A projected gradient method for αℓ_1-βℓ_2 sparsity regularization
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The non-convex α·_ℓ_1-β·_ℓ_2 (α≥β≥0) regularization has attracted attention in the field of sparse recovery. One way to obtain a minimizer of this regularization is the ST-(αℓ_1-βℓ_2) algorithm which is similar to the classical iterative soft thresholding algorithm (ISTA). It is known that ISTA converges quite slowly, and a faster alternative to ISTA is the projected gradient (PG) method. However, the conventional PG method is limited to the classical ℓ_1 sparsity regularization. In this paper, we present two accelerated alternatives to the ST-(αℓ_1-βℓ_2) algorithm by extending the PG method to the non-convex αℓ_1-βℓ_2 sparsity regularization. Moreover, we discuss a strategy to determine the radius R of the ℓ_1-ball constraint by Morozov's discrepancy principle. Numerical results are reported to illustrate the efficiency of the proposed approach.
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