A globally convergent derivative-free projection algorithm for signal processing

Abstract

In this paper, a hybrid derivative-free conjugate gradient method that inherits the structures of two conjugate gradient methods is introduced to recover sparse signal in compressive sensing by solving the nonlinear convex constrained equations. The global convergence of the proposed method is proved, under some appropriate assumptions. Numerical experiments and comparisons suggest that the proposed algorithm is an efficient approach for sparse signal and image reconstruction in compressive sensing.

Subject Classification:

• 65K05
• 90C52
• 90C56
• 94A08

Keywords:

• Compressive sensing
• Nonlinear equations
• Conjugate gradient method
• Projection method
• Convex constraints