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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

Time-frequency distributions obtained by: A—windowed Fourier transform (spectrogram), B—Rihaczek transform, C—Morlet wavelets, D—Wigner de Ville transform, E—MP with the enriched dictionary, F—MP with the Gabor dictionary.Components of simulated signal consisting of asymmetric waveform of frequency 15 Hz and two spindles of frequencies 12 Hz and 10 Hz are shown at the very top of the picture. On the horizontal axis time, on the vertical axis frequency in Hz. The colors represent: for four upper panels energy and for two lowest panels amplitude (red the strongest, dark blue the weakest).
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pone.0131007.g004: Time-frequency distributions obtained by: A—windowed Fourier transform (spectrogram), B—Rihaczek transform, C—Morlet wavelets, D—Wigner de Ville transform, E—MP with the enriched dictionary, F—MP with the Gabor dictionary.Components of simulated signal consisting of asymmetric waveform of frequency 15 Hz and two spindles of frequencies 12 Hz and 10 Hz are shown at the very top of the picture. On the horizontal axis time, on the vertical axis frequency in Hz. The colors represent: for four upper panels energy and for two lowest panels amplitude (red the strongest, dark blue the weakest).

Mentions: Comparison of t-f distributions obtained by different methods–spectrogram, Rihaczek distribution, Morlet wavelets, Wigner de Wille transform, MP including enriched dictionary and MP with Gabor dictionary are shown in Fig 4. The simulated signal consisted of an asymmetric long-lasting frequency component of 15 Hz similar to SSVEP and two frequency components of 12 Hz and 10 Hz of a spindle-like shape similar to alpha waves. White noise with the amplitude equal 10% of the synthetic signal was added. In all representations we can distinguish three components but with the differing resolution. The t-f resolution in the case of the spectrogram is not very good and representation of the 12 Hz component is corrupted by the 15 Hz wave. In the case of Rihaczek distribution and Wigner de Ville transform, strong interference terms occur. Additionally the latencies and time spans are not correctly reproduced. MP with the GD for alpha waves gives very good results, but for asymmetric component of 15 Hz the pre-echo effect is visible, and the latency of the component is not quite correct. For MP with the ED the representation is more than satisfactory. The MP based t-f distributions display the amplitude of the signals, not the energy therefore they are free from interference terms (for the GD they are absent anyway, but they appear for asymmetric functions). Concluding, we may say that MP with the dictionary including asymmetric functions and amplitude-time-frequency distribution is an optimal method of signal representation in t-f space.


Matching Pursuit with Asymmetric Functions for Signal Decomposition and Parameterization.

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

Time-frequency distributions obtained by: A—windowed Fourier transform (spectrogram), B—Rihaczek transform, C—Morlet wavelets, D—Wigner de Ville transform, E—MP with the enriched dictionary, F—MP with the Gabor dictionary.Components of simulated signal consisting of asymmetric waveform of frequency 15 Hz and two spindles of frequencies 12 Hz and 10 Hz are shown at the very top of the picture. On the horizontal axis time, on the vertical axis frequency in Hz. The colors represent: for four upper panels energy and for two lowest panels amplitude (red the strongest, dark blue the weakest).
© Copyright Policy
Related In: Results  -  Collection

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

pone.0131007.g004: Time-frequency distributions obtained by: A—windowed Fourier transform (spectrogram), B—Rihaczek transform, C—Morlet wavelets, D—Wigner de Ville transform, E—MP with the enriched dictionary, F—MP with the Gabor dictionary.Components of simulated signal consisting of asymmetric waveform of frequency 15 Hz and two spindles of frequencies 12 Hz and 10 Hz are shown at the very top of the picture. On the horizontal axis time, on the vertical axis frequency in Hz. The colors represent: for four upper panels energy and for two lowest panels amplitude (red the strongest, dark blue the weakest).
Mentions: Comparison of t-f distributions obtained by different methods–spectrogram, Rihaczek distribution, Morlet wavelets, Wigner de Wille transform, MP including enriched dictionary and MP with Gabor dictionary are shown in Fig 4. The simulated signal consisted of an asymmetric long-lasting frequency component of 15 Hz similar to SSVEP and two frequency components of 12 Hz and 10 Hz of a spindle-like shape similar to alpha waves. White noise with the amplitude equal 10% of the synthetic signal was added. In all representations we can distinguish three components but with the differing resolution. The t-f resolution in the case of the spectrogram is not very good and representation of the 12 Hz component is corrupted by the 15 Hz wave. In the case of Rihaczek distribution and Wigner de Ville transform, strong interference terms occur. Additionally the latencies and time spans are not correctly reproduced. MP with the GD for alpha waves gives very good results, but for asymmetric component of 15 Hz the pre-echo effect is visible, and the latency of the component is not quite correct. For MP with the ED the representation is more than satisfactory. The MP based t-f distributions display the amplitude of the signals, not the energy therefore they are free from interference terms (for the GD they are absent anyway, but they appear for asymmetric functions). Concluding, we may say that MP with the dictionary including asymmetric functions and amplitude-time-frequency distribution is an optimal method of signal representation in t-f space.

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