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arXiv · 1504.04266

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

Gerlind Plonka·Sebastian Hoffmann·Joachim Weickert
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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.

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Gerlind Plonka, Sebastian Hoffmann, Joachim Weickert. 2015-04-16. Pseudo-inverses of difference matrices and their application to sparse signal approximation. https://doi.org/10.1016/j.laa.2016.03.033

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