Pseudo-inverses of difference matrices and their application to sparse signal approximation

被引：5

作者：

Plonka, Gerlind ^{[1
]}

Hoffmann, Sebastian ^{[2
]}

Weickert, Joachim ^{[2
]}

机构：

[1] Univ Gottingen, Inst Numer & Appl Math, Lotzestr 16-18, D-37083 Gottingen, Germany

[2] Univ Saarland, Math Image Anal Grp, Fac Math & Comp Sci, Campus B1-7, D-66041 Saarbrucken, Germany

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2016年 / 503卷

关键词：

Moore-Penrose inverse; Fourier transform; Linear diffusion; Orthogonal matching pursuit; Partial differential equations; Interpolation; LEAST-SQUARES APPROXIMATION; SPLINES; CIRCULANT;

D O I：

10.1016/j.laa.2016.03.033

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We derive new explicit expressions for the components of Moore-Penrose inverses of symmetric difference matrices. These generalized inverses are applied in a new regularization approach for scattered data interpolation based on partial differential equations. The columns of the Moore-Penrose inverse then serve as elements of a dictionary that allow a sparse signal approximation. In order to find a set of suitable data points for signal representation we apply the orthogonal matching pursuit (OMP) method. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：26 / 47

页数：22

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