Lattice structures for synthesis and implementation of wavelet transforms

Abstract

In this paper the novel lattice structure composed of homogeneous invertible two-point operations which are connected in regular and simple structure is proposed. Further on the pipeline scheme for implementation of such a structure is presented. It is proved with the orthogonal variant of the presented scheme that with respect to the computational complexity it is equivalent to the lifting technique. It means that the proposed scheme belongs to the class of the most effective algorithms for calculation of orthogonal wavelet transforms. The variant of the lattice structure with simplified two-point operations is also proposed. Finally the fundamentals of the synthesis of lattice structure coefficients with the aid of artificial neural networks and some aspects of lattice structures implementation on basic computational architectures are discussed.