基于块稀疏贝叶斯学习的多任务压缩感知重构算法

A recovery algorithm for multitask compressive sensing based on block sparse Bayesian learning

本文提出一种基于块稀疏贝叶斯学习的多任务压缩感知重构算法,利用块稀疏的单测量矢量模型求解多任务重构问题.通过对信号统的计特性和稀疏块内的结构特性进行联合数学建模,将稀疏重构问题转贝叶斯框架下的特征参数的迭代更新问题.本文算法不需要信号稀疏度和噪声强度的先验信息,是一种高效的盲重构算法.仿真实验表明,本文算法能有效利用信号的统计特性和结构信息,在重构精度和收敛速率方面能够很好地折衷.

As a widely applied model for compressive sensing, the multitask compressive sensing can improve the performance of the inversion by appropriately exploiting the interrelationships of the tasks. The existing multitask compressive sensing recovery algorithms only utilize the statistical characteristics of a sparse signal, the structural characteristics of the sparse signal have not been taken into consideration. A multitask compressive sensing recovery algorithm is proposed in this paper based on the block sparse Bayesian learning. The block sparse single measurement vector model is applied to the multi-task problem. Both statistical and block structural characteristics of the sparse signal are used to build a mathematical model, and the sparse inverse problem is linked to the parameter iteration problems in the Bayesian framework. The proposed algorithm does not require the sparseness information and noise beforehand, which turns out to be an effective blind recovery algorithm. Extensive numerical experiments show that the proposed algorithm can exploit both statistical and structural characteristics of the signal, therefore it may reach a good trade-off between the recovery accuracy and the convergence rate.