Treffer: Theoretical and experimental analysis of a randomized algorithm for Sparse Fourier transform analysis

Title:
Theoretical and experimental analysis of a randomized algorithm for Sparse Fourier transform analysis
Authors:
JING ZOU, GILBERT, Anna, STRAUSS, Martin, DAUBECHIES, Ingrid
Source:
Journal of computational physics (Print). 211(2):572-595
Publisher Information:
Amsterdam: Elsevier, 2006.
Publication Year:
2006
Physical Description:
print, 13 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Theoretical physics, Physique théorique, Sciences exactes et technologie, Exact sciences and technology, Physique, Physics, Generalites, General, Méthodes mathématiques en physique, Mathematical methods in physics, Techniques de calcul, Computational techniques, Algorithme, Algorithms, Analyse Fourier, Fourier analysis, Espace temps, Space-time, Méthode calcul, Calculation methods, Probabilité, Probability, Technique calcul, Calculation, Transformation Fourier rapide, Fast Fourier transforms, Transformation Fourier, Fourier transformation, 42A10 RAlSFA, 65T50, 68W20, Fast Fourier transform, Randomized algorithm, Sparse Fourier representation, Sublinear algorithm
Document Type:
Fachzeitschrift Article
File Description:
text
Language:
English
Author Affiliations:
Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, United States
Department of Mathematics, University of Michigan, MI, United States
Departments of Mathematics and Electrical Engineering and Computer Science, University of Michigan, MI, United States
Program in Applied and Computational Mathematics and Department of Mathematics, Princeton University, Princeton, NJ 08544, United States
ISSN:
0021-9991
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=17469420
Rights:
Copyright 2006 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics

Theoretical physics
Accession Number:
edscal.17469420
Database:
PASCAL Archive

Weitere Informationen

We analyze a sublinear RAlFA (randomized algorithm for Sparse Fourier analysis) that finds a near-optimal B-term Sparse representation R for a given discrete signal S of length N, in time and space poly(B, log(N)), following the approach given in [A.C. Gilbert, S. Guha, P. Indyk, S. Muthukrishnan, M. Strauss, Near-Optimal Sparse Fourier Representations via Sampling, STOC, 2002]. Its time cost poly(log(N)) should be compared with the superlinear Q(N log N) time requirement of the Fast Fourier Transform (FFT). A straightforward implementation of the RAlSFA, as presented in the theoretical paper [A.C. Gilbert, S. Guha, P. Indyk, S. Muthukrishnan, M. Strauss, Near-Optimal Sparse Fourier Representations via Sampling, STOC, 2002], turns out to be very slow in practice. Our main result is a greatly improved and practical RAlSFA. We introduce several new ideas and techniques that speed up the algorithm. Both rigorous and heuristic arguments for parameter choices are presented. Our RAlSFA constructs, with probability at least 1 - δ, a near-optimal B-term representation R in time poly(B) log(N) log(1/δ)/∈2 log(M) such that ∥S - R∥22 ≤ (1 + ∈)∥S - Ropt∥22. Furthermore, this RAlSFA implementation already beats the FFTW for not unreasonably large N. We extend the algorithm to higher dimensional cases both theoretically and numerically. The crossover point lies at N ~ 70, 000 in one dimension, and at N ~ 900 for data on a N x N grid in two dimensions for small B signals where there is noise.