Copyright © 2012 Pengcheng Han and Junping Du. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Spatial images are inevitably mixed with different levels of noise and distortion. The contourlet transform can provide multidimensional sparse representations of images in a discrete domain. Because of its filter structure, the contourlet transform is not translation-invariant. In this paper, we use a nonsubsampled pyramid structure and a nonsubsampled directional filter to achieve multidimensional and translation-invariant image decomposition for spatial images. A nonsubsampled contourlet transform is used as the basis for an improved Bayesian nonlocal means (NLM) filter for different frequencies. The Bayesian model adds a sigma range in image a priori operations, which can be more effective in protecting image details. The NLM filter retains the image edge content and assigns greater weight to similarities for edge pixels. Experimental results both on standard images and spatial images confirm that the proposed algorithm yields significantly better performance than nonsubsampled wavelet transform, contourlet, and curvelet approaches.