressed sensing,that is,consider how to use the potential structure of signals to improve the performance of recon-struction algorithm.The main works include:1.Using the group structure of signals to improve algorithm performance.Exploiting”Spike and Slab” prior distribution,the group structure is integrated into the distribution,and an greedy-based optimization algorithm is proposed to solve the optimization problem transformed by the ”Spike and Slab” distribution.Experiments verify the superiority of the proposed method over existing algorithms.2.In many practical applications,the elements within the same group are often correlated.In order to learn the correlation of the elements within the same group and use the correlation to improve the performance,we embed a kernel matrix into the prior distribution.Using the cor-responding optimization algorithm to estimate the kernel matrix,we can then use the estimated correlation to improve the reconstruction performance.3.In addition to the group structure,the continuous structure of signals are also widely used.The continuous structure means that the positions of non-zero elements often appear continuously.We considers the continuious structure and multi-task structure simultaneously,and designs the corresponding model and optimization algorithm,which greatly improves the reconstruction performance.