Translation-invariant de-noising. (English) Zbl 0866.94008

Coifman, R. R.; Donoho, D. L.

Antoniadis, Anestis (ed.) et al., Wavelets and statistics. Proceedings of the 15th French-Belgian meeting of statisticians, held at Villard de Lans, France, November 16-18, 1994. New York, NY: Springer-Verlag. Lect. Notes Stat., Springer-Verlag. 103, 125-150 (1995).

Multiscale techniques for denoising signals and images have found widespread interest over the last few years. In particular, nonlinear thresholding in connection with suitable wavelet transforms have proved to be successful. The present paper is based on these methods, it discusses the effects of translation-invariant denoising, which can be achieved, e.g., by an averaging technique. This article is not a strict mathematical paper, it only sketches the underlying theory. However, many carefully chosen examples illustrate the properties of the described denoising techniques. The paper is written in a very readable style.
For the entire collection see [Zbl 0824.00042].

Reviewer: P.Maaß (Potsdam)

MSC:

94A12

Signal theory (characterization, reconstruction, filtering, etc.)

Keywords:

signal processing; denoising signals; wavelet transforms; translation-invariant denoising; averaging