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We propose a level set method to reconstruct unknown surfaces from point clouds, without assuming that the connections between points are known. We consider a variational formulation with a curvature constraint that minimizes the surface…

Tomographic reconstruction, despite its revolutionary impact on a wide range of applications, suffers from its ill-posed nature in that there is no unique solution because of limited and noisy measurements. Therefore, in the absence of…

This paper studies a class of double-loop (inner-outer) algorithms for convex composite optimization. For unconstrained problems, we develop a restarted accelerated composite gradient method that attains the optimal first-order complexity…

We propose a novel iterative numerical method to solve the three-dimensional inverse obstacle scattering problem of recovering the shape of the obstacle from far-field measurements. To address the inherent ill-posed nature of the inverse…

We propose a novel method to reconstruct volumetric flows from sparse views via a global transport formulation. Instead of obtaining the space-time function of the observations, we reconstruct its motion based on a single initial state. In…

High-quality point cloud data is a critical foundation for tasks such as autonomous driving and 3D reconstruction. However, LiDAR-based point cloud acquisition is often affected by various disturbances, resulting in a large number of noise…

We propose R3GS, a robust reconstruction and relocalization framework tailored for unconstrained datasets. Our method uses a hybrid representation during training. Each anchor combines a global feature from a convolutional neural network…

Point cloud is a crucial representation of 3D contents, which has been widely used in many areas such as virtual reality, mixed reality, autonomous driving, etc. With the boost of the number of points in the data, how to efficiently…

We propose a new reverse time migration method for reconstructing extended obstacles in the planar waveguide using acoustic waves at a fixed frequency. We prove the resolution of the reconstruction method in terms of the aperture and the…

Efficient point cloud compression is fundamental to enable the deployment of virtual and mixed reality applications, since the number of points to code can range in the order of millions. In this paper, we present a novel data-driven…

Elongated anisotropic Gaussian filters are used for the orientation estimation of fibers. In cases where computed tomography images are noisy, roughly resolved, and of low contrast, they are the method of choice even if being efficient only…

We introduce a novel technique to generate Benders' cuts from a conic relaxation ("corner") derived from a basis of a higher-dimensional polyhedron that we aim to outer approximate in a lower-dimensional space. To generate facet-defining…

For the arbitrary-Lagrangian-Eulerian (ALE) calculations, the geometric information needs to be calculated at each time step due to the movement of mesh. To achieve the high-order spatial accuracy, a large number of matrix inversions are…

Recently, immersive media and autonomous driving applications have significantly advanced through 3D Gaussian Splatting (3DGS), which offers high-fidelity rendering and computational efficiency. Despite these advantages, 3DGS as a…

Octree-based context learning has recently become a leading method in point cloud compression. However, its potential on lossy compression remains undiscovered. The traditional lossy compression paradigm using lossless octree representation…

Unoriented surface reconstruction is an important task in computer graphics and has extensive applications. Based on the compact support of wavelet and orthogonality properties, classic wavelet surface reconstruction achieves good and fast…

In this paper, we study the inverse boundary value problem for the wave equation with a view towards an explicit reconstruction procedure. We consider both the anisotropic problem where the unknown is a general Riemannian metric smoothly…

We present a new adaptive method for electronic structure calculations based on novel fast algorithms for reduction of multivariate mixtures. In our calculations, spatial orbitals are maintained as Gaussian mixtures whose terms are selected…

We present explicit reconstruction algorithms for fully anisotropic unknown elasticity tensors from knowledge of a finite number of internal displacement fields, with applications to transient elastography. Under certain rank-maximality…

We investigate the reconstruction of asymptotically anti-de Sitter (AdS) bulk geometries from boundary entanglement entropy data for ball-shaped entangling regions. By deriving an explicit inversion formula, we relate variations in…