Sparse Coding Algorithm with Negentropy and Weighted ℓ1-Norm for Signal Reconstruction

Abstract

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, p -norm, for 0 < p < 1. The p -norm, however, leads to a non-convex optimization problem which is difficult to solve efficiently. Herein we treat the p -norm as a serious of weighted 1 -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.

Negentropy-Based Sparsity-Promoting Reconstruction with Fast Iterative Solution from Noisy Measurements

“…We propose to exploit the negentropy of measurement error, , as the objective function as a new model. According to information theory, among all random variables with equal variance, the entropy of Gaussian variables is the largest [ 23 ]. Obviously, entropy can measure the Gaussian property of a variable, so negentropy can be used to measure its non-Gaussian property; the larger the negentropy is, the stronger the non-Gaussian variable is.…”

“…To achieve more accurate recovery, research focusing on the -LA minimization problem was reported in [ 22 ]. Meanwhile, it was demonstrated in [ 23 ] that the negentropy of measurement error can achieve good recovery performance with non-Gaussian noise. Whilst the focus of [ 23 ] is to present a novel method of error measurement, it also suggests an optimized algorithm that combines forward-backward splitting to solve the robust CS formulation.…”

“…Meanwhile, it was demonstrated in [ 23 ] that the negentropy of measurement error can achieve good recovery performance with non-Gaussian noise. Whilst the focus of [ 23 ] is to present a novel method of error measurement, it also suggests an optimized algorithm that combines forward-backward splitting to solve the robust CS formulation. However, the efficiency and capacity of the method proposed in [ 23 ] have not reached the requirement of real-world applications that require fast processing, such as magnetic resonance imaging (MRI), thus, we propose in this paper more computationally efficient algorithms to achieve the goal.…”

“…In this paper, we mainly study sparse signal reconstruction algorithms against non-Gaussian noise. A novel sparse representation model is proposed, which takes the negentropy [ 23 ] of measurement error as the objective function and norm as the sparsity measurement. The negentropy can be exploited to measure the non-Gaussian properties of random variables, here the fitting error, and the stronger the non-Gaussian noise is, the larger the negentropy value is.…”

Design of Sparse FIR Decision Feedback Equalizers in MIMO Systems Using Hybrid l1/l2 Norm Minimization and the OMP Algorithm

“…They achieve better performance than the method in [10] with the same number of nonzero taps. Furthermore, for the pursuit of both sparse promotion and improved accuracy, the sparse signals reconstruction algorithms inspired by l 1 and weighted l 1 regularization schemes are proposed in [17,18]; the joint smoothed l 0 norm algorithm for direction-of-arrival estimation in MIMO radar is proposed in [19]. …”