The Undecimated Dual Tree Complex Wavelet Transform and its application to bivariate image denoising using a Cauchy model

The Undecimated Dual Tree Complex Wavelet Transform (UDTCWT) is introduced together with its application to image denoising. The UDT-CWT extends the traditional DT-CWT using the methods of filter upsampling and the removal of downsampling developed for the Undecimated Discrete Wavelet Transform (UDWT). The UDTCWT results in a one-to-one relationship between co-located complex coefficients in all subbands and offers improved lower scale subband localisation together with improved directional selectivity (compared to the UDWT). These properties of the UDT-CWT have been exploited in the presented bivariate shrinkage denoising algorithm and gives quantitative improvements in the application to the denoising of images.