# Deterministic Sparse FFT Algorithms

 dc.contributor.advisor Plonka-Hoch, Gerlind Prof. Dr. dc.contributor.author Wannenwetsch, Katrin Ulrike dc.date.accessioned 2016-09-30T08:21:24Z dc.date.available 2016-09-30T08:21:24Z dc.date.issued 2016-09-30 dc.identifier.uri http://hdl.handle.net/11858/00-1735-0000-002B-7C10-0 dc.identifier.uri http://dx.doi.org/10.53846/goediss-5874 dc.language.iso eng de dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/4.0/ dc.subject.ddc 510 de dc.title Deterministic Sparse FFT Algorithms de dc.type doctoralThesis de dc.contributor.referee Plonka-Hoch, Gerlind Prof. Dr. dc.date.examination 2016-08-09 dc.description.abstracteng The discrete Fourier transform (DFT) is a well-known transform with many applications in various fields. By fast Fourier transform (FFT) algorithms, the DFT of a vector can be efficiently computed. Using these algorithms, one can reconstruct a complex vector x of length N from its discrete Fourier transform applying O(N log N) arithmetical operations. In order to improve the complexity of FFT algorithms, one needs additional a priori assumptions on the vector x. In this thesis, the focus is on vectors with small support or sparse vectors for which several new deterministic algorithms are proposed that have a lower complexity than regular FFT algorithms. We develop sublinear time algorithms for the reconstruction of complex vectors or matrices with small support from Fourier data as well as an algorithm for the reconstruction of real nonnegative vectors. The algorithms are analyzed and evaluated in numerical experiments. Furthermore, we generalize the algorithm for real nonnegative vectors with small support and propose an approach to the reconstruction of sparse vectors with real nonnegative entries. de dc.contributor.coReferee Potts, Daniel Prof. Dr. dc.subject.eng Discrete Fourier Transform de dc.subject.eng Fast Fourier Transform de dc.subject.eng sparse Fourier reconstruction de dc.subject.eng sparse FFT de dc.subject.eng vector reconstruction de dc.subject.eng small support de dc.identifier.urn urn:nbn:de:gbv:7-11858/00-1735-0000-002B-7C10-0-2 dc.affiliation.institute Fakultät für Mathematik und Informatik de dc.subject.gokfull Mathematics (PPN61756535X) de dc.identifier.ppn 869470280
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