Noise reduction using an undecimated discrete wavelet transform

TLDR

The authors build on Donoho and Johnstone’s thresholding approach by replacing the orthogonal wavelet transform with an undecimated, shift‑invariant, nonorthogonal transform, effectively applying the method across multiple shifts. The study introduces a nonlinear noise‑reduction method based on the discrete wavelet transform. The method applies thresholding in the undecimated, shift‑invariant wavelet domain using a nonorthogonal transform to suppress noise. The algorithm achieves markedly better noise reduction than the original wavelet approach, as demonstrated theoretically and experimentally across a broad class of signals.

Abstract

A new nonlinear noise reduction method is presented that uses the discrete wavelet transform. Similar to Donoho (1995) and Donohoe and Johnstone (1994, 1995), the authors employ thresholding in the wavelet transform domain but, following a suggestion by Coifman, they use an undecimated, shift-invariant, nonorthogonal wavelet transform instead of the usual orthogonal one. This new approach can be interpreted as a repeated application of the original Donoho and Johnstone method for different shifts. The main feature of the new algorithm is a significantly improved noise reduction compared to the original wavelet based approach. This holds for a large class of signals, both visually and in the l/sub 2/ sense, and is shown theoretically as well as by experimental results.