Related papers: Deep Equilibrium models for Poisson Imaging Invers…

This work deals with the reconstruction of dynamic images that incorporate characteristic dynamics in certain subregions, as arising for the kinetics of many tracers in emission tomography (SPECT, PET). We make use of a basis function…

State-of-the-art algorithms for imaging inverse problems (namely deblurring and reconstruction) are typically iterative, involving a denoising operation as one of its steps. Using a state-of-the-art denoising method in this context is not…

In this paper we show how to augment classical methods for inverse problems with artificial neural networks. The neural network acts as a prior for the coefficient to be estimated from noisy data. Neural networks are global, smooth function…

Neural networks have emerged as powerful surrogates for solving partial differential equations (PDEs), offering significant computational speedups over traditional methods. However, these models suffer from a critical limitation: error…

Image registration is a fundamental step in medical image analysis. Ideally, the transformation that registers one image to another should be a diffeomorphism that is both invertible and smooth. Traditional methods like geodesic shooting…

Deep learning has emerged as a promising approach for learning the nonlinear mapping between diffusion-weighted MR images and tissue parameters, which enables automatic and deep understanding of the brain microstructures. However, the…

Gradient descent can be surprisingly good at optimizing deep neural networks without overfitting and without explicit regularization. We find that the discrete steps of gradient descent implicitly regularize models by penalizing gradient…

Recently there has been a surge of interest in understanding implicit regularization properties of iterative gradient-based optimization algorithms. In this paper, we study the statistical guarantees on the excess risk achieved by…

Machine learning force fields show great promise in enabling more accurate molecular dynamics simulations compared to manually derived ones. Much of the progress in recent years was driven by exploiting prior knowledge about physical…

Model-based optimization methods and discriminative learning methods have been the two dominant strategies for solving various inverse problems in low-level vision. Typically, those two kinds of methods have their respective merits and…

Learning-to-optimize is an emerging framework that seeks to speed up the solution of certain optimization problems by leveraging training data. Learned optimization solvers have been shown to outperform classical optimization algorithms in…

Due to the development of deep learning-based denoisers, the plug-and-play strategy has achieved great success in image restoration problems. However, existing plug-and-play image restoration methods are designed for non-blind Gaussian…

Deep neural networks for medical image reconstruction are traditionally trained using high-quality ground-truth images as training targets. Recent work on Noise2Noise (N2N) has shown the potential of using multiple noisy measurements of the…

The spatial resolution of images of living samples obtained by fluorescence microscopes is physically limited due to the diffraction of visible light, which makes the study of entities of size less than the diffraction barrier (around 200…

An a posteriori error estimator based on an equilibrated flux reconstruction is proposed for defeaturing problems in the context of finite element discretizations. Defeaturing consists in the simplification of a geometry by removing…

Inverse problems span across diverse fields. In medical contexts, computed tomography (CT) plays a crucial role in reconstructing a patient's internal structure, presenting challenges due to artifacts caused by inherently ill-posed inverse…

Utilizing task-invariant knowledge acquired from related tasks as prior information, meta-learning offers a principled approach to learning a new task with limited data records. Sample-efficient adaptation of this prior information is a…

Selecting an appropriate prior to compensate for information loss due to the measurement operator is a fundamental challenge in imaging inverse problems. Implicit priors based on denoising neural networks have become central to widely-used…

Accuracy in neural PDE solvers often breaks down not because of limited expressivity, but due to poor optimisation caused by ill-conditioning, especially in multi-fidelity and stiff problems. We study this issue in Physics-Informed Extreme…

Solving image reconstruction problems of the form \(\mathbf{A} \mathbf{x} = \mathbf{y}\) remains challenging due to ill-posedness and the lack of large-scale supervised datasets. Deep Equilibrium (DEQ) models have been used successfully but…