Design of Nearly-Orthogonal Symmetric Wavelet Filter Banks Based on the Wavelet Orthogonalization Process

Abstract

This work proposes a new method for nearly-orthogonal wavelet filter banks design based on the wavelet orthogonalization process. A new procedure to extract semi-conjugate filters from non-orthogonal wavelets is used for such purposes. The proposed methodology allows the design of symmetrical odd length nearly-orthogonal wavelet filters according to the frequency domain specifications. Finite impulse response wavelet filters with linear phase are obtained, not implying significant gain distortions and satisfying perfect reconstruction condition as accurately as possible. A signal decomposition example is presented and the wavelet coefficients results are compared with orthogonal and biorthogonal wavelet filter banks. Considering such an example, the best result was obtained by one of the proposed nearly-orthogonal wavelet filter banks. Some nearly-orthogonal wavelet filter banks designed in this work are applied in the context of image compression, involving the reconstruction process. Image compression results from a nearly-orthogonal wavelet filter designed in this work are superior to those from some classical wavelet filters.