Translation-invariant contourlet transform and its application to image denoising

Most subsampled filter banks lack the feature of translation invariance, which is an important characteristic in denoising applications; In this paper, we study and develop new methods to convert a general multichannel, multidimensional filter bank to a corresponding translation-invariant (TI) framework. In particular, we propose a generalized algorithme a trous, which is an extension of the algorithme a trous introduced for 1-D wavelet transforms. Using the proposed algorithm, as well as incorporating modified versions of directional filter banks, we construct the TI contourlet transform (TICT). To reduce the high redundancy and complexity of the TICT, we also introduce semi-translation-invariant contourlet transform (STICT). Then, we employ an adapted bivariate shrinkage scheme to the STICT to achieve an efficient image denoising approach. Our experimental results demonstrate the benefits and potential of the proposed denoising approach. Complexity analysis and efficient realization of the proposed TI schemes are also presented.