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RESEARCH PRODUCT
A general framework for a class of non-linear approximations with applications to image restoration
Antonio FalcóVicente F. CandelaPantaleón D. Romerosubject
Mathematical optimization010103 numerical & computational mathematics01 natural sciencesProjection (linear algebra)ConvexityImage (mathematics)symbols.namesakeProgramming (Mathematics) in Works of art.Convergence (routing)Applied mathematics0101 mathematicsProgramación (Matemáticas) - Aplicaciones en Obras de arte.Art - Conservation and restoration.Image restorationMathematicsApplied MathematicsHilbert space.Hilbert spaceAlgoritmos computacionales.Hilbert Espacio de.Linear subspaceComputer algorithms.010101 applied mathematicsComputational MathematicsObras de arte - Restauración.symbolsDeconvolutionObras de arte - Conservación.description
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
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-03-01 | Journal of Computational and Applied Mathematics |