English

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

Numerical Analysis 2016-10-03 v1

Abstract

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 patching pursuit (OMP) method.

Keywords

Cite

@article{arxiv.1504.04266,
  title  = {Pseudo-inverses of difference matrices and their application to sparse signal approximation},
  author = {Gerlind Plonka and Sebastian Hoffmann and Joachim Weickert},
  journal= {arXiv preprint arXiv:1504.04266},
  year   = {2016}
}

Comments

16 pages

R2 v1 2026-06-22T09:17:22.678Z