2-dimensional translation invariant RI-spline wavelet and its application

We propose a 2-dimensional translation invariant real-imaginary spline wavelet (RI-spline wavelet) and develop a 2-dimensional complex discrete wavelet transform (2D CDWT). The main results obtained can be summarized as follows: (1) the problem of 2D translation variance which is caused by the DWT using a real mother wavelet can be solved by using the 2D RI-spline wavelet; (2) the 2D RI-spline wavelet is applied to image processing, and encouraging results are obtained.