Reconstruction of noisy signals by minimization of non-convex functionals
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Other documents of the author: Mederos, Boris; Mollineda, Ramón A.; Camarena, Julián Antolín
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comunitat-uji-handle2:10234/7038
comunitat-uji-handle3:10234/8634
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Title
Reconstruction of noisy signals by minimization of non-convex functionalsDate
2016-12Publisher
ElsevierISSN
1468-1218Bibliographic citation
MEDEROS, Boris; MOLLINEDA, Ramón A.; CAMARENA, Julián Antolín. Reconstruction of noisy signals by minimization of non-convex functionals. Nonlinear Analysis: Real World Applications, 2016, vol. 32, p. 355-376Type
info:eu-repo/semantics/articlePublisher version
http://www.sciencedirect.com/science/article/pii/S1468121816300396Version
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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 ... [+]
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. [-]
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Nonlinear Analysis: Real World Applications, 2016, vol. 32Rights
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