Ponencia presentada en el XIX Congreso Internacional de Acústica (ICA2007), Madrid, 2-7 Sep 2007.-- PACS: 43.60.Hj.Wavelet processing has become a popular and well-established technique that offers good results and great flexibility for noise reduction. The basic wavelet de-noising scheme consists of a thresholding of the Discrete Wavelet Transform (DWT) coefficients. Nevertheless, some improvements over this basic non-linear scheme can be obtained by the use of Undecimated Wavelet Transforms (UWT), also known as redundant, shift-invariant or stationary wavelet transforms, because they provide redundant and translation invariant representations. The introduction of redundancy produces less efficient signal representations but it can be useful in de-noising. Ultrasonic traces are frequently contaminated with structural or grain noise, which can not be removed by classical time averaging or band-pass filtering. An analysis of wavelet de-noising of some individual traces is presented. In addition, a significant number of synthetic ultrasonic signals are also processed for a statistical study and comparison of UWT and DWT de-noising in terms of the signal-to-noise ratio of the resulting traces.This work has been supported by the Spanish MEC, R&D Project CICYT Ref. DPI2005-00124 of the I+D National Plan and grant FPI BES-2004-5296.Peer reviewed