Noise Reduction Using an Undecimated Discrete Wavelet Transform

Conference PaperA 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, both the <i>l₂</i> error and visually, for a large class of signals. This is shown both theoretically as well as by experimental results