Effective Image Restorations Using a Novel Spatial Adaptive Prior
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Research Article Effective Image Restorations Using a Novel Spatial Adaptive Prior Yang Chen,1, 2 Yinsheng Li,1, 2 Yingmei Dong,3 Liwei Hao,2 Limin Luo,1 and Wufan Chen2 1 The
Laboratory of Image Science and Technology, Southeast University, Nanjing 210096, China School of Biomedical Engineering, Southern Medical University, Guangzhou 510515, China 3 Cadre Reset Institute, The Joint Logistics Department, Chengdu Military Region, Chengdu 610083, China 2 The
Correspondence should be addressed to Wufan Chen, [email protected] Received 20 October 2009; Revised 29 December 2009; Accepted 16 February 2010 Academic Editor: Liang-Gee Chen Copyright © 2010 Yang Chen 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. Bayesian or Maximum a posteriori (MAP) approaches can effectively overcome the ill-posed problems of image restoration or deconvolution through incorporating a priori image information. Many restoration methods, such as nonquadratic prior Bayesian restoration and total variation regularization, have been proposed with edge-preserving and noise-removing properties. However, these methods are often inefficient in restoring continuous variation region and suppressing block artifacts. To handle this, this paper proposes a Bayesian restoration approach with a novel spatial adaptive (SA) prior. Through selectively and adaptively incorporating the nonlocal image information into the SA prior model, the proposed method effectively suppress the negative disturbance from irrelevant neighbor pixels, and utilizes the positive regularization from the relevant ones. A twostep restoration algorithm for the proposed approach is also given. Comparative experimentation and analysis demonstrate that, bearing high-quality edge-preserving and noise-removing properties, the proposed restoration also has good deblocking property.
1. Introduction 1.1. Problem Formulation. As one of the most classical linear inverse problems, image restoration has its wide applications in remote sensing, radar imaging, tomographic imaging, microscopic imaging, astronomic imaging, digital photography, and so forth [1–4]. For linear and shiftinvariant imaging systems, the transformation from f to g is well described by following additive linear degradation model [3, 4]: g = A ∗ f + ε,
(1)
where g, f , and ε represent, respectively, the degraded observed image, the original true image, and the corrupting white Gaussian noise with variance σ 2 . Point-spread function (PSF) A is the imaging system and ∗ is the linear convolution operator. Throughout this paper we assume that the degradation model PSF A and noise variance σ 2 are known for they could be numerically estimated or calibrated. Based on the Gaussian statistics of the additive noise, maximum log-likelihood (ML) restoration method could be
applied to find the least-squares estimation of f . However, such ML restoration method o
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