Design of M-band optimal orthonormal wavelet of compact support for signal de-noising by using the principle of complexity regularization

A two stage algorithm is presented in this paper to design optimal M-band orthonormal wavelets of compact support for signal de-noising. A cost function d(.,.), suitable for the signal de-noising, is minimized to select the optimal basis. A parameterized representation of wavelet bases is used to constrain the values and reduce the number of independent parameters with the freedom of choice of basis. The complexity regularization criterion is used to broaden the search range for the optimal wavelet basis. Simulation results are presented to illustrate the efficacy of the proposed scheme.