Signal-Adapted Analytic Wavelet Packets in Arbitrary Dimensions
Matthias Bächle, Maximilian Schambach, Fernando Puente León · 2020
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.