A thresholding algorithm for sparse recovery via Laplace norm

作者：Wang, Qian; Qu, Gangrong^*; Han, Guanghui

来源：Signal, Image and Video Processing, 2019, 13(2): 389-395.

DOI：10.1007/s11760-018-1367-9

• Compressed sensing
• Sparse signal
• Regularization model
• Thresholding algorithm
• Signal processing

The last decade has witnessed rapidly growing interest in the studies of compressed sensing. p norm, an approximation to 0 norm, can be used to recover a sparse signal from underdetermined linear systems. In comparison with p norm, another approximation called Laplace norm is a closer approximation to 0 norm. The thresholding algorithm is a simple and efficient iterative process to solve the regularization problem. In this paper, we derive the thresholding point and a quasi-analytic thresholding representation for the Laplace regularization, and then a thresholding algorithm for the Laplace regularization is proposed. The numerical results show that the proposed algorithm has higher recovery rate than the p thresholding algorithms. This thresholding representation can be easily incorporated into the iterative thresholding framework to provide a tool for sparsity problems.

• 出版日期2019-3
• 单位北京交通大学; 天津商业大学