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We examine in this paper the problem of image registration from the new perspective where images are given by sparse approximations in parametric dictionaries of geometric functions. We propose a registration algorithm that looks for an…

Computer Vision and Pattern Recognition · Computer Science 2013-12-31 Alhussein Fawzi , Pascal Frossard

Recent works in medical image registration have proposed the use of Implicit Neural Representations, demonstrating performance that rivals state-of-the-art learning-based methods. However, these implicit representations need to be optimized…

Image and Video Processing · Electrical Eng. & Systems 2023-10-04 Louis D. van Harten , Jaap Stoker , Ivana Išgum

Standard regularization methods that are used to compute solutions to ill-posed inverse problems require knowledge of the forward model. In many real-life applications, the forward model is not known, but training data is readily available.…

Numerical Analysis · Mathematics 2015-06-19 Julianne Chung , Matthias Chung

In this paper, we investigate iterative methods that are based on sampling of the data for computing Tikhonov-regularized solutions. We focus on very large inverse problems where access to the entire data set is not possible all at once…

Numerical Analysis · Mathematics 2018-12-18 J. Tanner Slagel , Julianne Chung , Matthias Chung , David Kozak , Luis Tenorio

This paper introduces a new strategy for setting the regularization parameter when solving large-scale discrete ill-posed linear problems by means of the Arnoldi-Tikhonov method. This new rule is essentially based on the discrepancy…

Numerical Analysis · Mathematics 2013-07-02 Silvia Gazzola , Paolo Novati , Maria Rosaria Russo

State-of-the-art image reconstruction often relies on complex, highly parameterized deep architectures. We propose an alternative: a data-driven reconstruction method inspired by the classic Tikhonov regularization. Our approach iteratively…

Image and Video Processing · Electrical Eng. & Systems 2025-02-07 Mehrsa Pourya , Erich Kobler , Michael Unser , Sebastian Neumayer

An adaptive regularization algorithm for unconstrained nonconvex optimization is proposed that is capable of handling inexact objective-function and derivative values, and also of providing approximate minimizer of arbitrary order. In…

Optimization and Control · Mathematics 2021-11-30 N. I. M. Gould , Ph. L. Toint

A regularized version of Mixture Models is proposed to learn a principal graph from a distribution of $D$-dimensional data points. In the particular case of manifold learning for ridge detection, we assume that the underlying manifold can…

Machine Learning · Computer Science 2023-07-13 Tony Bonnaire , Aurélien Decelle , Nabila Aghanim

We address rotation averaging (RA) and its application to real-world 3D reconstruction. Local optimisation based approaches are the de facto choice, though they only guarantee a local optimum. Global optimisers ensure global optimality in…

Computer Vision and Pattern Recognition · Computer Science 2021-03-30 Yu Chen , Ji Zhao , Laurent Kneip

The random coefficients model $Y_i={\beta_0}_i+{\beta_1}_i {X_1}_i+{\beta_2}_i {X_2}_i+\ldots+{\beta_d}_i {X_d}_i$, with $\mathbf{X}_i$, $Y_i$, $\mathbf{\beta}_i$ i.i.d, and $\mathbf{\beta}_i$ independent of $X_i$ is often used to capture…

Methodology · Statistics 2021-08-17 Fabian Dunker , Emil Mendoza , Marco Reale

Distribution shift severely degrades the performance of deep forecasting models. While this issue is well-studied for individual time series, it remains a significant challenge in the spatio-temporal domain. Effective solutions like…

Machine Learning · Computer Science 2026-04-20 Zhaobo Hu , Vincent Gauthier , Mehdi Naima

Optimization techniques have been widely used in deformable registration, allowing for the incorporation of similarity metrics with regularization mechanisms. These regularization mechanisms are designed to mitigate the effects of trivial…

Computer Vision and Pattern Recognition · Computer Science 2014-04-10 Martin Rajchl , John S. H. Baxter , Wu Qiu , Ali R. Khan , Aaron Fenster , Terry M. Peters , Jing Yuan

Regularization approaches have demonstrated their effectiveness for solving ill-posed problems. However, in the context of variational restoration methods, a challenging question remains, which is how to find a good regularizer. While total…

Optimization and Control · Mathematics 2011-10-25 Nelly Pustelnik , Caroline Chaux , Jean-Christophe Pesquet

We analyse and explain the increased generalisation performance of iterate averaging using a Gaussian process perturbation model between the true and batch risk surface on the high dimensional quadratic. We derive three phenomena…

Machine Learning · Statistics 2021-11-02 Diego Granziol , Xingchen Wan , Samuel Albanie , Stephen Roberts

Deep learning-based image registration approaches have shown competitive performance and run-time advantages compared to conventional image registration methods. However, existing learning-based approaches mostly require to train separate…

Image and Video Processing · Electrical Eng. & Systems 2023-03-21 Yinsong Wang , Huaqi Qiu , Chen Qin

Hyperspectral analysis has gained popularity over recent years as a way to infer what materials are displayed on a picture whose pixels consist of a mixture of spectral signatures. Computing both signatures and mixture coefficients is known…

Optimization and Control · Mathematics 2017-06-29 Adrien Faivre , Clément Dombry

In this work, we consider the inverse problem of reconstructing the internal structure of an object from limited x-ray projections. We use a Gaussian process prior to model the target function and estimate its (hyper)parameters from…

Computer Vision and Pattern Recognition · Computer Science 2019-07-04 Zenith Purisha , Carl Jidling , Niklas Wahlström , Simo Särkkä , Thomas B. Schön

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

Covariance tapering is a popular approach for reducing the computational cost of spatial prediction and parameter estimation for Gaussian process models. However, tapering can have poor performance when the process is sampled at spatially…

Computation · Statistics 2016-02-22 David Bolin , Jonas Wallin

We study the non-parametric estimation of a multidimensional unknown density f in a tomography problem based on independent and identically distributed observations, whose common density is proportional to the Radon transform of f. We…

Statistics Theory · Mathematics 2023-06-28 Sergio Brenner Miguel , Janine Steck