We present a new optimization based method for designing orthonormal filter banks in wavelet denoising. We formulate the design problem as a nonlinear optimization problem whose objective is to minimize the mean squared error (MSE) between the original and the denoised signal. In contrast to previous methods that design filter banks separately from the other operations in noise suppression, our formulation allows us to search for the filters in the context of a denoising algorithm to minimize the MSE. Due to the nonlinear nature of the performance metric, the optimization problem is solved by using the simulated annealing global-search method. We apply the optimization method to find good filter banks for different training signals corrupted by impulsive noise and select the one that performs best across all training signals to be the final solution. In experimental results, we show that the filter bank designed by our method reduces the MSE of the best existing filter bank on sixteen benchmark signals contaminated by either impulsive or Gaussian noise.
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