Abstract
In this study, we propose a 2-Dimensional Complex Discrete Wavelet Transform (2-D CDWT) that extends the 2-dimensional Complex Multi Resolution Analysis (CMRA) using the RI-Spline wavelet, and try to approximately realize shift invariance in image processing. We then apply the 2-D CDWT to Medical image de-noising and the inspection problem of textile surfaces. The main results obtained can be summarized as follows: 1) 2-dimensional shift variance which occurred using the discrete wavelet transform with a real mother wavelet has been improved by using the 2-D CDWT. 2) In the Medical image de-noising and the inspection problem of textile surfaces, the 2-D CDWT has better performance than the standard 2-D DWT and obtained very encouraging results.
