压缩感知中一种改进的迭代硬阈值算法

A Modified Iterative Hard Thresholding Algorithm in Compressed Sensing

研究了压缩感知理论中一种改进的迭代硬阈值稀疏信号重构算法。针对现有IHT算法类最优秀的BIHT算法中回溯操作无法保证稀疏信号重构误差递减的问题,对稀疏重构误差及其差值进行了简单介绍和分析,提出了一种能够保证重构误差随迭代进行单调减小的重构算法,在每次迭代的回溯操作中选择能够保证重构误差逐渐减小的原子,并将其指标与估计支撑集合并,最后基于最小二乘法进行伪逆运算获取稀疏信号估计。对高斯稀疏信号和0-1稀疏信号进行了仿真,证明了优于IHT、NIHT以及BIHT算法的稀疏信号重构性能。

This paper proposes a modified iterative hard thresholding algorithm to reconstruct sparse signal in Compressive Sensing.The backtracking procedure in BIHT algorithm,which is the best algorithm in IHT-type class,can’t guarantee the reduction of sparse signal reconstruction error.Aiming at this problem,this paper briefly introduces and analyzes the sparse signal reconstruction error and its difference,and then proposes a reconstruction algorithm that guarantees the reduction of sparse signal reconstruction error.In the backtracking procedure of each iteration,the atoms guaranteeing the reduction of sparse signal reconstruction error will be selected,and then combined to the estimated support to obtain the sparse signal estimation with pseudo inverse based on the least square.The simulation results indicate that the reconstruction efficiency and effectiveness of the proposed algorithms on Gaussian sparse signal and zero-one signal are obviously better than that of IHT,NIHT and BIHT algorithms.