Signal processing using translation invariant RI-spline wavelet

De-noising using wavelet shrinkage has a translation variance problem, which we solve 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 without increasing the computational cost very much. Then we apply this translation invariant RI-spline wavelet for translation invariant denoising. Experimental results show that our method, when applied to ECG data and a music signal, can obtain better de-noising results than wavelet shrinkage.