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

Pseudo-inverses of difference matrices and their application to sparse signal approximation 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Linear Algebra and its Applications Elsevier

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

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Publisher
Elsevier
Copyright
Copyright © 2016 Elsevier Inc.
ISSN
0024-3795
eISSN
1873-1856
D.O.I.
10.1016/j.laa.2016.03.033
Publisher site
See Article on Publisher Site

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 matching pursuit (OMP) method.

Journal

Linear Algebra and its ApplicationsElsevier

Published: Aug 15, 2016

References

  • Least squares splines with free knots: global optimization approach
    Beliakov, G.
  • Signal recovery from random measurements via orthogonal matching pursuit
    Tropp, J.A.; Gilbert, A.C.

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