基于差分的稀疏度自适应重构算法

Adaptive Sparse Recovery Based on Difference Algorithm

针对压缩感知贪婪迭代重构算法要求给定信号稀疏度或迭代阈值的缺点,提出一种基于差分的稀疏度自适应重构算法.该算法在信号稀疏度未知的情况下,利用测量矩阵Φ与残差的相关系数的变化的不均衡特性,来选择重构信号的支撑集,以此逼近原始信号的稀疏度,达到重构的效果.仿真结果表明,在相同采样率下,文中算法可以获得较好的重构效果,尤其在采样率较低(采样率≤0.5)的情况下,这种优势更加明显.

To improve the disadvantages that iterative reconstruction algorithms of compressed sensing need priori knowledge of the sparsity of original signal or iterative threshold, an adaptive sparse recovery based on difference algorithm is proposed. When the sparsity of original signal is unknown, the proposed algorithm takes advantage of unbalance of correlation coefficient between the measurement matrix and residual. With those properties, the proposed algorithm can select the support set of the original signal, and approach the sparsity of the original signal. Simulation results show that the proposed algorithm obtains better recovery results under the same conditions. Especially in the lower sampling rate, the advantage is more obvious.