Efficient algorithm to find a jointly optimal time-frequency segmentation using time-varying filter banks

Abstract

We examine the question of how to choose a time-varying filter bank representation for a signal which is optimal with respect to an additive cost function. We present in detail an efficient algorithm for the Haar filter set which finds the optimal basis, given the constraint that the time and frequency segmentations are binary. Extension to multiple dimensions is simple, and use of arbitrary filter sets is also possible. We verify that the algorithm indeed produces a lower cost representation than any of the wavelet packet representations for compression of images using a simple Rate-Distotion cost.