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

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.