南京大学学报：自然科学版2012，Vol.48Issue(4)：475-481,7.
基于前向后向算子分裂的稀疏信号重构
Sparse signal recovery based on forward backward operator splitting
摘要
Abstract
Compressive sensing consists of compressive sampling and sparse reconstruction. Compressive sampling breaks through the limitation of traditional Shannon sampling theorem, reduces the acquisition data amount hence becoming an emerging method for data acquisition. Sparse reconstruction algorithm is the key step for successfully recovering the original data in high dimension and has become the hot research topic in signal processing and related area. In this paper, an sparse recovery algorithm is designed and named FPSP3, which includes three key components： fixed point iteration, non-monotone line search SPG2 and warm start skill. The optimal solution of LI norm penalized Least Square problem is represented as the zero point of sum of gradient and sub-differential operator, and forward backward operator splitting method is used to derive the optimal solution＇ s fixed pointiteration, which consists of forward gradient and backward proximal step. The proof of backward proximal step corresponding to the proximity operator of L1 norm, namely soft thresholding shrinkage, demonstrates that fixed point iteration can be implemented by gradient descent and soft thresholding. The analysis for convergent step size condition is simplified by proving the strong monotonicity of inverse of gradient operator. The brief proof is given to illustrate the fixed point iteration converges in linear rate to the optimal solution. The introduction of non-monotone line search SPG2 and warm start skill significantly accelerate the practical efficiency of proposed algorithm. Comparisons are made in sparse recovery experiments with some state of the art L1 norm methods, which demonstrates the advantages of running time and recovering accuracy of FPSP3.关键词
压缩感知/稀疏重构/算子分裂/不动点迭代/非单调线搜索Key words
compressive sensing/sparse recovery/operator splitting/fixed point iteration/non-monotoneline search分类
计算机与自动化引用本文复制引用
谢志鹏..基于前向后向算子分裂的稀疏信号重构[J].南京大学学报：自然科学版,2012,48(4):475-481,7.基金项目
国家自然科学基金 （）
