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In recent years, 3D Gaussian splatting (3DGS) has achieved remarkable progress in novel view synthesis. However, accurately reconstructing glossy surfaces under complex illumination remains challenging, particularly in scenes with strong…

Several learning applications require solving high-dimensional regression problems where the relevant features belong to a small number of (overlapping) groups. For very large datasets and under standard sparsity constraints, hard…

Fully implicit Runge-Kutta (IRK) methods have many desirable properties as time integration schemes in terms of accuracy and stability, but high-order IRK methods are not commonly used in practice with numerical PDEs due to the difficulty…

Reconstructing a gene network from high-throughput molecular data is often a challenging task, as the number of parameters to estimate easily is much larger than the sample size. A conventional remedy is to regularize or penalize the model…

Many scientific and engineering challenges can be formulated as optimization problems which are constrained by partial differential equations (PDEs). These include inverse problems, control problems, and design problems. As a major…

This paper presents the first results to combine two theoretically sound methods (spectral projection and multigrid methods) together to attack ill-conditioned linear systems. Our preliminary results show that the proposed algorithm applied…

3D Gaussian Splatting (3DGS) has emerged as a promising approach for 3D scene representation, offering a reduction in computational overhead compared to Neural Radiance Fields (NeRF). However, 3DGS is susceptible to high-frequency artifacts…

Recovering the intrinsic physical attributes of a scene from images, generally termed as the inverse rendering problem, has been a central and challenging task in computer vision and computer graphics. In this paper, we present GUS-IR, a…

Computed Tomography (CT) is a prominent example of Imaging Inverse Problem highlighting the unrivaled performances of data-driven methods in degraded measurements setups like sparse X-ray projections. Although a significant proportion of…

Gaussian splatting (GS) for 3D reconstruction has become quite popular due to their fast training, inference speeds and high quality reconstruction. However, GS-based reconstructions generally consist of millions of Gaussians, which makes…

Two new hybrid algorithms are proposed for large-scale linear discrete ill-posed problems in general-form regularization. They are both based on Krylov subspace inner-outer iterative algorithms. At each iteration, they need to solve a…

Recently, Gaussian Splatting (GS) has received a lot of attention in surface reconstruction. However, while 3D objects can be of complex and diverse shapes in the real world, existing GS-based methods only limitedly use a single type of…

Pre-conditioning is a well-known concept that can significantly improve the convergence of optimization algorithms. For noise-free problems, where good pre-conditioners are not known a priori, iterative linear algebra methods offer one way…

For the large-scale linear discrete ill-posed problem $\min\|Ax-b\|$ or $Ax=b$ with $b$ contaminated by white noise, the Golub-Kahan bidiagonalization based LSQR method and its mathematically equivalent CGLS, the Conjugate Gradient (CG)…

3D Gaussian Splatting (3DGS) achieves impressive rendering fidelity and speed for novel view synthesis. However, its substantial data size poses a significant challenge for practical applications. While many compression techniques have been…

Krylov subspace methods are among the most efficient solvers for large scale linear algebra problems. Nevertheless, classic Krylov subspace algorithms do not scale well on massively parallel hardware due to synchronization bottlenecks.…

This paper introduces a computational framework to incorporate flexible regularization techniques in ensemble Kalman methods for nonlinear inverse problems. The proposed methodology approximates the maximum a posteriori (MAP) estimate of a…

Integrating inverse rendering with multi-view photometric stereo (MVPS) yields more accurate 3D reconstructions than the inverse rendering approaches that rely on fixed environment illumination. However, efficient inverse rendering with…

Preconditioning techniques are crucial for enhancing the efficiency of solving large-scale linear equation systems that arise from partial differential equation (PDE) discretization. These techniques, such as Incomplete Cholesky…

This work addresses the fundamental linear inverse problem in compressive sensing (CS) by introducing a new type of regularizing generative prior. Our proposed method utilizes ideas from classical dictionary-based CS and, in particular,…