Reconstruction of noisy signals by minimization of non-convex functionals. (December 2016)

• Record Type: Journal Article
• Authors: Mederos, Boris; Mollineda, Ramón A.; Camarena, Julián Antolín
• Is Part Of: Nonlinear analysis. Volume 32(2016)
• Page Start: 355
• Page End: 376
• Publication Date: 2016-12
• Subjects: Non-convex functional -- Signal denoising -- Minimizer -- Calculus of variations; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.05.007
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: Non-convex functionals have shown sharper results in signal reconstruction as compared to convex ones, although the existence of a minimum has not been established in general. This paper addresses the study of a general class of either convex or non-convex functionals for denoising signals which combines two general terms for fitting and smoothing purposes, respectively. The first one measures how close a signal is to the original noisy signal. The second term aims at removing noise while preserving some expected characteristics in the true signal such as edges and fine details. A theoretical proof of the existence of a minimum for functionals of this class is presented. The main merit of this result is to show the existence of minimizer for a large family of non-convex functionals.