Eslami Ramin, Radha Hayder
Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON L8S 4K1, Canada.
IEEE Trans Image Process. 2006 Nov;15(11):3362-74. doi: 10.1109/tip.2006.881992.
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 à trous, which is an extension of the algorithme à 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.
大多数下采样滤波器组缺乏平移不变性这一特性，而平移不变性在去噪应用中是一个重要特征。在本文中，我们研究并开发新方法，将一般的多通道、多维滤波器组转换为相应的平移不变（TI）框架。特别地，我们提出了一种广义的步长为2的算法，它是为一维小波变换引入的步长为2的算法的扩展。使用所提出的算法，并结合方向滤波器组的改进版本，我们构建了TI轮廓波变换（TICT）。为了降低TICT的高冗余度和复杂度，我们还引入了半平移不变轮廓波变换（STICT）。然后，我们将一种适配的双变量收缩方案应用于STICT，以实现一种高效的图像去噪方法。我们的实验结果证明了所提出的去噪方法的优势和潜力。还给出了所提出的TI方案的复杂度分析和高效实现。
