Time-Frequency Jigsaw Puzzle: Adaptive Multiwindow and Multilayered Gabor Expansions

We describe a new adaptive multiwindow Gabor expansion, which dynamically adapts the windows to the signal's features in time-frequency space. The adaptation is based on local time-frequency sparsity criteria, and also yields as by-product an expansion of the signal into layers corresponding to different windows. As an illustration, we show that simply using two different windows with different sizes leads to decompositions of audio signals into transient and tonal layers. We also discuss potential applications to transient detection and denoising.