On the design of matched orthonormal wavelets with compact support

We develop new algorithms for designing matched wavelets and matched scaling functions using a new parametrization of compactly supported orthonormal wavelets that is developed in [4]. The parametrization specifies the wavelet filter coefficients as a continuous function of an arbitrary vector of half its length. Therefore, the wavelets and the scaling functions are also continuous functions of this vector through the use of the cascade algorithm. Hence, standard minimization procedures can be employed for wavelet design. In the case of matched scaling function we propose a new optimization algorithm that significantly reduces the problem complexity. We provide several design examples that illustrate the effectiveness of the proposed algorithm.