Adaptive Gabor frames by projection onto time-frequency subspaces

The application of adaptive, time-frequency based signal analysis has recently attracted increasing attention. While using adapted time-frequency atoms has shown promising results for example in audio processing, the reconstruction from the corresponding analysis coefficients usually exhibits significant error. In this contribution we propose a method to reduce the reconstruction error by using modified time-frequency atoms in the transition region between adjacent areas of time-frequency adaptation. The modification is obtained by projecting the relevant atoms onto a system of weighted vectors which are optimally concentrated inside the desired regions of adaptation. We give a theoretical derivation of the improvement of error and illustrate our method with numerical examples.