联合稀疏信号恢复的贪婪增强贝叶斯算法

A Greedy Refinement Bayesian Approach to Joint Sparse Signal Recovery

本文针对联合稀疏信号恢复问题,提出了一种贪婪增强贝叶斯算法.算法首先利用联合稀疏的特点对信号进行建模,然后在贝叶斯框架下,提出一种贪婪推理方式对信号恢复问题进行迭代求解.在迭代过程中,提出算法利用贝叶斯估计的方差信息来增强支撑恢复的结果,极大地提高了算法对信号恢复性能.理论分析表明:提出算法与同步正交匹配追踪算法具有相同的计算复杂度,远低于其他联合稀疏信号恢复算法.提出方法在具有高恢复精度和较低计算复杂度的同时,兼具贝叶斯方法和贪婪算法的优点.数值仿真验证了理论分析的有效性.

In this paper,a new greedy refinement bayesian approach （ GRBA）, used to solve the joint sparse signal recovery problem, is proposed. The joint sparse property of signals is first used to model the signals. Based on the model, a greedy Bayesian inference method used to estimate the signals is then presented. In order to enhance the performance of the recovery, the covariance matrix got by the Bayesian inference is utilized to refine the support recovery results in our inference process. The analytical results show that GRBA outperforms the reported algorithms in the literature in terms of both the sig- nal recovery accuracy and computational complexity. It keeps both the advantages of Bayesian methods and greedy methods. Numerical simulations verify the effectiveness of the analytical results.