A general framework for a class of non-linear approximations with applications to image restoration

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:330

Article

Candela, V.¹  Falco, A.²  Romero, Pantaleon D.² 

[1] Univ Valencia, Dept Matemat, Campus Burjassot,Carrer Dr Moliner 50, E-46100 Valencia, Spain

[2] Univ CEU Cardenal Herrera, Dept Matemat Fis & Cicadas Tecnol, Carrer San Bartolome 55, Valencia 46115, Spain

关键词: Non-linear approximation;    Fractional deconvolution;    Image restoration;    Weakly-closed non-convex cone;   

DOI  :  10.1016/j.cam.2017.03.008

来源: Elsevier

【 摘 要 】

In this paper, we establish sufficient conditions for the existence of optimal non-linear 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. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free