Iterative method for creating wavelet dictionaries

A method is proposed for creating dictionaries of near-perfect reconstruction wavelets. Choosing a wavelet from a wavelet dictionary is an attractive alternative to customizing a wavelet for a specific task. The method is based on a modified simulated annealing scheme that implements unconstrained minimization. The amount of vanishing moments for the decomposition wavelets was fixed before the iteration. The iteration strived to produce wavelets with good time localization. We used the method to create two wavelet dictionaries. The first set was comprised of 269 wavelets, each having two vanishing moments. The second set of 33 wavelets had three vanishing moments.