University of Göttingen - Institute for Numerical and Applied Mathematics
Research group for Mathematical Signal and Image Processing


Efficient function reconstruction using eigenfunctions of linear operators



(07/2014-06/2017)

Solitoneneigenschaften
Individual research grant of the German Research Foundation

Goal of this project is the generalization of nonlinear reconstruction methods that are based on Prony's method. Here we apply a new view on this approach, namely that the classical Prony method for parameter identification in exponential sums as well as the Ben-Or and Tiwari algorithm for sparse polynomial interpolation can be understood as nonlinear reconstruction techniques for M-term expansions of eigenfunctions of special linear operators. We are particularly interested in deriving fast and numerically stable reconstruction schemes as well as new error estimates in case of noisy input data.



Principal investigator: Gerlind Plonka-Hoch
Staff: Katrin Wannenwetsch

Corresponding publications
Application of the AAK theory for sparse approximation of exponential sums
Gerlind Plonka, Vlada Pototskaia
University of Göttingen, Institute for Numerical and Applied Mathematics, 2016, preprint as download.
A sparse Fast Fourier algorithm for real nonnegative vectors
Gerlind Plonka, Katrin Wannenwetsch
Journal of Computational and Applied Mathematics 321, 532-539, 2017, preprint as download.
Deterministic Sparse FFT Algorithms
Katrin Wannenwetsch
Dissertation, 2016, published online on 30 September 2016, http://hdl.handle.net/11858/00-1735-0000-002B-7C10-0.
Sparse approximation by Prony's method and AAK theory
Gerlind Plonka, Vlada Pototskaia
Oberwolfach Reports, Volume 33, pp. 16-19, 2016, preprint as download.
Reconstruction of polygonal shapes from sparse Fourier samples
Marius Wischerhoff, Gerlind Plonka
Journal of Computational and Applied Mathematics 297, 117-131, 2016, preprint as download.
A deterministic sparse FFT algorithm for vectors with small support
Gerlind Plonka, Katrin Wannenwetsch
Numerical Algorithms 71(4), 889-905, 2016, preprint as download.
Deterministic sparse FFT algorithms
Gerlind Plonka, Katrin Wannenwetsch
Proc. Appl. Math. Mech. Volume 15, Issue 1, pp. 667-668, October 2015, DOI: 10.1002/pamm.201510323, preprint as download.
Prony's Method for Multivariate Signals
Thomas Peter, Gerlind Plonka, Robert Schaback
Proc. Appl. Math. Mech. Volume 15, Issue 1, pp. 665-666, October 2015, DOI: 10.1002/pamm.201510322, preprint as download.
A deterministic sparse FFT algorithm for vectors with short support
Gerlind Plonka, Katrin Wannenwetsch
Oberwolfach Reports, Volume 38, pp. 41-44, 2015,
Prony methods for recovery of structured functions
Gerlind Plonka, M. Tasche
GAMM-Mitt. 37(2), 2014, 239-258, revised preprint as download.


Corresponding software
Sparse FFT (small support)
A new deterministic sparse FFT algorithm for vectors with small support.
Katrin Wannenwetsch, Gerlind Plonka
Sparse FFT (real non-negative)
A new deterministic sparse FFT algorithm for real non-negative vectors.
Katrin Wannenwetsch, Gerlind Plonka



Research Group for Mathematical Signal and Image Processing

Institute for Numerical and Applied Mathematics
Lotzestr. 16-18
37083 Göttingen