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Matching Pursuit with Asymmetric Functions for Signal Decomposition and Parameterization
Tomasz Spustek1, Wiesław Wiktor Jedrzejczak2, Katarzyna Joanna Blinowska3
1Department of Biomedical Physics, Warsaw University, Warszawa, Poland.
Plos One
|June 27, 2015
Summary
This study introduces an adaptive signal decomposition method using a versatile dictionary of asymmetric waveforms. This approach enhances the analysis of biomedical signals like Otoacoustic Emissions and Evoked Potentials by improving sparsity and accuracy.
Area of Science:
- Biomedical Signal Processing
- Mathematical Modeling
- Time-Frequency Analysis
Background:
- Matching Pursuit decomposes signals using predefined functions (atoms) from a dictionary.
- Gabor functions (symmetric) are commonly used but may not optimally represent asymmetric biomedical waveforms.
- Biomedical signals often contain asymmetric components with rapid rise and slow decay.
Purpose of the Study:
- To develop an enhanced dictionary for Matching Pursuit incorporating asymmetric waveforms.
- To improve the decomposition accuracy of biomedical signals with asymmetric components.
- To introduce a more suitable time-frequency-amplitude distribution for asymmetric atom representation.
Main Methods:
- Introduced a dictionary of functions with varying degrees of asymmetry.
- Applied the enriched dictionary to analyze Otoacoustic Emissions and Steady-State Visually Evoked Potentials.
- Developed a time-frequency-amplitude distribution tailored for asymmetric atoms.
Main Results:
- The proposed method achieved a more sparse signal representation.
- Accurate determination of component latencies was enabled.
- The 'energy leakage' effect caused by ill-fitting symmetric waveforms was mitigated.
- The new time-frequency-amplitude distribution proved more adequate for asymmetric components.
Conclusions:
- The enriched dictionary significantly improves the decomposition of biomedical signals containing asymmetric waveforms.
- This method offers a more accurate and robust analysis of physiological and medical signals.
- The developed time-frequency-amplitude distribution enhances the interpretability of signal components.
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