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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: 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 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 SSVEP signal recorded at electrode O2 (shown at the very top) obtained by the enriched dictionary (on the left) and by Gabor dictionary (on the right). Below: time-frequency-amplitude maps, at the bottom the first five atoms of the decomposition. In Table 3, parameters (frequency, amplitude, time occurrence and time span) describing the first five atoms are shown. In the time-frequency map harmonics at 30 Hz is not shown in order to make the figure more compact.
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pone.0131007.g006: The decomposition of the SSVEP signal recorded at electrode O2 (shown at the very top) obtained by the enriched dictionary (on the left) and by Gabor dictionary (on the right). Below: time-frequency-amplitude maps, at the bottom the first five atoms of the decomposition. In Table 3, parameters (frequency, amplitude, time occurrence and time span) describing the first five atoms are shown. In the time-frequency map harmonics at 30 Hz is not shown in order to make the figure more compact.

Mentions: For SSVEP analysis we applied the MP method with the dictionary encompassing asymmetric waveforms and for comparison the dictionary with symmetric atoms only. In Fig 6 the time-frequency-amplitude maps and the five strongest atoms obtained by decomposition of the SSVEP registered at electrode O2 are shown for the enriched and Gabor dictionaries. The t-f representations reveal the very narrow-band characteristics of SSVEP. In the case of Gabor representation we can observe the “energy leakage” effect–the energy of the signal appears before the start of the signal. The symmetric dictionary is unable to clearly show the onset of SSVEP. In the case of the ED the first and second atoms correspond to the basic frequency of 15 Hz and its harmonics. However, in the case of the GD only the third atom corresponds to the harmonics, since the second atom is needed to improve the representation of the 15 Hz component. In the case of the ED the third atom of very short duration represents the fast onset of SSVEP, and its latency of 5.05 ms corresponds very well to the start of the stimulus. The GD does not allow accurate determination of the onset of SSVEP. In Table 3 and Table 4, amplitudes, frequencies, latencies and time spans of the displayed atoms are given. It is easy to see that for both representations the frequencies of harmonics reproduce the stimulating frequency very accurately.


Matching Pursuit with Asymmetric Functions for Signal Decomposition and Parameterization.

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

The decomposition of the SSVEP signal recorded at electrode O2 (shown at the very top) obtained by the enriched dictionary (on the left) and by Gabor dictionary (on the right). Below: time-frequency-amplitude maps, at the bottom the first five atoms of the decomposition. In Table 3, parameters (frequency, amplitude, time occurrence and time span) describing the first five atoms are shown. In the time-frequency map harmonics at 30 Hz is not shown in order to make the figure more compact.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0131007.g006: The decomposition of the SSVEP signal recorded at electrode O2 (shown at the very top) obtained by the enriched dictionary (on the left) and by Gabor dictionary (on the right). Below: time-frequency-amplitude maps, at the bottom the first five atoms of the decomposition. In Table 3, parameters (frequency, amplitude, time occurrence and time span) describing the first five atoms are shown. In the time-frequency map harmonics at 30 Hz is not shown in order to make the figure more compact.
Mentions: For SSVEP analysis we applied the MP method with the dictionary encompassing asymmetric waveforms and for comparison the dictionary with symmetric atoms only. In Fig 6 the time-frequency-amplitude maps and the five strongest atoms obtained by decomposition of the SSVEP registered at electrode O2 are shown for the enriched and Gabor dictionaries. The t-f representations reveal the very narrow-band characteristics of SSVEP. In the case of Gabor representation we can observe the “energy leakage” effect–the energy of the signal appears before the start of the signal. The symmetric dictionary is unable to clearly show the onset of SSVEP. In the case of the ED the first and second atoms correspond to the basic frequency of 15 Hz and its harmonics. However, in the case of the GD only the third atom corresponds to the harmonics, since the second atom is needed to improve the representation of the 15 Hz component. In the case of the ED the third atom of very short duration represents the fast onset of SSVEP, and its latency of 5.05 ms corresponds very well to the start of the stimulus. The GD does not allow accurate determination of the onset of SSVEP. In Table 3 and Table 4, amplitudes, frequencies, latencies and time spans of the displayed atoms are given. It is easy to see that for both representations the frequencies of harmonics reproduce the stimulating frequency very accurately.

Bottom Line: 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 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