Projection-Based Wavelet Denoising [Lecture Notes]

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A. Enis Çetin, Mohammad Tofighi

Published: 2015, Last Modified: 27 Feb 2026IEEE Signal Process. Mag. 2015EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: In this lecture note, we describe a wavelet domain denoising method consisting of making orthogonal projections of wavelet (subbands) signals of the noisy signal onto an upside down pyramid-shaped region in a multidimensional space. Each horizontal slice of the upside down pyramid is a diamond shaped region and it is called an -ball. The upside down pyramid is called the epigraph set of the -norm cost function. We show that the method leads to soft-thresholding as in standard wavelet denoising methods. Orthogonal projection operations automatically determine the soft-threshold values of the wavelet signals.