Linear convergence and support recovery for non-convex multi-penalty regularization

08/07/2019

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by   Zeljko Kereta, et al.

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We provide a comprehensive convergence study of the iterative multi-penalty q-thresholding algorithm, with 0<q≤ 1, for recovery of a signal mixture. Leveraging recent results in optimisation, signal processing, and regularization, we present novel results on linear convergence of iterates to local minimizers for studied non-convex multi-penalty functionals. We also provide explicitly compute the convergence constant and establish its dependence with respect to the measurement matrix and parameters of the problem. Finally, we present extensive numerical results, that confirm the theoretical findings, and compare the efficiency of the iterative multi-penalty thresholding algorithm with single-penalty counterpart.