Pseudo-inverses of difference matrices and their application to sparse signal approximation
arXiv:1504.04266 · doi:10.1016/j.laa.2016.03.033
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.
16 pages