Design of optimal shift-invariant orthonormal wavelet filter banks via genetic algorithm

摘要

Although the orthonormal discrete wavelet transform offers the advantage of computation efficiency, it is generally not shift-invariant thereby yielding different transform coefficient values when applied to the same signal with different time shifts. Proposed in this paper is a new design method based on the genetic algorithm for the construction of orthonormal wavelet filter banks with an optimal shift-invariant property. In particular, the paper presents transformation of the multi-objective filter bank design problem to a single-objective constrained optimisation problem, chromosome representation of filter coefficients, the shift-invariant objective function for chromosome fitness evaluation, as well as a special constraint to discard infeasible solutions thereby confining the search for the optimum, based on the natural evolution mechanisms, within the wavelet sub-space. Furthermore, using denoising as an example, the performance of the wavelet filter bank constructed is compared with the classical wavelet filter banks to demonstrate its optimality.