Efficient algorithm to find a jointly optimal time-frequency segmentation using time-varying filter banks
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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. The tree structure gives segmentations of the signal in frequency, while the time-varying nature of the tree gives segmentations in time. We present an efficient algorithm which finds the optimal basis, given the constraint that the time and frequency segmentations are binary. Extension to multiple dimensions is simple. 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-distortion cost.