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.
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