An Adaptive Non-local Total Variation Blind Deconvolution Employing Split Bregman Iteration
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An Adaptive Non-local Total Variation Blind Deconvolution Employing Split Bregman Iteration Zhiyong Zuo · Tianxu Zhang · Xia Lan · Luxin Yan
Received: 25 October 2012 / Revised: 13 March 2013 © Springer Science+Business Media New York 2013
Abstract Total variation (TV) has been used as a popular and effective image prior model in regularization-based image restoration, because of its ability to preserve edges. However, as the total variation model favors a piecewise constant solution, the processing results in the flat regions of the image are poor, and the amplitude of the edges will be underestimated; the underlying cause of the problem is that the model is based on derivation which only considers the local feature of the image. In this paper, we first propose an adaptive non-local total variation image blind restoration algorithm for deblurring a single image via a non-local total variation operator, which exploits the correlation in the image, and then an extended split Bregman iteration is proposed to address the joint minimization problem. Second, the maximum average absolute difference (MAAD) method is employed to estimate the blur support and initialize the blur kernel. Extensive experiments demonstrate that the proposed approach produces results superior to most methods in both visual image quality and quantitative measures. Keywords Blind deconvolution · Deblurring · Image restoration · Inverse problem · Point spread function · Split Bregman Z. Zuo () · T. Zhang · L. Yan Institute for Pattern Recognition and Artificial Intelligence, Huazhong University of Science and Technology, Wuhan 430074, China e-mail: [email protected] T. Zhang e-mail: [email protected] L. Yan e-mail: [email protected] X. Lan School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China e-mail: [email protected]
Circuits Syst Signal Process
1 Introduction Images are ubiquitous in modern communication. However, in many applications, such as microscopy imaging, remote sensing, and astronomical imaging, observed images are often degraded by blurring [31]. Image restoration can be used to settle this problem, which is one of the most fundamental, widely studied, and largely unsolved problems in image processing and computer vision. In general, the assumed image degradation model can be formulated as follows [12]: g=h∗f +n
(1)
where g, h, f and n are the acquired image, the point spread function (or blur kernel), the original image, and the zero-mean Gaussian white noise with standard variance σ , respectively. The operator (∗) in (1) denotes 2-D convolution, given by h(s)f (x − s) (2) (h ∗ f )(x) = s∈S
where S ⊂ R 2 is the support of the point spread function (PSF). If the PSF is exactly known as a prior, recovering the original image is called a non-blind deconvolution problem; otherwise it is called a blind deconvolution problem. It is known that the non-blind deconvolution problem is an ill-posed problem for its sensitivity to noise. Blind deconvolution is even more ill-posed. Because both the PSF a
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