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The problem of restoring images corrupted by Poisson noise is common in many application fields and, because of its intrinsic ill posedness, it requires regularization techniques for its solution. The effectiveness of such techniques…

Numerical Analysis · Mathematics 2021-04-30 Daniela di Serafino , Germana Landi , Marco Viola

A bilevel training scheme is used to introduce a novel class of regularizers, providing a unified approach to standard regularizers $TV$, $TGV^2$ and $NsTGV^2$. Optimal parameters and regularizers are identified, and the existence of a…

Analysis of PDEs · Mathematics 2019-02-05 Elisa Davoli , Irene Fonseca , Pan Liu

In the present paper we propose two new algorithms of tensor completion for three-order tensors. The proposed methods consist in minimizing the average rank of the underlying tensor using its approximate function namely the tensor nuclear…

Numerical Analysis · Mathematics 2021-02-23 A. H. Bentbib , A. El Hachimi , K. Jbilou , A. Ratnani

Total Variation (TV) is a popular regularization strategy that promotes piece-wise constant signals by constraining the $\ell_1$-norm of the first order derivative of the estimated signal. The resulting optimization problem is usually…

Optimization and Control · Mathematics 2020-10-20 Hamza Cherkaoui , Jeremias Sulam , Thomas Moreau

Numerous total variation (TV) regularizers, engaged in image restoration problem, encode the gradients by means of simple $[-1,1]$ FIR filter. Despite its low computational processing, this filter severely deviates signal's high frequency…

Optimization and Control · Mathematics 2015-06-17 Mahdi S. Hosseini , Konstantinos N. Plataniotis

We study the qualitative properties of optimal regularisation parameters in variational models for image restoration. The parameters are solutions of bilevel optimisation problems with the image restoration problem as constraint. A general…

Optimization and Control · Mathematics 2020-02-13 Juan Carlos De Los Reyes , Carola-Bibiane Schönlieb , Tuomo Valkonen

We propose a novel discrete concept for the total generalized variation (TGV), which has originally been derived to reduce the staircasing effect in classical total variation (TV) regularization, in image denoising problems. We describe…

Numerical Analysis · Mathematics 2022-09-27 Lukas Baumgärtner , Ronny Bergmann , Roland Herzog , Stephan Schmidt , José Vidal-Núñez

We show how total variation regularization of images in arbitrary dimensions can be approximately performed by applying appropriate shrinkage to some Haar wavelets coefficients. The approach works directly on the wavelet coefficients and is…

Numerical Analysis · Mathematics 2024-11-04 Tomas Sauer , A. Michael Stock

We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…

Computer Vision and Pattern Recognition · Computer Science 2014-04-15 J. Balzer , S. Soatto

We present a new vectorial total variation method that addresses the problem of color consistent image filtering. Our approach is inspired from the double-opponent cell representation in the human visual cortex. Existing methods of…

Computer Vision and Pattern Recognition · Computer Science 2016-05-20 Freddie Åström , Christoph Schnörr

Total variation (TV) is a powerful regularization method that has been widely applied in different imaging applications, but is difficult to apply to diffuse optical tomography (DOT) image reconstruction (inverse problem) due to complex and…

Computer Vision and Pattern Recognition · Computer Science 2019-04-08 Wenqi Lu , Jinming Duan , David Orive-Miguel , Lionel Herve , Iain B Styles

Many methods for processing scalar and vector valued images, volumes and other data in the context of inverse problems are based on variational formulations. Such formulations require appropriate regularization functionals that model…

Numerical Analysis · Mathematics 2019-09-20 Martin Holler , Andreas Weinmann

In this work we introduce a formulation for a non-local Hessian that combines the ideas of higher-order and non-local regularization for image restoration, extending the idea of non-local gradients to higher-order derivatives. By carefully…

Numerical Analysis · Mathematics 2014-11-03 Jan Lellmann , Konstantinos Papafitsoros , Carola Schoenlieb , Daniel Spector

Purpose: To develop a synergistic image reconstruction framework that exploits multicontrast (MC), multicoil, and compressed sensing (CS) redundancies in magnetic resonance imaging (MRI). Approach: CS, MC acquisition, and parallel imaging…

Image and Video Processing · Electrical Eng. & Systems 2022-02-22 Erfan Ebrahim Esfahani

We introduce a new non-smooth variational model for the restoration of manifold-valued data which includes second order differences in the regularization term. While such models were successfully applied for real-valued images, we introduce…

Numerical Analysis · Mathematics 2018-12-10 Miroslav Bačák , Ronny Bergmann , Gabriele Steidl , Andreas Weinmann

We present a novel variational approach to image restoration (e.g., denoising, inpainting, labeling) that enables to complement established variational approaches with a histogram-based prior enforcing closeness of the solution to some…

Optimization and Control · Mathematics 2013-07-18 Paul Swoboda , Christoph Schnörr

We propose two new variational models aimed to outperform the popular total variation (TV) model for image restoration with L$_2$ and L$_1$ fidelity terms. In particular, we introduce a space-variant generalization of the TV regularizer,…

Image and Video Processing · Electrical Eng. & Systems 2019-06-28 Alessandro Lanza , Serena Morigi , Monica Pragliola , Fiorella Sgallari

In many imaging applications where segmented features (e.g. blood vessels) are further used for other numerical simulations (e.g. finite element analysis), the obtained surfaces do not have fine resolutions suitable for the task. Increasing…

Analysis of PDEs · Mathematics 2023-09-19 Yiyao Zhang , Ke Chen , Shang-Hua Yang

The modeling of phenomenological structure is a crucial aspect in inverse imaging problems. One emerging modeling tool in computational imaging is the optimal transport framework. Its ability to model geometric displacements across an…

Image and Video Processing · Electrical Eng. & Systems 2020-05-12 John Lee , Nicholas P. Bertrand , Christopher J. Rozell

We address the image restoration problem under Poisson noise corruption. The Kullback-Leibler divergence, which is typically adopted in the variational framework as data fidelity term in this case, is coupled with the second-order Total…

Numerical Analysis · Mathematics 2022-05-27 Daniela di Serafino , Monica Pragliola