Computational approaches to non-convex, sparsity-inducing multi-penalty regularization. (20th April 2021)

• Record Type: Journal Article
• Authors: Kereta, Željko; Maly, Johannes; Naumova, Valeriya
• Is Part Of: Inverse problems. Volume 37:Number 5(2021)
• Publication Date: 2021-04-20
• Subjects: multi-penalty regularization -- iterative thresholding -- non-convex optimization -- lq-regularization (0 < q < 1); Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/abdd46
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this work we consider numerical efficiency and convergence rates for solvers of non-convex multi-penalty formulations when reconstructing sparse signals from noisy linear measurements. We extend an existing approach, based on reduction to an augmented single-penalty formulation, to the non-convex setting and discuss its computational intractability in large-scale applications. To circumvent this limitation, we propose an alternative single-penalty reduction based on infimal convolution that shares the benefits of the augmented approach but is computationally less dependent on the problem size. We provide linear convergence rates for both approaches, and their dependence on design parameters. Numerical experiments substantiate our theoretical findings.