The denoise based on translation invariance wavelet transform and its applications

De-noising algorithm based on traditional wavelet transform may produce artifacts on discontinuities of the signal. The reason of phenomena is that the de-noising algorithm lacks of wavelet translation invariant. This paper proposed a de-noising method based on translation invariant. The method performs the cycle-spinning for the signal to be analyzed. And then, the soft (hard) thresholding is used to shrink the wavelet coefficient of the signal and reconstruct the signal. Consequently, the shift dependence of wavelet basis is eliminated. This method can suppress the artifacts effectively so that de-noised signal is more smooth and better approximation to original signal.