Matching Pursuit (MP) is an iterative procedure of finding a sub-optimal
signal's representation in a highly redundant dictionary of functions,
proposed by Mallat and Zhang (1). Used with a time-frequency dictionary
of Gabor functions it provides a high-resolution adaptive parametrization
of signal's structures. From this parametrization time-frequency maps of
signal's energy density (Wigner plots) can be constructed by adding Wigner
distributions of structures selected for signal's representation.
To illustrate the idea of adaptive time-frequency decomposition we construct
a sample simulated signal from a sum of sine A,
Gabor functions (Gauss-modulated sines) C,
D, E and one-point
discontinuity (Dirac's delta) B:. Click here for the plot of this signal and its components.
Now we add to this signal a white noise with variances giving signal to noise ratios 1/2 (-3 dB) and 1/4 (-6 dB). Click here to display resulting signals.
MP results for S/N=1/2 (-3 dB): MP results for S/N=1/4 (-6 dB):From the real-world signals, one trace of sleep EEG
- Wigner plot and chosen waveforms - is available.
There is also an example of superimposed sleep spindles, resolved by MP parametrization
You may also download the simulated signals used for this presentation
in ASCII: no noise, S/N=1/2
and S/N=1/4 , and 10 sec
of sleep EEG sampled 128 Hz for comparison.
Note: simulated signal was constructed from waveforms present in applied
MP dictionary, which greatly simplifies the decomposition.
