基于Cholesky矩阵分解的贝叶斯压缩感知信号处理

Bayesian compressed sensing signal processing basedon Cholesky matrix decomposition

随着雷达、卫星遥感技术的的高速发展,信号重构精度和效率的要求越来越高。针对传统贝叶斯压缩感知(Bayesian compressed sensing,BCS)算法需要进行高维矩阵反复求逆致使算法复杂度过高、运算时间过长的问题,结合Cholesky矩阵分解快速求逆方法,提出一种基于矩阵分解的改进贝叶斯压缩感知算法。通过仿真比较传统的BCS算法、最小l 1范数算法和正交匹配追踪算法(OMP),笔者改进的BCS算法在不损失信号重构精度的同时大幅缩减了算法运算时间,重构效果得到改善。

With the rapid development of radar and satellite remote sensing technology,the requirements of signal reconstruction accuracy and efficiency are higher and higher.The traditional Bayesian compressed sensing(BCS)algorithm needs to perform high-dimensional matrix inversion repeatedly,resulting in high complexity and long computing time.Combined with the fast inversion method of Cholesky matrix decomposition,an improved BCS algorithm based on matrix decomposition is proposed.By comparing the traditional BCS algorithm,the minimum l 1 norm algorithm and the orthogonal matching pursuit algorithm(OMP)through simulation,the improved BCS algorithm proposed in this paper greatly reduces the algorithm operation time without loss of signal reconstruction accuracy,and improves the reconstruction effect.