Abstract
Compressive sensing theory has attracted widespread attention in recent years and sparse signal reconstruction has been widely used in signal processing and communication. This paper addresses the problem of sparse signal recovery especially with non-Gaussian noise. The main contribution of this paper is the proposal of an algorithm where the negentropy and reweighted schemes represent the core of an approach to the solution of the problem. The signal reconstruction problem is formalized as a constrained minimization problem, where the objective function is the sum of a measurement of error statistical characteristic term, the negentropy, and a sparse regularization term, ℓp-norm, for 0 < p < 1. The ℓp-norm, however, leads to a non-convex optimization problem which is difficult to solve efficiently. Herein we treat the ℓp -norm as a serious of weighted ℓ1-norms so that the sub-problems become convex. We propose an optimized algorithm that combines forward-backward splitting. The algorithm is fast and succeeds in exactly recovering sparse signals with Gaussian and non-Gaussian noise. Several numerical experiments and comparisons demonstrate the superiority of the proposed algorithm.
Highlights
Sparse signal reconstruction, or compressed sensing, is an emerging field in signal processing and communication [1,2,3,4,5,6]
According to the compressed sensing theory, sparse signal reconstruction problem can be formalized as a constrained minimization problem, where the objective function defines the sparsity
We propose an algorithm with two main steps: first we use the gradient-based maximization only to the negentropy; we find a sparser solution within the neighborhood of what has been obtained in the gradient-based maximization
Summary
Compressed sensing, is an emerging field in signal processing and communication [1,2,3,4,5,6]. In the case of a discrete, finite domain, the signals can be viewed as vectors in an n-dimensional Euclidean space, denoted by Rn. According to the compressed sensing theory, sparse signal reconstruction problem can be formalized as a constrained minimization problem, where the objective function defines the sparsity. We focus on the problem of sparse signal reconstruction especially with non-Gaussian noise. This problem is formalized as a constrained minimization problem and verified by simulation. We propose a sparse coding algorithm in which the sparse signal is recovered by applying the negentropy [22] as the error measurement andp -norm as the sparsity regularization. The sparse signals can be estimated by applying the negentropy as the error measurement and weighted1 -norm as the sparsity regularization.
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