Study the Gibbs phenomenon in the de-noising by wavelet

De-noising based on wavelet may bring artifacts (Gibbs) on the discontinuity points of signals. Because of great translation work of the method- translation invariance that can eliminate Gibbs, the partial translation invariance is presented. Haar wavelet that can eliminate Gibbs if the discontinuity is in the middle of the signals is analyzed firstly, then the method detecting the location of discontinuity points is produced, finally the method of partial translation invariance is descried in detail. Experiment of simulation indicates that partial translation invariance can also eliminate Gibbs while reducing translation work.