基于压缩感知的步长自适应前向后向追踪重建算法

压缩感知(CS)是一种新的信号采样、处理和恢复理论,能够显著地降低高频窄带信号的采样频率。针对稀疏度未知信号的重建,提出了步长自适应前向后向追踪(AFBP)算法。不同于固定步长前向后向追踪(FBP)算法,AFBP的步长可变。它利用一种自适应阈值的方法选取前向步长,然后对候选支撑集进行正则化处理以保证其可靠性,接着用自适应阈值与变步长双向控制的方法选取后向步长以减少重建时间。AFBP能够自适应后向删除估计支撑集中部分错误索引以提高信号准确重建概率。在稀疏信号非零值服从常见分布条件下,用AFBP、FBP等算法进行重建的结果表明,AFBP的准确重建概率、重建精度与FBP相当,重建时间明显少于FBP,能够更高效地重建稀疏度未知信号。

Adaptive Step Length Forward-backward Pursuit Algorithm for Signal Reconstruction Based on Compressed Sensing

Compressed sensing (CS) is a new theory of signal sampling,processing and recovering,which can significantly reduce the sampling frequency of signal with high frequency and narrow band.Aiming at reconstructing signals with unknown sparsity,we proposed a novel signal reconstruction algorithm called the adaptive forward-backward pursuit (AFBP).Unlike the Forward-backward Pursuit algorithm with fixed step length,AFBP works with varied step length.It utilizes an adaptive thresholding method to adaptively choose the forward step length and conducts the regularize process towards the candidate support estimate to ensure its reliability.We adopted a method which combines the adaptive thresholding and the variable step length afterwards to decide the backward step length in order to reduce the necessary reconstruction time.Some incorrect indexes included in the support estimate can be deleted adaptively in order to improve the exact reconstruction rate.The AFBP reconstruction experiment was conducted including recovery of random sparse signals with common nonzero coefficient distributions.The results demonstrate that AFBP and FBP contribute to similar exact reconstruction rate as well as similar reconstruction error,while the reconstruction time of AFBP is sharply shorter than that of FBP.So AFBP can realize more efficient reconstruction of sparse signals with unknown sparsity than FBP.