Abstract
Compressed sensing provides an elegant framework for recovering sparse signals from compressed measurements. This paper addresses the problem of sparse signal reconstruction from compressed measurements that is more robust to complex, especially non-Gaussian noise, which arises in many applications. For this purpose, we present a method that exploits the maximum negentropy theory to promote the adaptability to noise. This problem is formalized as a constrained minimization problem, where the objective function is the negentropy of measurement error with sparse constraint -norm. On the minimization issue of the problem, although several promising algorithms have been proposed in the literature, they are very computationally demanding and thus cannot be used in many practical situations. To improve on this, we propose an efficient algorithm based on a fast iterative shrinkage-thresholding algorithm that can converge fast. Both the theoretical analysis and numerical experiments show the better accuracy and convergent rate of the proposed method.
Highlights
In recent years, compressed sensing (CS) has attracted considerable attention in areas of computer science, signal processing and wireless communication [1,2,3,4,5]
We propose a sparse signal recovery model based on negentropy maximization
To improve the robustness of the sparse signal recovery algorithm under different types of noise interference, `p norm is adopted as the sparsity constraint
Summary
In recent years, compressed sensing (CS) has attracted considerable attention in areas of computer science, signal processing and wireless communication [1,2,3,4,5]. Criteria [6], x ∈ RM is a low-dimensional measurement signal, n ∈ RM is an unknown noise vector and α ∈ RN is a sparse signal or a sparse representation of the signal in a transform basis This is solving an underdetermined equation, and there are infinite solutions. There are a variety of algorithms that have been used for solving optimization problems in applications such as digital signal process and wireless communication. In these fields, noise inevitably affects the performance of the algorithm. It is necessary to develop new methods and algorithms that are applicable to tasks with non-Gaussian noise
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