Best basis selection using sparsity driven multi-family wavelet transform
Romain Cosentino, Randall Balestriero, Behnaam Aazhang · 2016
A common tool for time-frequency analysis is based on wavelets. However, these representations are computed with only one wavelet family and thus might not be able to match exactly with different features of various frequency bands. We thus introduce the Multi-family Discrete Wavelet Transform, a computationally tractable adaptive wavelet transform leading to sparse optimized representations which will select the optimal wavelet family at each frequency band. The approach is an optimized Discrete Wavelet Transform where at each level of the decomposition the best wavelet basis is selected as well as the optimum depth by means of information theory tools. This development is motivated by the need to have an unsupervised sparse representation of a priori unknown signals. Our representation is finally applied on intracranial EEG (iEEG) data in order to show its efficacy.