Variable metric extrapolation proximal iterative hard thresholding method for ℓ_0 minimization problem

08/07/2021

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by   Xue Zhang, et al.

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In this paper, we consider the ℓ_0 minimization problem whose objective function is the sum of ℓ_0-norm and convex differentiable function. A variable metric type method which combines the PIHT method and the skill in quasi-newton method, named variable metric extrapolation proximal iterative hard thresholding (VMEPIHT) method, is proposed. Then we analyze its convergence, linear convergence rate and superlinear convergence rate under appropriate assumptions. Finally, we conduct numerical experiments on compressive sensing problem and CT image reconstruction problem to confirm VMPIHT method's efficiency, compared with other state-of-art methods.