Image processing using 2-D translation invariant RI-spline wavelet

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