Gradient-based optimization of mother wavelets
We present a general framework for the design of a mother wavelet best adapted to a specific signal or to a class of signals. The filter’s coefficients are obtained via optimization of a smooth objective function. We develop an unconstrained gradient-based optimization algorithm for a discrete wavelet transform. The algorithm is extended to the joint optimization of the mother wavelet and of the wavelet packets basis. Keywords— Wavelets, Wavelet Pakets, Filter Banks, Polyphase Matrix, Lattice Decomposition, Optimization.