On the conjugate gradient subspace pursuit algorithm

Abstract

In this paper, a novel algorithm is proposed as the conjugate gradient subspace pursuit (CGSP). The main idea of CGSP is given to combine the subspace pursuit (SP) algorithm with the conjugate gradient method. Then, with mild assumption, the recovery guarantee condition is established, which implied that the algorithm can converge to an exact sparse solution after a finite number of iterations. Finally, the numerical simulation of CGSP is given. The simulation results show that the sparse signal satisfied the specific conditions can be recovered by CGSP with high probability and the high sampling rate, and CGSP has the best performance.

Keywords:

• Compressed sensing
• greedy algorithm
• restricted isometry property
• subspace pursuit algorithm
• conjugate gradient method

2020 Mathematics Subject Classifications:

• 46N10
• 94A08
• 94A12

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This project is supported by the National Natural Science Foundation of China (No. 62071262) and K. C. Wong Magna Fund in Ningbo University.