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We introduce a regularization loss based on kernel mean embeddings with rotation-invariant kernels on the hypersphere (also known as dot-product kernels) for self-supervised learning of image representations. Besides being fully competitive…

Computer Vision and Pattern Recognition · Computer Science 2023-03-09 Léon Zheng , Gilles Puy , Elisa Riccietti , Patrick Pérez , Rémi Gribonval

In this paper we present a generalized Deep Learning-based approach for solving ill-posed large-scale inverse problems occuring in medical image reconstruction. Recently, Deep Learning methods using iterative neural networks and cascaded…

Image and Video Processing · Electrical Eng. & Systems 2020-08-26 Andreas Kofler , Markus Haltmeier , Tobias Schaeffter , Marc Kachelrieß , Marc Dewey , Christian Wald , Christoph Kolbitsch

Implicit Neural Representations (INRs) are a learning-based approach to accelerate Magnetic Resonance Imaging (MRI) acquisitions, particularly in scan-specific settings when only data from the under-sampled scan itself are available.…

Image and Video Processing · Electrical Eng. & Systems 2024-12-11 Yamin Arefeen , Brett Levac , Zach Stoebner , Jonathan Tamir

In this paper, a new regularization term is proposed to solve mathematical image problems. By using difference operators in the four directions; horizontal, vertical and two diagonal directions, an estimation of derivative amplitude is…

Numerical Analysis · Mathematics 2022-09-14 Alireza Hosseini

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

Tensor decomposition methods allow us to learn the parameters of latent variable models through decomposition of low-order moments of data. A significant limitation of these algorithms is that there exists no general method to regularize…

Machine Learning · Statistics 2019-05-28 Omer Gottesman , Weiwei Pan , Finale Doshi-Velez

The development of energy selective, photon counting X-ray detectors allows for a wide range of new possibilities in the area of computed tomographic image formation. Under the assumption of perfect energy resolution, here we propose a…

Computer Vision and Pattern Recognition · Computer Science 2015-06-16 Oguz Semerci , Ning Hao , Misha E. Kilmer , Eric L. Miller

Manifold-valued signal- and image processing has received attention due to modern image acquisition techniques. Recently, a convex relaxation of the otherwise nonconvex Tikhonov-regularization for denoising circle-valued data has been…

Numerical Analysis · Mathematics 2024-05-17 Robert Beinert , Jonas Bresch , Gabriele Steidl

We propose a novel approach to denoising diffusion magnetic resonance images (dMRI) using convolutional neural networks, that exploits the benefits of data acquired at multiple b-values to offset the need for many redundant observations.…

Image and Video Processing · Electrical Eng. & Systems 2024-10-23 Jakub Jurek , Andrzej Materka , Kamil Ludwisiak , Agata Majos , Filip Szczepankiewicz

We develop a general mathematical framework for variational problems where the unknown function assumes values in the space of probability measures on some metric space. We study weak and strong topologies and define a total variation…

Numerical Analysis · Mathematics 2018-06-12 Thomas Vogt , Jan Lellmann

Diffusion magnetic resonance imaging (dMRI) plays a vital role in both clinical diagnostics and neuroscience research. However, its inherently low signal-to-noise ratio (SNR), especially under high diffusion weighting, significantly…

Quantitative Methods · Quantitative Biology 2026-02-27 Jine Xie , Zhicheng Zhang , Yunwei Chen , Yanqiu Feng , Xinyuan Zhang

In the context of image processing, given a $k$-th order, homogeneous and linear differential operator with constant coefficients, we study a class of variational problems whose regularizing terms depend on the operator. Precisely, the…

Numerical Analysis · Mathematics 2022-11-15 Valerio Pagliari , Kostas Papafitsoros , Bogdan Raiţă , Andreas Vikelis

In this paper, we develop a new regularized version of the Factorization Method for positive operators mapping a complex Hilbert Space into it's dual space. The Factorization Method uses Picard's Criteria to define an indicator function to…

Analysis of PDEs · Mathematics 2021-12-08 Isaac Harris

Seismic full-waveform inversion is a core technology for obtaining high-resolution subsurface model parameters. However, its highly nonlinear characteristics and strong dependence on the initial model often lead to the inversion process…

Machine Learning · Computer Science 2026-03-25 Caiyun Liu , Siyang Pei , Qingfeng Yu , Jie Xiong

In this paper, we propose to use the general $L^2$-based Sobolev norms, i.e., $H^s$ norms where $s\in \mathbb{R}$, to measure the data discrepancy due to noise in image processing tasks that are formulated as optimization problems. As…

Numerical Analysis · Mathematics 2022-03-01 Bowen Zhu , Jingwei Hu , Yifei Lou , Yunan Yang

In this work, we address the limitations of denoising diffusion models (DDMs) in image restoration tasks, particularly the shape and color distortions that can compromise image quality. While DDMs have demonstrated a promising performance…

Computer Vision and Pattern Recognition · Computer Science 2024-12-18 Xinlong Cheng , Tiantian Cao , Guoan Cheng , Bangxuan Huang , Xinghan Tian , Ye Wang , Xiaoyu He , Weixin Li , Tianfan Xue , Xuan Dong

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

Mumford-Shah and Potts functionals are powerful variational models for regularization which are widely used in signal and image processing; typical applications are edge-preserving denoising and segmentation. Being both non-smooth and…

Numerical Analysis · Mathematics 2016-02-11 Andreas Weinmann , Laurent Demaret , Martin Storath

Depth maps captured with commodity sensors often require super-resolution to be used in applications. In this work we study a super-resolution approach based on a variational problem statement with Tikhonov regularization where the…

Computer Vision and Pattern Recognition · Computer Science 2021-12-22 Milena Gazdieva , Oleg Voynov , Alexey Artemov , Youyi Zheng , Luiz Velho , Evgeny Burnaev

In this paper, a variational, multi-dimensional model for image reconstruction is proposed, in which the regularization term consists of the $r$-order (an)-isotropic total variation seminorms $TV^r$, with $r\in \mathbb R^+$, defined via the…

Analysis of PDEs · Mathematics 2019-01-17 Pan Liu , Xin Yang Lu