Estimating signal-adapted wavelets using sparseness criteria

Multiresolution transforms have been shown to be effective for a variety of digital signal processing tasks. Recently, the task of adapting these usually fixed transforms to the statistics of the data has attracted much attention. So far, however, the methods proposed have been based exclusively on the second-order statistics of the signal. We show how to take into account higher order statistics to estimate a multiresolution transform from white data. The method is tested on speech data from the TIMIT database and is shown to give filters well adapted to the structure of the data.