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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

Examples of functions with different asymmetry used in the enriched dictionary.
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pone.0131007.g001: Examples of functions with different asymmetry used in the enriched dictionary.

Mentions: The dictionary of functions used here consists of asymmetric functions described by Eq 6 and symmetric Gabor functions (which can be considered as a special case of the function in Eq 6). Examples of functions described by Eq 6 are shown in Fig 1. They include functions of different shapes, from almost symmetric to highly asymmetric. The ED used in our approach is larger than the standard Gabor Dictionary (GD) and its size depends on the number of asymmetries present in the signal components. Here we have used a dictionary of Gabor functions consisting of 107 atoms. The ED was about 13 times bigger.


Matching Pursuit with Asymmetric Functions for Signal Decomposition and Parameterization.

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

Examples of functions with different asymmetry used in the enriched dictionary.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0131007.g001: Examples of functions with different asymmetry used in the enriched dictionary.
Mentions: The dictionary of functions used here consists of asymmetric functions described by Eq 6 and symmetric Gabor functions (which can be considered as a special case of the function in Eq 6). Examples of functions described by Eq 6 are shown in Fig 1. They include functions of different shapes, from almost symmetric to highly asymmetric. The ED used in our approach is larger than the standard Gabor Dictionary (GD) and its size depends on the number of asymmetries present in the signal components. Here we have used a dictionary of Gabor functions consisting of 107 atoms. The ED was about 13 times bigger.

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