Study on 2-dimensional complex multiresolution analysis and its application for image denoising

We have already proposed complex multiresolution analysis (CMRA), which can provide shift invariance. In this study, we propose 2-dimensional complex multiresolution analysis (2-D CMRA), which can provide 2-dimensional shift invariance, and applied it to image denoising. The main results obtained can be summarized as follows: 1) the lack of 2-dimensional shift invariance in the discrete wavelet transform when using a real mother wavelet has been improved by using the 2-D CMRA. 2) The discrete wavelet transform corresponding to the 2-D CMRA has been applied to image denoising, and very encouraging results were obtained.