Approximating Methods of Orthogonal Wavelet Filter Banks Based on Lattice Structure

In this paper, we present a kind of wavelet filter approximating method based on lattice structure. By virtues of the properties of the lattice structure, two processes, step-by-step lattice optimization and random lattice optimization, are adopted to construct wavelet filters. During the step-by-step lattice optimization, we give two selections: throw-out principle and remained principle, and the two selections are proved to be equivalent to each other. Thus the throw-out principle can ensure that our optimization algorithm is optimal in each step. And we also extend the kind of method to construct wavelet filter banks with different length. In this paper, the algorithm is successfully applied in the following problem: constructing two channel orthogonal wavelet filter banks close to linear phase and constructing signal-adapted wavelet filter banks with finite impulse responses (Principal Component Filter Banks). Parts of results in the step-by-step optimization have been accepted by IEEE ICIP2003.