Adaptive time-frequency decompositions

Abstract

Computing the optimal expansion of a signal in a redundant dictionary of waveforms is an NP-hard problem. We introduce a greedy algorithm, called a matching pursuit, which computes a suboptimal expansion. The dictionary waveforms that best match a signal's structures are chosen iteratively. An orthogonalized version of the matching pursuit is also developed. Matching pursuits are general procedures for computing adaptive signal representations. With a dictionary of Gabor functions, a matching pursuit defines an adaptive time-frequency transform. Matching pursuits are chaotic maps whose attractors define a generic noise with respect to the dictionary. We derive an algorithm that isolates the coherent structures of a signal and describe an application to pattern extraction from noisy signals.

Keywords

Matching pursuitComputer scienceAlgorithmMatching (statistics)WaveformSIGNAL (programming language)ChaoticSignal processingNoise (video)Pattern matchingPattern recognition (psychology)Time–frequency analysisArtificial intelligenceCompressed sensingImage (mathematics)MathematicsComputer visionTelecommunications

Affiliated Institutions

New York University US

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Publication Info

Year: 1994
Type: article
Volume: 33
Issue: 7
Pages: 2183-2183
Citations: 348
Access: Closed

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APA Style

                            
                                    Geoffrey M. Davis, 
                                
                                    Stéphane Mallat, 
                                
                                    Zhifeng Zhang
                                
                            (1994). 
                            Adaptive time-frequency decompositions. 
                            Optical Engineering
                            , 33
                            (7)
                            , 2183-2183.
                            https://doi.org/10.1117/12.173207

Identifiers

DOI: 10.1117/12.173207