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The matching pursuit (MP) algorithm is an iterative procedure of adaptive approximation of a signal using a redundant dictionary of functions. The exceptional strength of MP is that a sparse representation of the signal is obtained, which means that even a complex signal may be reconstructed by a few functions only. Moreover, the application of MP is not restricted to any a-priori choices concerning the parameters of the functions used for the signal approximation, i.e. it is free of any bias which — in the traditional short-time Fourier transform (STFT) or continuous wavelet transform (CWT) — stems from the prior setting of the trade-off between time and frequency resolutions in terms of optimal window length or chosen wavelet type.
In practice, dictionaries composed of Gabor functions (sines with amplitude modulated by Gaussian envelopes) are frequently used, these functions being characterized by four parameters only: tn – translation, fn – frequency, sn – scale, and fn – phase. They offer the best trade-off between time and frequency resolution, and thus optimally fit to the local signal structures.
Matching pursuit can be implemented in significantly different ways, as single-channel, multi-channel or multi-trial versions. The superior high resolution both in time and frequency makes the various matching pursuit algorithms a powerful tool in the (pre-)processing and the analysis of electroencephalographic (EEG) and magnetoencephalographic (MEG) signals.
In one of our projects, we use the multivariate matching pursuit (MMP) algorithm to study event-related brain dynamics on a single-trial level using an experimental paradigm consisting of a simple auditory stimulus (1-kHz sine tone). The basic approach (model) is to assume that the evoked response in single trials can be composed of Gabor functions, and that the parameters of these Gabor functions – except for the amplitude – are kept invariant across all trials, yet, not having been assigned to any particular value a-priori. The trial-dependent peak amplitude of an evoked magnetic field like the auditory M100 waveform is determined by the amplitude weighting factor, and the inter-trial variability of the corresponding M100-peak latency is extracted from the superposition of a few Gabor functions (typically, about 3–5 iterations seem to be sufficient).
Deutscher Akademischer Austauschdienst / Project based personnel exchange programme (PPP) with Poland
Prof. P. Durka and his group, Department of Biomedical Physics, Institute of Experimental Physics, Warsaw University, Poland