Wavelet denoising with evolutionary algorithms

In recent years several wavelet thresholding schemes for denoising have been proposed. However, thresholding rules depend heavily on the choice of the parameters. Wavelet thresholding rules are typically nonlinear, leading to nonconvex target functions. In this paper, we present an evolutionary computation approach for parameter elicitation in penalized wavelet models. We begin with parameter models for global hard- and soft-thresholding. Then, we extend the methodology for parameter elicitation in two directions: block thresholding and best-basis denoising. The proposed evolutionary approach enables the joint optimization of wavelet basis selection and thresholding parameters for signal denoising. Numerical simulations are used to illustrate the proposed methodology and compare the behavior of the various denoising procedures.