Denoising 1D signal using wavelets

Abstract

Signal denoising is one of the most important areas in signal processing. In the present paper, we have denoised a 1D piecewise constant (PWC) signal corrupted by additive white Gaussian noise (AWGN) using the thresholded Haar wavelet denoising method. The central idea of the wavelet transform is the multiresolution decomposition of signals. This becomes advantageous because small objects require high resolution and low resolution is suitable for large objects. In multiresolution decomposition, an approximation component is created using a scaling function, which is often termed as a lowpass filter. Detail components are obtained using wavelet functions, which are often known as highpass filters. A series of approximations of a signal is thus obtained, which has difference in resolution among them by a factor 2. Detail components contain the difference between adjacent approximations. Proper thresholding of the transformed signal results in reduced noise because, in general, the noise component of a signal has a relatively smaller magnitude and wider bandwidth. We show that our method outperforms recently reported non-convex regularisation-based convex 1D total variation denoising method on PWC signals. © 2020 Inderscience Enterprises Ltd.