Nonlinear noise suppression using a parametric class of wavelet shrinkage functions

Donoho developed nonlinear techniques known as wavelet shrinkage. They have since been successfully applied for noise suppression. This paper introduces a new parametric shrinkage technique and compares its performance to the soft threshold introduced by Donoho and the differentiable shrinkage function introduced by Zhang. Termed the polynomial hard threshold this new shrinkage technique is better able to represent polynomial behavior than the previous techniques. It is also able to represent a wider class of shrinkage functions making it ideal for use in adaptive noise suppression. This class of shrinkage functions includes both Donoho’s soft and the classical hard threshold. By using a priori knowledge to adjust its parameters this threshold can be tailored to perform well for a particular signal type.