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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

The decomposition of the TOAE signal shown at the very top; obtained by the enriched dictionary (on the left) and by Gabor dictionary (on the right). Below the time-frequency-amplitude maps, at the bottom the first five (strongest) atoms of the decomposition. The maxima of amplitudes of the first five atoms are marked by crosses.
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pone.0131007.g005: The decomposition of the TOAE signal shown at the very top; obtained by the enriched dictionary (on the left) and by Gabor dictionary (on the right). Below the time-frequency-amplitude maps, at the bottom the first five (strongest) atoms of the decomposition. The maxima of amplitudes of the first five atoms are marked by crosses.

Mentions: OAEs are the time series in which the application of the ED appears to be indispensable An example of the decomposition of TEOAE by means of enriched and Gabor dictionaries is shown in Fig 5. Inspecting the t-f map we can observe, in the case of GD, "energy leakage"- energy preceding the stimulus. The effect is especially clearly visible in the second strongest frequency component of 2.30 kHz. Fig 5 shows that the GD does not represent well the long-lasting components of a steep rise. They are approximated by more than one atom.


Matching Pursuit with Asymmetric Functions for Signal Decomposition and Parameterization.

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

The decomposition of the TOAE signal shown at the very top; obtained by the enriched dictionary (on the left) and by Gabor dictionary (on the right). Below the time-frequency-amplitude maps, at the bottom the first five (strongest) atoms of the decomposition. The maxima of amplitudes of the first five atoms are marked by crosses.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0131007.g005: The decomposition of the TOAE signal shown at the very top; obtained by the enriched dictionary (on the left) and by Gabor dictionary (on the right). Below the time-frequency-amplitude maps, at the bottom the first five (strongest) atoms of the decomposition. The maxima of amplitudes of the first five atoms are marked by crosses.
Mentions: OAEs are the time series in which the application of the ED appears to be indispensable An example of the decomposition of TEOAE by means of enriched and Gabor dictionaries is shown in Fig 5. Inspecting the t-f map we can observe, in the case of GD, "energy leakage"- energy preceding the stimulus. The effect is especially clearly visible in the second strongest frequency component of 2.30 kHz. Fig 5 shows that the GD does not represent well the long-lasting components of a steep rise. They are approximated by more than one atom.

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