Improving energy compaction of a wavelet transform using genetic algorithm and fast neural network

Abstract

In this paper a new method for adaptive synthesis of a smooth orthogonal wavelet, using fast neural network and genetic algorithm, is introduced. Orthogonal lattice structure is presented. A new method of supervised training of fast neural network is introduced to synthesize a wavelet with desired energy distribution between output signals from low-pass and high-pass filters on subsequent levels of a Discrete Wavelet Transform. Genetic algorithm is proposed as a global optimization method for defined objective function, while neural network is used as a local optimization method to further improve the result. Proposed approach is tested by synthesizing wavelets with expected energy distribution between low- and high-pass filters. Energy compaction of proposed method and Daubechies wavelets is compared. Tests are performed using image signals.