Normalization Effects in Matching Pursuit Algorithm with Gabor Dictionaries
PDF

Keywords

matching pursuit
time-frequency
wavelet
EEG analysis

How to Cite

Różański, P. T. (2018). Normalization Effects in Matching Pursuit Algorithm with Gabor Dictionaries. Journal of Applied Computer Science, 26(2), 187-200. https://doi.org/10.34658/jacs.2018.26.2.187-200

Abstract

The matching pursuit (MP) algorithm is a greedy method for signal decomposition used in video coding, data compression, and, particularly, analysis of EEG signals in various paradigms, including P300 and ER(D)S (motor imagery). An important issue for MP implementation is a correct treatment of normalization of atoms (functions) used in computations. Failing to account for normalization-related effects may affect both the numerical stability and the reliability of the algorithm. This paper describes these normalization effects, evaluates their impact on the algorithm’s performance, and describe the proper approach together with a ready-to-use implementation, available under a General Public Licence (GPL). Several performance optimizations used as a part of this implementation are also described.

https://doi.org/10.34658/jacs.2018.26.2.187-200
PDF

References

Mallat, S. G. and Zhang, Z., Matching pursuits with time-frequency dictionaries, IEEE Transactions on Signal Processing, Vol. 41, No. 12, Dec 1993, pp. 3397–3415.

Durka, P. J., Ircha, D., Neuper, C., and Pfurtscheller, G., Time-frequency microstructure of event-related electro-encephalogram desynchronisation andsynchronisation, Medical and Biological Engineering and Computing, Vol. 39, 2001, pp. 315–321.

Sieluzycki, C., Konig, R., Matysiak, A., Kus, R., Ircha, D., and Durka, P. J., Single-Trial Evoked Brain Responses Modeled by Multivariate Matching Pursuit, IEEE Transactions on Biomedical Engineering, Vol. 56, No. 1, Jan 2009, pp. 74–82.

Durka, P. J., Matysiak, A., Montes, E. M., Sosa, P. V., and Blinowska, K. J., Multichannel matching pursuit and EEG inverse solutions. Journal of neuro-science methods, Vol. 148 1, 2005, pp. 49–59.

Durka, P. J., Malinowska, U., Zieleniewska, M., O’Reilly, C., Różański, P. T., and ̇Zygierewicz, J., Spindles in Svarog: framework and software for parametrization of EEG transients, Front. Hum. Neurosci., 2015.

Kuś, R., Różański, P. T., and Durka, P. J., Multivariate matching pursuit inoptimal Gabor dictionaries: theory and software with interface for EEG/MEGvia Svarog, BioMedical Engineering OnLine, Vol. 12, No. 1, Sep 2013, pp. 94.

Krstulovic, S. and Gribonval, R., MPTK: Matching Pursuit made Tractable, In: Proc. Int. Conf. Acoust. Speech Signal Process. (ICASSP’06), Vol. 3, Toulouse, France, May 2006, pp. III–496 – III–499.

Cormen, T. H., Leiserson, C. E., Rivest, R. L., and Stein, C., Introduction to Algorithms, Third Edition, The MIT Press, 3rd ed., 2009.

Downloads

Download data is not yet available.