Open AccessComputational approaches to non-convex, sparsity-inducing multi-penalty regularization
Author(s) -
Željko Kereta,
Johannes Maly,
Valeriya Naumova
Publication year - 2021
Publication title -
inverse problems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.003
H-Index - 119
eISSN - 1361-6420
pISSN - 0266-5611
DOI - 10.1088/1361-6420/abdd46
Subject(s) - regularization (linguistics) , mathematics , mathematical optimization , penalty method , convolution (computer science) , convergence (economics) , reduction (mathematics) , regular polygon , convex optimization , rate of convergence , convex function , algorithm , computer science , artificial intelligence , key (lock) , geometry , computer security , artificial neural network , economics , economic growth
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.