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3D Gaussian Splatting (3DGS) has emerged as a promising approach for CT reconstruction. However, existing methods rely on the average gradient magnitude of points within the view, often leading to severe needle-like artifacts under…

The density matrix renormalization group (DMRG) algorithm is a popular alternating minimization scheme for solving high-dimensional optimization problems in the tensor train format. Classical DMRG, however, is based on sequential…

We propose a new fast algorithm for solving one of the standard formulations of image restoration and reconstruction which consists of an unconstrained optimization problem where the objective includes an $\ell_2$ data-fidelity term and a…

Synthetic aperture radar (SAR) tomography (TomoSAR) enables the reconstruction and three-dimensional (3D) localization of targets based on multiple two-dimensional (2D) observations of the same scene. The resolving along the elevation…

Large linear systems with sparse, non-symmetric matrices arise in the modeling of Markov chains or in the discretization of convection-diffusion problems. Due to their potential to solve sparse linear systems with an effort that is linear…

We propose a sparse grids based adaptive noise reduction strategy for electrostatic particle-in-cell (PIC) simulations. Our approach is based on the key idea of relying on sparse grids instead of a regular grid in order to increase the…

Adaptive gradient methods including Adam, AdaGrad, and their variants have been very successful for training deep learning models, such as neural networks. Meanwhile, given the need for distributed computing, distributed optimization…

Implicit time integration is key to robustly simulating stiff materials and large deformations, but its performance is often dominated by repeatedly solving large linear systems. Adaptive coarsening can reduce this cost by concentrating…

Image compression using neural networks have reached or exceeded non-neural methods (such as JPEG, WebP, BPG). While these networks are state of the art in ratedistortion performance, computational feasibility of these models remains a…

Algebraic multigrid (AMG) is known to be an effective solver for many sparse symmetric positive definite (SPD) linear systems. For SPD systems, the convergence theory of AMG is well-understood in terms of the $A$-norm, but in a nonsymmetric…

3D Gaussian Splatting (3DGS) has demonstrated impressive novel view synthesis performance. While conventional methods require per-scene optimization, more recently several feed-forward methods have been proposed to generate pixel-aligned…

Sparsity regularized loss minimization problems play an important role in various fields including machine learning, data mining, and modern statistics. Proximal gradient descent method and coordinate descent method are the most popular…

Remote sensing images are frequently degraded by adverse weather conditions, particularly clouds and haze, which severely impair downstream applications. Existing restoration methods typically rely on computationally heavy architectures or…

Isogeometric analysis (IgA) offers enhanced approximation capabilities for the discretization of elliptic boundary-value problems, yet it results in large, sparse, and increasingly ill-conditioned linear systems due to higher…

We present an algorithm for resampling a function from its values on a non-Cartesian grid onto a Cartesian grid. This problem arises in many applications such as MRI, CT, radio astronomy and geophysics. Our algorithm, termed SParse Uniform…

Coarse-graining (CG) accelerates molecular simulations of protein dynamics by simulating sets of atoms as singular beads. Backmapping is the opposite operation of bringing lost atomistic details back from the CG representation. While…

In the present article, novel Coarse-Graining (CG) algorithms for the Eulerian-Lagrangian (EL) simulation of particle-laden flows are proposed. These include different variants of Reproducing Kernel Particle Methods (RKPM) and an extended…

3D Gaussian Splatting (3DGS) provides an efficient method for high-quality scene reconstruction using anisotropic Gaussians. Recently, 3DGS-based methods have significantly improved the rendering quality of human avatars while enabling…

Stochastic gradient descent (SGD) is a widely adopted iterative method for optimizing differentiable objective functions. In this paper, we propose and discuss a novel approach to scale up SGD in applications involving non-convex functions…

A tomographic technique called full-waveform inversion has recently shown promise as a fast, affordable, and safe modality to image the brain using ultrasound. However, its high computational cost and memory footprint currently limit its…