基于自适应次梯度投影算法的压缩感知信号重构

Adaptive Subgradient Projection Method for Sparse Reconstruction in Compressed Sensing

本文提出一种利用自适应次梯度投影算法(Adaptive Subgridient Projection Method,ASPM)进行压缩感知(Compressed Sensing,CS)信号重构的方案。ASPM算法首先根据CS重构模型建立包含稀疏重构信号并具有随机属性的凸集,然后运用并行次梯度投影的思想将对该凸集的投影转化为对多个闭合半平面的投影,最后将更新后的干扰抑制滤波器系数矢量投影到限定集合上。同时为了获得快速收敛性,本文设计了在迭代的不同阶段自适应地调节该膨胀系数的机制。理论分析和仿真结果表明,本算法具有快速收敛性和较低的重构误差,在不同的噪声强度下具有较高的鲁棒性。

Adaptive subgradient projection method（ASPM） is proposed in this paper for sparse reconstruction in compressed sensing（CS）.Stochastic property convex set which contains the sparse reconstruction signal is established by the CS reconstruction model firstly.Then parallel subgradient projection is adopted to convert projection onto convex sets to projection into multiple closed halfspaces.Finally,the updated sparse reconstruction signal vector is projected onto the constrained set.Meanwhile,mechanism which adaptively adjusts inflation parameter in different iterations has been designed for fast convergence.Theoretical analysis and simulation results conclude that this algorithm has fast convergence,lower reconstruction error,and exhibits higher robustness in different noise intensity.