Title: Image restoration using anisotropic multivariate shrinkage function in contourlet domain

Authors: Huimin Lu; Yujie Li; Shiyuan Yang; Seiichi Serikawa

Addresses: Department of Electrical Engineering and Electronics, Kyushu Institute of Technology, Kitakyushu, 804-8550, Japan; Japan Society for the Promotion of Science, Tokyo, 102-0083, Japan ' Department of Electrical Engineering and Electronics, Kyushu Institute of Technology, Kitakyushu, 804-8550, Japan ' Department of Electrical Engineering and Electronics, Kyushu Institute of Technology, Kitakyushu, 804-8550, Japan ' Department of Electrical Engineering and Electronics, Kyushu Institute of Technology, Kitakyushu, 804-8550, Japan

Abstract: We describe a method for removing non-Gaussian image noise in natural images, underwater images and biomedical images, based on a statistical model of the decomposed contourlet coefficients. This method utilises the non-Gaussian multivariate shrinkage (NGMS) probability density function (PDF) to model neighbourhood contourlet coefficients. Then, according to the proposed PDF model, we design a maximum a posteriori (MAP) estimator, which relies on a Bayesian statistics representation for the contourlet coefficients of noisy images. There are three obvious virtues of this method. Firstly, contourlet transform decomposition prior to curvelet transform and wavelet transform by using ellipse sampling grid. Secondly, NGMS model is more effective in presentation of the noisy image contourlet coefficients. Thirdly, the NGMS model takes full account of the correlation between coefficients. Some comparisons with the best available results will be presented in order to illustrate the effectiveness of the proposed method.

Keywords: contourlet transform; image denoising; statistical modelling; signal processing; image restoration; non-Gaussian multivariate shrinkage; probability density function; natural images; underwater images; biomedical images; wavelet transform; ellipse sampling grid.

DOI: 10.1504/IJCSE.2016.076210

International Journal of Computational Science and Engineering, 2016 Vol.12 No.2/3, pp.95 - 103

Received: 03 Jan 2013
Accepted: 11 Mar 2013
Published online: 30 Apr 2016 *

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