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Matching Pursuit with Asymmetric Functions for Signal Decomposition and Parameterization.

Spustek T, Jedrzejczak WW, Blinowska KJ - PLoS ONE (2015)

Bottom Line: The application of this enriched dictionary to Otoacoustic Emissions and Steady-State Visually Evoked Potentials demonstrated the advantages of the proposed method.The approach provides more sparse representation, allows for correct determination of the latencies of the components and removes the "energy leakage" effect generated by symmetric waveforms that do not sufficiently match the structures of the analyzed signal.Additionally, we introduced a time-frequency-amplitude distribution that is more adequate for representation of asymmetric atoms than the conventional time-frequency-energy distribution.

View Article: PubMed Central - PubMed

Affiliation: Department of Biomedical Physics, Warsaw University, Warszawa, Poland.

ABSTRACT
The method of adaptive approximations by Matching Pursuit makes it possible to decompose signals into basic components (called atoms). The approach relies on fitting, in an iterative way, functions from a large predefined set (called dictionary) to an analyzed signal. Usually, symmetric functions coming from the Gabor family (sine modulated Gaussian) are used. However Gabor functions may not be optimal in describing waveforms present in physiological and medical signals. Many biomedical signals contain asymmetric components, usually with a steep rise and slower decay. For the decomposition of this kind of signal we introduce a dictionary of functions of various degrees of asymmetry--from symmetric Gabor atoms to highly asymmetric waveforms. The application of this enriched dictionary to Otoacoustic Emissions and Steady-State Visually Evoked Potentials demonstrated the advantages of the proposed method. The approach provides more sparse representation, allows for correct determination of the latencies of the components and removes the "energy leakage" effect generated by symmetric waveforms that do not sufficiently match the structures of the analyzed signal. Additionally, we introduced a time-frequency-amplitude distribution that is more adequate for representation of asymmetric atoms than the conventional time-frequency-energy distribution.

No MeSH data available.


Related in: MedlinePlus

At the very top: simulated signal. Below: time-frequency-energy representations of the simulated signal obtained by: A—asymmetric dictionary and B—Gabor dictionary; time-frequency-amplitude representations obtained by: C—asymmetric dictionary and D—Gabor dictionary. Crosses mark the centers of the atoms.
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pone.0131007.g002: At the very top: simulated signal. Below: time-frequency-energy representations of the simulated signal obtained by: A—asymmetric dictionary and B—Gabor dictionary; time-frequency-amplitude representations obtained by: C—asymmetric dictionary and D—Gabor dictionary. Crosses mark the centers of the atoms.

Mentions: However, the Wigner distribution is not an optimal choice in the case of asymmetric dictionaries. This can be illustrated with the simulation presented in Fig 2. The maximum of energy in the Wigner distribution for the dictionary of Gabor functions is shifted in relation to the maximum of of instataneous amplitude of the signal. Moreover, it is easy to see that expantion in Gabor dictionary needs 4 atoms to represent the function. In the case of ED, with asymmetric functions, only one atom is sufficient to represent energy of the function in t-f space. However, the squaring procedure inherent in the Wigner distribution creates cross-terms or “ghost-like” structures.


Matching Pursuit with Asymmetric Functions for Signal Decomposition and Parameterization.

Spustek T, Jedrzejczak WW, Blinowska KJ - PLoS ONE (2015)

At the very top: simulated signal. Below: time-frequency-energy representations of the simulated signal obtained by: A—asymmetric dictionary and B—Gabor dictionary; time-frequency-amplitude representations obtained by: C—asymmetric dictionary and D—Gabor dictionary. Crosses mark the centers of the atoms.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4482735&req=5

pone.0131007.g002: At the very top: simulated signal. Below: time-frequency-energy representations of the simulated signal obtained by: A—asymmetric dictionary and B—Gabor dictionary; time-frequency-amplitude representations obtained by: C—asymmetric dictionary and D—Gabor dictionary. Crosses mark the centers of the atoms.
Mentions: However, the Wigner distribution is not an optimal choice in the case of asymmetric dictionaries. This can be illustrated with the simulation presented in Fig 2. The maximum of energy in the Wigner distribution for the dictionary of Gabor functions is shifted in relation to the maximum of of instataneous amplitude of the signal. Moreover, it is easy to see that expantion in Gabor dictionary needs 4 atoms to represent the function. In the case of ED, with asymmetric functions, only one atom is sufficient to represent energy of the function in t-f space. However, the squaring procedure inherent in the Wigner distribution creates cross-terms or “ghost-like” structures.

Bottom Line: The application of this enriched dictionary to Otoacoustic Emissions and Steady-State Visually Evoked Potentials demonstrated the advantages of the proposed method.The approach provides more sparse representation, allows for correct determination of the latencies of the components and removes the "energy leakage" effect generated by symmetric waveforms that do not sufficiently match the structures of the analyzed signal.Additionally, we introduced a time-frequency-amplitude distribution that is more adequate for representation of asymmetric atoms than the conventional time-frequency-energy distribution.

View Article: PubMed Central - PubMed

Affiliation: Department of Biomedical Physics, Warsaw University, Warszawa, Poland.

ABSTRACT
The method of adaptive approximations by Matching Pursuit makes it possible to decompose signals into basic components (called atoms). The approach relies on fitting, in an iterative way, functions from a large predefined set (called dictionary) to an analyzed signal. Usually, symmetric functions coming from the Gabor family (sine modulated Gaussian) are used. However Gabor functions may not be optimal in describing waveforms present in physiological and medical signals. Many biomedical signals contain asymmetric components, usually with a steep rise and slower decay. For the decomposition of this kind of signal we introduce a dictionary of functions of various degrees of asymmetry--from symmetric Gabor atoms to highly asymmetric waveforms. The application of this enriched dictionary to Otoacoustic Emissions and Steady-State Visually Evoked Potentials demonstrated the advantages of the proposed method. The approach provides more sparse representation, allows for correct determination of the latencies of the components and removes the "energy leakage" effect generated by symmetric waveforms that do not sufficiently match the structures of the analyzed signal. Additionally, we introduced a time-frequency-amplitude distribution that is more adequate for representation of asymmetric atoms than the conventional time-frequency-energy distribution.

No MeSH data available.


Related in: MedlinePlus