基于观测矩阵优化的自适应压缩感知算法

摘要

为提高传统压缩感知(CS)恢复算法的抗噪性能,结合观测矩阵优化和自适应观测的思想,提出一种自适应压缩感知(ACS)算法.该算法将观测能量全部分配在由传统CS恢复算法估计的支撑位置,由于估计支撑集中包含支撑位置,这样可有效提高观测信噪比(SNR);再从优化观测矩阵的角度推导出最优的新观测向量,即其非零部分设计为Gram矩阵的特征向量.仿真结果表明,随着观测数增大,Gram矩阵非对角元素的能量增速小于传统CS算法,并且分别在观测次数、稀疏度和SNR相同的条件下,所提算法的重构归一化均方误差低于传统CS恢复算法10 dB以上,低于典型的贝叶斯方法5 dB以上.分析表明,所提自适应观测机制可有效提高传统CS恢复算法的能量利用效率和抗噪性能.%In order to improve the anti-noise performance of the traditional Compressed Sensing (CS) recovery algorithm,a kind of Adaptive Compressed Sensing (ACS) algorithm was proposed based on the idea of observation matrix optimization and adaptive observation.The observed energy was all allocated in the support position estimated by the traditional CS recovery algorithm,which could effectively improve the observed Signal-to-Noise Ratio (SNR) owing to the support positions contained in the estimated support set.Then,the optimal new observation vector was derived from the perspective of observation matrix optimization,that is,its nonzero part was designed as the eigenvector of Gram matrix.The simulation results show that,the energy growth rate of non-diagonal elements of Gram matrix is less than that of the traditional CS algorithm with the increase of the number of observations.And the reconstruction normalized mean square error of the proposed algorithm is respectively lower than that of the traditional CS algorithm and the typical Bayesian method above 10 dB and 5 dB under the same conditions of number of observations,sparsity and SNR.The analysis shows that the proposed adaptive observation mechanism can effectively improve the energy efficiency and anti-noise performance of the traditional CS recovery algorithm.