Sparse signal recovery by accelerated ℓ_q (0<q<1) thresholding algorithm

ABSTRACT

The nonconvex ${\ell }_q(0<q<1)$ regularization, which has superiority on sparsity-inducing over the convex counterparts, has been proposed in many areas of engineering and science. In this paper, we present an accelerated ${\ell }_q$ regularization thresholding algorithm for sparse signal recovery, which can be viewed as an extension of the well-known Nesterov's accelerated gradient method from convex optimization to nonconvex case. It has shown numerically that the proposed algorithm keeps fast convergence, and also maintains high recovery precision. Extensive numerical experiments have been to demonstrate the effectiveness of the proposed algorithm. It is also mentioned that the proposed algorithm has much faster convergence and higher recovery precision in sparse signal recovery over the commonly non-accelerated ${\ell }_q$ thresholding algorithm.

KEYWORDS:

• Compressed sensing
• sparse signal recovery
• thresholding algorithm
• ${\ell }_q$ regularization
• nonlinear optimization

2010 AMS SUBJECT CLASSIFICATIONS:

• 68W40
• 45Q05
• 90C30

Disclosure statement

No potential conflict of interest was reported by the authors.