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Sparse hyperspectral unmixing has been a hot topic in recent years. Joint sparsity assumes that each pixel in a small neighborhood of hyperspectral images (HSIs) is composed of the same endmembers, which results in a few nonzero rows in the abundance matrix. Recall that a plethora of unmixing algorithms transform a 3-D HSI into a 2-D matrix with vertical priority. The transformation makes matrix computation easier. It is, however, hard to maintain the horizontal spatial information in HSIs in many cases. To make further use of the spatial information of HSIs, in this article, we propose a bilateral joint-sparse structure for hyperspectral unmixing in an attempt to exploit the local joint sparsity of the abundance matrix in both the vertical and horizontal directions. In particular, we introduce a permutation matrix to realize the bilateral joint-sparse representation and there is no need to construct the matrix explicitly. Moreover, we propose to simultaneously impose the bilateral joint-sparse structure and low rankness on the abundance and develop a new algorithm named bilateral joint-sparse and low-rank unmixing. The proposed algorithm is based on the alternating direction method of multipliers framework and employs a reweighting strategy. The convergence analysis of the proposed algorithm is investigated. Simulated and real-data experiments show the effectiveness of the proposed algorithm.

In this paper, we propose a Group-Sparse Representation-based method with applications to Face Recognition (GSR-FR). The novel sparse representation variational model includes a non-convex sparsity-inducing penalty and a robust non-convex loss function. The penalty encourages group sparsity by using an approximation of the $\ell _{0}$ -quasinorm, and the loss function is chosen to make the algorithm robust to noise, occlusions, and disguises. The solution of the non-trivial non-convex optimization problem is efficiently obtained by a majorization-minimization strategy combined with forward-backward splitting, which, in particular, reduces the solution to a sequence of easier convex optimization sub-problems. Extensive experiments on widely used face databases show the potentiality of the proposed model and demonstrate that the GSR-FR algorithm is competitive with the state-of-the-art methods based on sparse representation, especially for very low dimensional feature spaces. [ABSTRACT FROM AUTHOR]

This paper addresses the issue of beampattern synthesis with flexible magnitude response and low sidelobe in a frequency diverse array radar. It is formulated as an optimization problem in terms of $\ell _1$-norm minimization, which encourages the sparsity of array pattern. An $\ell _1$ iterative phase compensation (IPC) technique is employed to transform the nonconvex constraint to phase compensation form. Then, to further reduce the sidelobe level, a reweighted $\ell _1$ -IPC algorithm is devised, in which a sparsity-enhanced scheme is utilized to convert the $\ell _1$-norm to a new cost function that more closely resembles $\ell _0$-norm. Numerical results are presented to demonstrate the effectiveness of the proposed approach in different scenarios. [ABSTRACT FROM AUTHOR]

Hyperspectral unmixing (HSU) plays an important role in hyperspectral image (HSI) analysis. Recently, the HSU method based on sparse regression has drawn much attention. This paper presents a new weighted sparse regression problem for HSU and proposes two iterative reweighted algorithms for solving this problem, where the weights used for the next iteration are computed from the value of the current solution, and all the mixed pixels of an HSI are unmixed simultaneously. The proposed algorithms can be seen as the combinations of alternating direction method of multipliers and iterative reweighting procedure. Experimental results on both synthetic and real data demonstrate some advantages of the proposed algorithms over some other state-of-the-art sparse unmixing approaches. [ABSTRACT FROM AUTHOR]

In this paper, we propose a reweighted low-rank matrix recovery method and demonstrate its application for robust image restoration. In the literature, principal component pursuit solves low-rank matrix recovery problem via a convex program of mixed nuclear norm and \ell1 norm. Inspired by reweighted \ell1 minimization for sparsity enhancement, we propose reweighting singular values to enhance low rank of a matrix. An efficient iterative reweighting scheme is proposed for enhancing low rank and sparsity simultaneously and the performance of low-rank matrix recovery is prompted greatly. We demonstrate the utility of the proposed method both on numerical simulations and real images/videos restoration, including single image restoration, hyperspectral image restoration, and background modeling from corrupted observations. All of these experiments give empirical evidence on significant improvements of the proposed algorithm over previous work on low-rank matrix recovery. [ABSTRACT FROM PUBLISHER]

The bilateral filter represents a wide group of nonlinear filters for edge-preserving image smoothing. In this work, we study the convergence properties of the bilateral filter algorithm. The understanding is established that the bilateral filter is an optimization procedure. We demonstrate that the bilateral filter is equivalent to minimizing a robust cost criterion using iterative reweighting, which is a good approximation to the very fast but unstable Newton's method. Further, the results of the analysis allow us to derive an improved hybrid smoothing scheme with concerns of computational efficiency and edge preservation. [ABSTRACT FROM AUTHOR]