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We propose a new space-variant anisotropic regularisation term for variational image restoration, based on the statistical assumption that the gradients of the target image distribute locally according to a bivariate generalised Gaussian…

Numerical Analysis · Mathematics 2019-04-04 Luca Calatroni , Alessandro Lanza , Monica Pragliola , Fiorella Sgallari

A recently designed hyperspectral imaging device enables multiplexed acquisition of an entire data volume in a single snapshot thanks to monolithically-integrated spectral filters. Such an agile imaging technique comes at the cost of a…

Computer Vision and Pattern Recognition · Computer Science 2015-02-09 K. Degraux , V. Cambareri , L. Jacques , B. Geelen , C. Blanch , G. Lafruit

In electrical impedance tomography, algorithms based on minimizing a linearized residual functional have been widely used due to their flexibility and good performance in practice. However, no rigorous convergence results have been…

Analysis of PDEs · Mathematics 2018-10-11 Bastian Harrach , Mach Nguyet Minh

This paper concerns a class of composite image reconstruction models for impluse noise removal, which is rather general and covers existing convex and nonconvex models proposed for reconstructing images with impluse noise. For this…

Optimization and Control · Mathematics 2024-03-27 Bujin Li , Shaohua Pan , Tieyong Zeng

This work is concerned with the determination of the diffusion coefficient from distributed data of the state. This problem is related to homogenization theory on the one hand and to regularization theory on the other hand. An approach is…

Optimization and Control · Mathematics 2018-05-07 Christian Clason , Florian Kruse , Karl Kunisch

The pel-recursive computation of 2-D optical flow has been extensively studied in computer vision to estimate motion from image sequences, but it still raises a wealth of issues, such as the treatment of outliers, motion discontinuities and…

Computer Vision and Pattern Recognition · Computer Science 2016-11-04 Vania V. Estrela , Matthias O. Franz , Ricardo T. Lopes , G. P. De Araujo

A supervised learning approach is proposed for regularization of large inverse problems where the main operator is built from noisy data. This is germane to superresolution imaging via the sampling indicators of the inverse scattering…

Numerical Analysis · Mathematics 2025-08-22 Fatemeh Pourahmadian , Yang Xu

In this paper we present a new regularization term for variational image restoration which can be regarded as a space-variant anisotropic extension of the classical isotropic Total Variation (TV) regularizer. The proposed regularizer comes…

Image and Video Processing · Electrical Eng. & Systems 2019-08-05 Luca Calatroni , Alessandro Lanza , Monica Pragliola , Fiorella Sgallari

Magnetic resonance (MR)-$T_2^*$ mapping is widely used to study hemorrhage, calcification and iron deposition in various clinical applications, it provides a direct and precise mapping of desired contrast in the tissue. However, the long…

Image and Video Processing · Electrical Eng. & Systems 2020-08-06 Shuai Huang , James J. Lah , Jason W. Allen , Deqiang Qiu

We consider the variational reconstruction framework for inverse problems and propose to learn a data-adaptive input-convex neural network (ICNN) as the regularization functional. The ICNN-based convex regularizer is trained adversarially…

Confocal microscopy has long been a cornerstone technique for visualizing complex interactions and processes within cellular structures. However, achieving super-resolution imaging of multiple organelles and their interactions…

Optics · Physics 2025-08-19 Qinglin Chen , Luwei Wang , Jia Li , Dan Shao , Xiaoyu Weng , Liwei Liu , Dayong Jin , Junle Qu

Acquisition of Magnetic Resonance Imaging (MRI) scans can be accelerated by under-sampling in k-space (i.e., the Fourier domain). In this paper, we consider the problem of optimizing the sub-sampling pattern in a data-driven fashion. Since…

Image and Video Processing · Electrical Eng. & Systems 2019-05-02 Cagla Deniz Bahadir , Adrian V. Dalca , Mert R. Sabuncu

Multi-energy CT takes advantage of the non-linearly varying attenuation properties of elemental media with respect to energy, enabling more precise material identification than single-energy CT. The increased precision comes with the cost…

Medical Physics · Physics 2020-02-14 Jussi Toivanen , Alexander Meaney , Samuli Siltanen , Ville Kolehmainen

We present a new approach for representing and reconstructing multidimensional magnetic resonance imaging (MRI) data. Our method builds on a novel, learned feature-based image representation that disentangles different types of features,…

Image and Video Processing · Electrical Eng. & Systems 2026-01-01 Ruiyang Zhao , Fan Lam

Non-Local Total Variation (NLTV) has emerged as a useful tool in variational methods for image recovery problems. In this paper, we extend the NLTV-based regularization to multicomponent images by taking advantage of the Structure Tensor…

Computer Vision and Pattern Recognition · Computer Science 2014-12-11 Giovanni Chierchia , Nelly Pustelnik , Beatrice Pesquet-Popescu , Jean-Christophe Pesquet

In this paper, we propose a global framework that includes a detailed model of the photo-switching and acoustic processes for photo-switching optoacoustic mesoscopy, based on the underlying physics. We efficiently implement two forward…

Optics · Physics 2025-10-29 Yan Liu , Jonathan Chuah , Michael Unser , Jonathan Dong

We introduce a new paradigm for solving regularized variational problems. These are typically formulated to address ill-posed inverse problems encountered in signal and image processing. The objective function is traditionally defined by…

Optimization and Control · Mathematics 2021-04-22 Jean-Christophe Pesquet , Audrey Repetti , Matthieu Terris , Yves Wiaux

Compressed Sensing (CS) significantly speeds up Magnetic Resonance Image (MRI) processing and achieves accurate MRI reconstruction from under-sampled k-space data. According to the current research, there are still several problems with…

Image and Video Processing · Electrical Eng. & Systems 2023-10-24 Junpeng Tan , Chunmei Qing , Xiangmin Xu

In parallel magnetic resonance imaging (pMRI) reconstruction without using estimation of coil sensitivity functions, one group of algorithms reconstruct sensitivity encoded images of the coils first followed by the magnitude only image…

Medical Physics · Physics 2013-11-12 Cishen Zhang , Ifat Al Baqee

MRI is an inherently slow process, which leads to long scan time for high-resolution imaging. The speed of acquisition can be increased by ignoring parts of the data (undersampling). Consequently, this leads to the degradation of image…

Image and Video Processing · Electrical Eng. & Systems 2022-02-22 Soumick Chatterjee , Mario Breitkopf , Chompunuch Sarasaen , Hadya Yassin , Georg Rose , Andreas Nürnberger , Oliver Speck
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