A general framework for a class of non-linear approximations with applications to image restoration
| Autor: | Antonio Falcó, Vicente F. Candela, Pantaleón D. Romero |
|---|---|
| Přispěvatelé: | UCH. Departamento de Matemáticas, Física y Ciencias Tecnológicas, Producción Científica UCH 2018 |
| Rok vydání: | 2018 |
| Předmět: |
Mathematical optimization
010103 numerical & computational mathematics 01 natural sciences Projection (linear algebra) Convexity Image (mathematics) symbols.namesake Programming (Mathematics) in Works of art Convergence (routing) Applied mathematics 0101 mathematics Programación (Matemáticas) - Aplicaciones en Obras de arte Art - Conservation and restoration Image restoration Mathematics Applied Mathematics Hilbert space Algoritmos computacionales Hilbert Espacio de Linear subspace Computer algorithms 010101 applied mathematics Computational Mathematics Obras de arte - Restauración symbols Deconvolution Obras de arte - Conservación |
| Zdroj: | CEU Repositorio Institucional Fundación Universitaria San Pablo CEU (FUSPCEU) |
| ISSN: | 0377-0427 |
| DOI: | 10.1016/j.cam.2017.03.008 |
| Popis: | Este artículo se encuentra disponible en la página web de la revista en la siguiente URL: https://www.sciencedirect.com/science/article/abs/pii/S0377042717301188 Este es el pre-print del siguiente artículo: Candela, V., Falcó, A. & Romero, PD. (2018). A general framework for a class of non-linear approximations with applications to image restoration. Journal of Computational and Applied Mathematics, vol. 330 (mar.), pp. 982-994, que se ha publicado de forma definitiva en https://doi.org/10.1016/j.cam.2017.03.008 This is the pre-peer reviewed version of the following article: Candela, V., Falcó, A. & Romero, PD. (2018). A general framework for a class of non-linear approximations with applications to image restoration. Journal of Computational and Applied Mathematics, vol. 330 (mar.), pp. 982-994, which has been published in final form at https://doi.org/10.1016/j.cam.2017.03.008 In this paper, we establish sufficient conditions for the existence of optimal nonlinear approximations to a linear subspace generated by a given weakly-closed (non-convex) cone of a Hilbert space. Most non-linear problems have difficulties to implement good projection-based algorithms due to the fact that the subsets, where we would like to project the functions, do not have the necessary geometric properties to use the classical existence results (such as convexity, for instance). The theoretical results given here overcome some of these difficulties. To see this we apply them to a fractional model for image deconvolution. In particular, we reformulate and prove the convergence of a computational algorithm proposed in a previous paper by some of the authors. Finally, some examples are given. Preprint |
| Databáze: | OpenAIRE |
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