Signal-Adapted Analytic Wavelet Packets in Arbitrary Dimensions
Bächle, M., Schambach, M., and Heizmann, M.
2020 28th European Signal Processing Conference (EUSIPCO), 2021
The analytic wavelet packet transform, based on the dual-tree approach, represents a complex-valued extension of the wavelet packet transform. A generalization to multiple dimensions can be realized using fully separable wavelet trees, but this restricts the possible subband combinations. To overcome these limitations, we present a flexible framework to calculate N-D analytic wavelet packets with configurable decomposition structures and filter types. By introducing a new subband notation for the nodes of the N-D wavelet binary tree, both anisotropic and isotropic decomposition structures can be realized. Based on this subband notation, a full frame in N dimensions is defined and combined with an optimal basis selection, which we generalized to arbitrary dimensions, to find signal-adapted decomposition structures. As a multi-dimensional example, the framework is applied to the compression and denoising of a 4D light field. The results are evaluated in terms of the PSNR and SSIM and compared with the discrete cosine transform.