Image denoising using translation-invariant contourlet transform

The contourlet transform, one of the recent geometrical image transforms, lacks the feature of translation invariance due to subsampling in its filter bank (FB) structure. In this paper, we develop a translation-invariant (TI) scheme of a general multi-channel multidimensional FB and apply our findings to the contourlet transform to obtain a TI contourlet transform (TICT). Further, we employ the proposed TICT for image denoising, where we show that a significant improvement in the PSNR values as well as visual results is gained. Moreover, we demonstrate that this proposed denoising scheme outperforms the TI wavelet denoising approach for most experiments. We also introduce a less-redundant variety of the TICT, where we merely make the first stage of contourlets, translation invariant. We show that this transform, which we call semi-TICT (STICT), achieves a performance near that of the TICT in image denoising.