Iterative Constrained Minimization for Vectorial TV Image Deblurring

Chen, K.; Piccolomini, Elena Loli; Zama, Fabiana

doi:10.1007/s10851-015-0599-3

Cited by 2 publications

(2 citation statements)

References 30 publications

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“…The problem of image restoration is finding the restored image u = u ( x ) given the damaged image f = f ( x ), x ∈ ℜ d , where ℜ is a bounded domain with a Lipschitz boundary. For a grayscale image, the image repair model is f = Au + η , where η is the noise information and A is a blurring operator [ 5 – 7 ]. The image restoration problem can then be formulated as the minimization of the following energy functional, …”

Section: Introductionmentioning

confidence: 99%

New dual method for elastica regularization

Song

Pan²,

Ding³

et al. 2022

PLoS ONE

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The Euler’s elastica energy regularizer has been widely used in image processing and computer vision tasks. However, finding a fast and simple solver for the term remains challenging. In this paper, we propose a new dual method to simplify the solution. Classical fast solutions transform the complex optimization problem into simpler subproblems, but introduce many parameters and split operators in the process. Hence, we propose a new dual algorithm to maintain the constraint exactly, while using only one dual parameter to transform the problem into its alternate optimization form. The proposed dual method can be easily applied to level-set-based segmentation models that contain the Euler’s elastic term. Lastly, we demonstrate the performance of the proposed method on both synthetic and real images in tasks image processing tasks, i.e. denoising, inpainting, and segmentation, as well as compare to the Augmented Lagrangian method (ALM) on the aforementioned tasks.

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Section: Introductionmentioning

confidence: 99%

New dual method for elastica regularization

Song

Pan²,

Ding³

et al. 2022

PLoS ONE

View full text Add to dashboard Cite

show abstract

“…An additive image restoration model assumes z=scriptAu+η0 with η 0 representing some unknown Gaussian noise of mean zero and deviation σ , and scriptA a blurring operator. 1–6 The additive image restoration model minimises the fidelity to z and leads to the least-square problem according to the maximum likelihood principle. 7 Here scriptA=I for image denoising.…”

Section: Introductionmentioning

confidence: 99%

A new augmented Lagrangian primal dual algorithm for elastica regularization

Zhang

Chen

2016

Journal of Algorithms & Computational Technology

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Regularization is a key element of variational models in image processing. To overcome the weakness of models based on total variation, various high order (typically second order) regularization models have been proposed and studied recently. Among these, Euler's elastica energy based regularizer is perhaps the most interesting in terms of both mathematical and physical justifications. More importantly its success has been proven in applications; however it has been a major challenge to develop fast and effective algorithms. In this paper we propose a new idea for deriving a primal dual algorithm, based on Legendre–Fenchel transformations, for representing the elastica regularizer. Combined with an augmented Lagrangian for-mulation, we are able to derive an equivalent unconstrained optimization that has fewer variables to work with than previous works based on splitting methods. We shall present our algorithms for both the image restoration problem and the image segmentation model. The idea applies to other models where the elastica regularizer is required. Numerical experiments show that the proposed method can produce highly competitive results with better efficiency.

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Iterative Constrained Minimization for Vectorial TV Image Deblurring

Cited by 2 publications

References 30 publications

New dual method for elastica regularization

New dual method for elastica regularization

A new augmented Lagrangian primal dual algorithm for elastica regularization

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