Wavelet Signal Denoising (Soft Thresholding)

Wavelet signal denoising, introduced by David Donoho in 1995, is a non-parametric technique that removes noise from one-dimensional or multidimensional signals by decomposing them into wavelet coefficients, suppressing small coefficients that likely represent noise via a soft-thresholding operator, and reconstructing a smooth estimate. It is widely used in biomedical signal processing, geophysics, audio engineering, and image analysis where the underlying signal is assumed to be sparse or piecewise smooth.