TRANSLATION INVARIANT RI-SPLINE WAVELET AND ITS APPLICATION ON DE-NOISING

Wavelet Shrinkage using DWT has been widely used in de-noising although DWT has a translation variance problem. In this study, we solve this problem by using the translation invariant DWT. For this purpose, we propose a new complex wavelet, the Real-Imaginary Spline Wavelet (RI-Spline wavelet). We also propose the Coherent Dual-Tree algorithm for the RI-Spline wavelet and extend it to the 2-Dimensional. Then we apply this translation invariant RI-Spline wavelet for translation invariant de-noising. Experimental results show that our method, when applied to ECG data, the medical image and the textile surface inspection can obtain better de-noising results than that of conventional Wavelet Shrinkage.