关键词: 压缩感知,稀疏信号重建,贪婪算法,稀疏度自适应,前向后向更新,步长自适应

Abstract: 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.

Key words: Compressed sensing,Sparse signal reconstruction,Greedy algorithm,Sparsity adaptive,Forward-backward search,Step length adaptive