Image reconstruction and restoration: overview of common estimation structures and problems

Demoment, G.

doi:10.1109/29.45551

Cited by 580 publications

(365 citation statements)

References 99 publications

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“…Prior information on the underlying image can then help the restoration off . A flexible means of combining the forward model with priors is regularization, which is formally equivalent to maximum a posteriori (MAP) estimation [7,18,22]. The solutionf is defined as the (global) minimizer of a cost function J(f ) of the form…”

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confidence: 99%

Efficient Reconstruction of Piecewise Constant Images Using Nonsmooth Nonconvex Minimization

Nikolova¹,

Ng²,

Zhang³

et al. 2008

SIAM J. Imaging Sci.

180

171

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Abstract. We consider the restoration of piecewise constant images where the number of the regions and their values are not fixed in advance, with a good difference of piecewise constant values between neighboring regions, from noisy data obtained at the output of a linear operator (e.g., a blurring kernel or a Radon transform). Thus we also address the generic problem of unsupervised segmentation in the context of linear inverse problems. The segmentation and the restoration tasks are solved jointly by minimizing an objective function (an energy) composed of a quadratic data-fidelity term and a nonsmooth nonconvex regularization term. The pertinence of such an energy is ensured by the analytical properties of its minimizers. However, its practical interest used to be limited by the difficulty of the computational stage which requires a nonsmooth nonconvex minimization. Indeed, the existing methods are unsatisfactory since they (implicitly or explicitly) involve a smooth approximation of the regularization term and often get stuck in shallow local minima. The goal of this paper is to design a method that efficiently handles the nonsmooth nonconvex minimization. More precisely, we propose a continuation method where one tracks the minimizers along a sequence of approximate nonsmooth energies {Jε}, the first of which being strictly convex and the last one the original energy to minimize. Knowing the importance of the nonsmoothness of the regularization term for the segmentation task, each Jε is nonsmooth and is expressed as the sum of an 1 regularization term and a smooth nonconvex function. Furthermore, the local minimization of each Jε is reformulated as the minimization of a smooth function subject to a set of linear constraints. The latter problem is solved by the modified primal-dual interior point method, which guarantees the descent direction at each step. Experimental results are presented and show the effectiveness and the efficiency of the proposed method. Comparison with simulated annealing methods further shows the advantage of our method.

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mentioning

confidence: 99%

Efficient Reconstruction of Piecewise Constant Images Using Nonsmooth Nonconvex Minimization

Nikolova¹,

Ng²,

Zhang³

et al. 2008

SIAM J. Imaging Sci.

180

171

View full text Add to dashboard Cite

show abstract

“…A natural way to deal with this kind of problem is to use probabilities (see, for instance Bouman and Sauer (1993), Chellappa and Jain (1993), Demoment (1989), Geman and Geman (1984)) i.e., the approach that we have also adopted in our work. Our approach is not only based on the probability of occurrence of the colors in the map but also the spatial neighborhood of the pixel whose color is to be replaced…”

Section: Methodsmentioning

confidence: 99%

Automatic Text Removal and Replacement in Scanned Meteorological Thematic Maps

Abdullah¹,

Alshamat²,

Bakhashwain³

et al. 2015

Journal of Computer Science

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Geo-referenced data is required in many Geographic Information System (GIS) applications and one source of such data being maps. Meteorological maps are color-coded with different regions corresponding to different values of a parameter, parsing the image to convert into data is not very difficult. However, text and different planimetric elements overlaid on the regions in the map makes accurate image to data conversion a challenging problem, because it is almost impossible to exactly replace what was underneath the text or icons i.e., the need for inpainting. In this study, we propose a probabilistic technique that uses the probability of occurrence of colors present in the map along with the occurrence of those colors in the spatial neighborhood of the pixel (corresponding to text) whose color is required to be replaced. We test the limits of our proposed technique using simulated data and compare results with a popular image editing tool using public domain data with promising results.

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“…Two frameworks have been developed to describe the use of prior information as an aid in image recovery: the deterministic formulation with regularization [8] and the statistical formulation [4]. Conceptually, these frameworks are quite different, but in many applications they lead to identical algorithms.…”

Section: Introductionmentioning

confidence: 99%