title: Adaptive phase extraction: incorporating the Gabor transform in the matching pursuit algorithm.
abstract: Short-time Fourier transform (STFT), Gabor transform (GT), wavelet transform (WT), and the Wigner-Ville distribution (WVD) are just some examples of time-frequency analysis methods which are frequently applied in biomedical signal analysis. However, all of these methods have their individual drawbacks. The STFT, GT, and WT have a time-frequency resolution that is determined by algorithm parameters and the WVD is contaminated by cross terms. In 1993, Mallat and Zhang introduced the matching pursuit (MP) algorithm that decomposes a signal into a sum of atoms and uses a cross-term free pseudo-WVD to generate a data-adaptive power distribution in the time-frequency space. Thus, it solved some of the problems of the GT and WT but lacks phase information that is crucial e.g., for synchronization analysis. We introduce a new time-frequency analysis method that combines the MP with a pseudo-GT. Therefore, the signal is decomposed into a set of Gabor atoms. Afterward, each atom is analyzed with a Gabor analysis, where the time-domain gaussian window of the analysis matches that of the specific atom envelope. A superposition of the single time-frequency planes gives the final result. This is the first time that a complete analysis of the complex time-frequency plane can be performed in a fully data-adaptive and frequency-selective manner. We demonstrate the capabilities of our approach on a simulation and on real-life magnetoencephalogram data.
authors.affiliation: Bernstein Group for Computational Neuroscience Jena, Institute of Medical Statistics, Computer Sciences and Documentation, Jena University Hospital—Friedrich-Schiller-University Jena, 07740 Jena, Germany. matthias.wacker@mti.uni-jena.de
authors.forename: Matthias
authors.initials: M
authors.lastname: Wacker
authors.forename: Herbert
authors.initials: H
authors.lastname: Witte
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D006801:Humans; D015225:Magnetoencephalography; D012815:Signal Processing, Computer-Assisted