A gradient projection method for the sparse signal reconstruction in compressive sensing

Abstract

Many problems arising from machine learning, compressive sensing, linear inverse problem, and statistical inference involve finding sparse solutions to under-determined or ill-conditioned equations. In this paper, a gradient projection method is proposed to recover sparse signal in compressive sensing by solving the nonlinear convex constrained equations. The global convergence is established with the backtracking line search. Preliminary numerical experiments coping with the sparse signal reconstruction in compressive sensing are performed, which show that the proposed method is very effective and stable.

Keywords:

• Compressive sensing
• nonlinear equations
• conjugate gradient method
• projection method
• global convergence

AMS Subject Classifications:

• 90C30
• 65K05

Acknowledgements

The authors would like to express their thanks to Professor Y.H. Xiao for his kind offer of the source codes for CGD method.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the Chongqing Research Program of Basic Research and Frontier Technology [grant number cstc2017jcyjA0364]; the fund of Scientific and Technological Research Program of Chongqing Municipal Education Commission [grant number KJ1501003], [grant number KJ1710251] and Program for Innovation Team Building at Institutions of Higher Education in Chongqing [grant number CXTDX201601035].