English
Related papers

Related papers: A variational model with fractional-order regulari…

200 papers

In this paper, we propose a level set regularization approach combined with a split strategy for the simultaneous identification of piecewise constant diffusion and absorption coefficients from a finite set of optical tomography data…

Numerical Analysis · Mathematics 2020-12-23 J. P. Agnelli , A. De Cezaro , A. Leitao , M. Marques Alves

Diffusion Magnetic Resonance Imaging (dMRI) is a non-invasive tool for watching the microstructure of fibrous nerve and muscle tissue. From dMRI, it is possible to estimate 2-rank diffusion tensors imaging (DTI) fields, that are widely used…

Computer Vision and Pattern Recognition · Computer Science 2016-06-28 Hernan Dario Vargas Cardona , Mauricio A. Alvarez , Alvaro A. Orozco

In this present paper, we introduce and study a dynamical systems involving fractional derivative operator and nonlocal condition, which is constituted of a fractional evolution equation and a time-dependent variational inequality, and is…

General Mathematics · Mathematics 2023-10-11 Jinxia Cen , J. Vanterler da C. Sousa , Wei Wu

Fractional order differential and difference equations are used to model systems with memory. Variable order fractional equations are proposed to model systems where the memory changes in time. We investigate stability conditions for linear…

Dynamical Systems · Mathematics 2025-02-12 Prashant M. Gade , Sachin Bhalekar , Janardhan Chevala

Dielectric tensor tomography reconstructs the three-dimensional dielectric tensors of microscopic objects and provides information about the crystalline structure orientations and principal refractive indices. Because dielectric tensor…

Optics · Physics 2022-10-13 Herve Hugonnet , Seungwoo Shin , Yongkeun Park

Diffusion MRI (dMRI) is an advanced imaging technique characterizing tissue microstructure and white matter structural connectivity of the human brain. The demand for high-quality dMRI data is growing, driven by the need for better…

Image and Video Processing · Electrical Eng. & Systems 2024-08-26 Xi Zhu , Wei Zhang , Yijie Li , Lauren J. O'Donnell , Fan Zhang

We consider the problem of conditional text-to-image synthesis with diffusion models. Most recent works need to either finetune specific parts of the base diffusion model or introduce new trainable parameters, leading to deployment…

Computer Vision and Pattern Recognition · Computer Science 2024-11-19 Tripti Shukla , Srikrishna Karanam , Balaji Vasan Srinivasan

The linearization principle states that the stability (or instability) of solutions to a suitable linearization of a nonlinear problem implies the stability (or instability) of solutions to the original nonlinear problem. In this work, we…

Analysis of PDEs · Mathematics 2025-07-04 Sofwah Ahmad , Szymon Cygan , Grzegorz Karch

We tackle the problem of reflectance estimation from a set of multi-view images, assuming known geometry. The approach we put forward turns the input images into reflectance maps, through a robust variational method. The variational model…

Computer Vision and Pattern Recognition · Computer Science 2018-01-24 Jean Mélou , Yvain Quéau , Jean-Denis Durou , Fabien Castan , Daniel Cremers

In this paper we propose Discretely Indexed flows (DIF) as a new tool for solving variational estimation problems. Roughly speaking, DIF are built as an extension of Normalizing Flows (NF), in which the deterministic transport becomes…

Machine Learning · Statistics 2022-04-05 Elouan Argouarc'h , François Desbouvries , Eric Barat , Eiji Kawasaki , Thomas Dautremer

We define hyperbolic fractional-order Fourier transformations by replacing the circular trigonometric functions in the integral expressions of conventional fractional-order Fourier transformations with hyperbolic trigonometric functions. We…

Optics · Physics 2025-09-29 Pierre Pellat-Finet

The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…

Numerical Analysis · Mathematics 2024-04-25 A. Torres-Hernandez , F. Brambila-Paz

We study outlier tokens in Diffusion Transformers (DiTs) for image generation. Prior work has shown that Vision Transformers (ViTs) can produce a small number of high-norm tokens that attract disproportionate attention while carrying…

Computer Vision and Pattern Recognition · Computer Science 2026-05-07 Xiaoyu Wu , Yifei Wang , Tsu-Jui Fu , Liang-Chieh Chen , Zhe Gan , Chen Wei

This paper considers a new fuzzy fractional differential variational inequality with integral boundary conditions comprising a fuzzy fractional differential inclusion with integral boundary conditions and a variational inequality in…

Optimization and Control · Mathematics 2026-03-31 Zengbao Wu , Quanguo Zhang , Tao Chen , Yibin Xiao , Tianyin Wang , Chunyan Yang

In this paper we present numerical methods - finite differences and finite elements - for solution of partial differential equation of fractional order in time for one-dimensional space. This equation describes anomalous diffusion which is…

Mathematical Physics · Physics 2007-05-23 Mariusz Ciesielski , Jacek Leszczynski

We give a comprehensive survey on a class of higher order variational problems which are motivated by applications in mathematical imaging. The overall aim of this note is to investigate if and in which manner results from the first…

Analysis of PDEs · Mathematics 2018-03-28 Martin Fuchs , Jan Mueller

Diffusion Magnetic Resonance Imaging (dMRI) is an imaging technique with exquisite sensitivity to the microstructural properties of heterogeneous media. The conventionally adopted acquisition schemes involving single pulsed field gradients…

Biological Physics · Physics 2023-01-04 Deneb Boito , Cem Yolcu , Evren Özarslan

Diverse inverse problems in imaging can be cast as variational problems composed of a task-specific data fidelity term and a regularization term. In this paper, we propose a novel learnable general-purpose regularizer exploiting recent…

Optimization and Control · Mathematics 2020-02-19 Erich Kobler , Alexander Effland , Karl Kunisch , Thomas Pock

This work unifies pseudo-time and inexact regularization techniques for nonmonotone classes of partial differential equations, into a regularized pseudo-time framework. Convergence of the residual at the predicted rate is investigated…

Numerical Analysis · Mathematics 2016-11-29 Sara Pollock

In this paper we propose a new class of iterative regularization methods for solving ill-posed linear operator equations. The prototype of these iterative regularization methods is in the form of second order evolution equation with a…

Numerical Analysis · Mathematics 2020-06-24 Rongfang Gong , B. Hofmann , Ye Zhang