The presented paper introduces a new class of wavelets that includes the simplest Haar wavelet (Daubechies-2) as well as the Daubechies-4 wavelet. This class is shown to have several properties similar to the Daubechies wavelets. In application, the new class of wavelets has been shown to effectively denoise ECG signals. In addition, the paper introduces a new polynomial soft threshold technique for denoising through wavelet shrinkage. The polynomial soft threshold technique is able to represent a wide class of polynomial behaviors, including classical soft thresholding.
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.