Noise reduction using an undecimated discrete wavelet transform

A new nonlinear noise reduction method is presented that uses the discrete wavelet transform, Similar to Donoho and Johnstone, we employ thresholding in the wavelet transform domain but, following a suggestion by Coifman, we 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(2) sense, and is shown theoretically as well as by experimental results.