Related papers: Discontinuous Galerkin Neural Operator for Patholo…

Blind image deblurring remains a challenging problem for modern artificial neural networks. Unlike other image restoration problems, deblurring networks fail behind the performance of existing deblurring algorithms in case of uniform and 3D…

In recent years, deep learning has dominated progress in the field of medical image analysis. We find however, that the ability of current deep learning approaches to represent the complex geometric structures of many medical images is…

Learning under non-smooth objectives remains a fundamental challenge in machine learning, as abrupt changes in conditioning variables can induce highly non-smooth loss landscapes and destabilize optimization. This difficulty is particularly…

Single image defocus deblurring aims to recover an all-in-focus image from a defocus counterpart, where accurately modeling spatially varying blur kernels remains a key challenge. Most existing methods rely on spatial features for kernel…

The modern digital engineering design often requires costly repeated simulations for different scenarios. The prediction capability of neural networks (NNs) makes them suitable surrogates for providing design insights. However, only a few…

MRI super-resolution (SR) and denoising tasks are fundamental challenges in the field of deep learning, which have traditionally been treated as distinct tasks with separate paired training data. In this paper, we propose an innovative…

Disentangled representations can be useful in many downstream tasks, help to make deep learning models more interpretable, and allow for control over features of synthetically generated images that can be useful in training other models…

We present a finite element implementation for the steady-state nonlocal Dirichlet problem with homogeneous volume constraints. Here, the nonlocal diffusion operator is defined as integral operator characterized by a certain kernel…

Occlusion and the scarcity of labeled surgical data are significant challenges in disparity estimation for stereo laparoscopic images. To address these issues, this study proposes a Depth Guided Occlusion-Aware Disparity Refinement Network…

We present a deep learning driven computational approach to overcome the limitations of self-interference digital holography that imposed by inferior axial imaging performances. We demonstrate a 3D deep neural network model can…

While variational methods have been among the most powerful tools for solving linear inverse problems in imaging, deep (convolutional) neural networks have recently taken the lead in many challenging benchmarks. A remaining drawback of deep…

The goal of this project is to build a deep-learning solution that deblurs cornea scans, used for medical examination. The spherical shape of the eye prevents ophtamologist from having completely sharp image. Provided with a stack of…

Ultrasound images are widespread in medical diagnosis for musculoskeletal, cardiac, and obstetrical imaging due to the efficiency and non-invasiveness of the acquisition methodology. However, the acquired images are degraded by acoustic…

High-order Discontinuous Galerkin Spectral Element Methods (DGSEM) provide excellent accuracy for complex flow simulations, but their computational cost increases sharply with higher polynomial orders. %that provide very accurate solutions.…

A classical approach to designing binary image operators is Mathematical Morphology (MM). We propose the Discrete Morphological Neural Networks (DMNN) for binary image analysis to represent W-operators and estimate them via machine…

Historically, the machine learning community has derived spectral decompositions from graph-based approaches. We break with this approach and prove the statistical and computational superiority of the Galerkin method, which consists in…

Deep Neural Networks (DNNs) are generated by sequentially performing linear and non-linear processes. Using a combination of linear and non-linear procedures is critical for generating a sufficiently deep feature space. The majority of…

We present a new approach to stabilizing high-order Runge-Kutta discontinuous Galerkin (RKDG) schemes using weighted essentially non-oscillatory (WENO) reconstructions in the context of hyperbolic conservation laws. In contrast to RKDG…

Image deblurring is an ill-posed problem with multiple plausible solutions for a given input image. However, most existing methods produce a deterministic estimate of the clean image and are trained to minimize pixel-level distortion. These…

The finite element method, finite difference method, finite volume method and spectral method have achieved great success in solving partial differential equations. However, the high accuracy of traditional numerical methods is at the cost…