Scalar Orthogonal Matched Wavelet Design

This Matlab software bundle implements the matched wavelet design from the paper: Karel, J., Peeters, R. Orthogonal Matched Wavelets with Vanishing Moments: A Sparsity Design Approach. Circuits Syst Signal Process 37, 3487–3514 (2018). https://doi-org.mu.idm.oclc.org/10.1007/s00034-017-0716-1 It allows for designing orthogonal wavelets such that they maximize sparsity for a prototype signal. This can be by either L1 minimization (criterion V1) or L4 maximization (criterion V4). Furthermore, this is both for critically sampled representation, as well when using the stationary wavelet transform to ensure shift invariance. Additionally, it allows for masking in the time domain as well as specifying weights to scale so effectively masking in the time-frequency domain is possible as well as compensating for the overrepresentation of course scales when employing the stationary wavelet transform. Always there is the 0th order vanishing moment, which is enforced in the parameterization, and the 1st order vanishing moment can be enforced as well. Currently the 2nd order vanishing moment is not implemented since it needs to be added as a constraint, whereas this version focusses on a large range of optimization options. Compared to the paper, there is a facility to use the global optimization toolbox for designing wavelets. We have provided files to replicate the result from the paper.