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Mathematical Problems in Engineering
Volume 2015, Article ID 851313, 13 pages
Research Article

Normal Inverse Gaussian Model-Based Image Denoising in the NSCT Domain

1School of Mathematics, Northwest University, Xi’an 710127, China
2School of Information Science and Technology, Northwest University, Xi’an 710127, China
3Luoyang Normal University, Luoyang 471022, China

Received 15 October 2015; Revised 8 December 2015; Accepted 9 December 2015

Academic Editor: Daniel Zaldivar

Copyright © 2015 Jian Jia et al. 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.


The objective of image denoising is to retain useful details while removing as much noise as possible to recover an original image from its noisy version. This paper proposes a novel normal inverse Gaussian (NIG) model-based method that uses a Bayesian estimator to carry out image denoising in the nonsubsampled contourlet transform (NSCT) domain. In the proposed method, the NIG model is first used to describe the distributions of the image transform coefficients of each subband in the NSCT domain. Then, the corresponding threshold function is derived from the model using Bayesian maximum a posteriori probability estimation theory. Finally, optimal linear interpolation thresholding algorithm (OLI-Shrink) is employed to guarantee a gentler thresholding effect. The results of comparative experiments conducted indicate that the denoising performance of our proposed method in terms of peak signal-to-noise ratio is superior to that of several state-of-the-art methods, including BLS-GSM, K-SVD, BivShrink, and BM3D. Further, the proposed method achieves structural similarity (SSIM) index values that are comparable to those of the block-matching 3D transformation (BM3D) method.