Dual-density-based reweighted ℓ_1-algorithms for a class of ℓ_0-minimization problems
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The optimization problem with sparsity arises in many areas of science and engineering such as compressed sensing, image processing, statistical learning and data sparse approximation. In this paper, we study the dual-density-based reweighted ℓ_1-algorithms for a class of ℓ_0-minimization models which can be used to model a wide range of practical problems. This class of algorithms is based on certain convex relaxations of the reformulation of the underlying ℓ_0-minimization model. Such a reformulation is a special bilevel optimization problem which, in theory, is equivalent to the underlying ℓ_0-minimization problem under the assumption of strict complementarity. Some basic properties of these algorithms are discussed, and numerical experiments have been carried out to demonstrate the efficiency of the proposed algorithms. Comparison of numerical performances of the proposed methods and the classic reweighted ℓ_1-algorithms has also been made in this paper.
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