Translation-Invariant De-Noising

De-Noising with the traditional (orthogonal, maximally-decimated) wavelet transform sometimes exhibits visual artifacts; we attribute some of these -- for example, Gibbs phenomena in the neighborhood of discontinuities -- to the lack of translation invariance of the wavelet basis. One method to suppress such artifacts, termed "cycle spinning" by Coifman, is to "average out" the translation dependence. For a range of shifts, one shifts the data (right or left as the case may be), De-Noises the...