Related papers: Curvelet-Regularized SPDE Inversion on Piecewise-P…
In this paper, we present a theoretical analysis of separating images consisting of pointlike and $C^{ \beta}$-curvelike structures, where $\beta \in (1,2] $. Our approach is based on $l_1$-minimization, in which the sparsity of the desired…
We develop a transfer matrix formalism to visualize the framing of discrete piecewise linear curves in three dimensional space. Our approach is based on the concept of an intrinsically discrete curve, which enables us to more effectively…
The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…
In compressible fluid flow, reconstructing shocks, discontinuities, rarefactions, and their interactions from sparse measurements is an important inverse problem with practical applications. Moreover, physics-informed machine learning has…
This paper studies structured sparse training of CNNs with a gradual pruning technique that leads to fixed, sparse weight matrices after a set number of epochs. We simplify the structure of the enforced sparsity so that it reduces overhead…
In this paper, we consider the problem of sparse recovery from nonlinear measurements, which has applications in state estimation and bad data detection for power networks. An iterative mixed $\ell_1$ and $\ell_2$ convex program is used to…
Achieving a consistent and compact 3D segmentation field is crucial for maintaining semantic coherence across views and accurately representing scene structures. Previous 3D scene segmentation methods rely on video segmentation models to…
Approximating field variables and data vectors from sparse samples is a key challenge in computational science. Widely used methods such as gappy proper orthogonal decomposition and empirical interpolation rely on linear approximation…
Robots operating in unstructured environments often require accurate and consistent object-level representations. This typically requires segmenting individual objects from the robot's surroundings. While recent large models such as Segment…
Sparse-view 3D Gaussian Splatting (3DGS) presents significant challenges in reconstructing high-quality novel views, as it often overfits to the widely-varying high-frequency (HF) details of the sparse training views. While frequency…
Many modern data analysis algorithms either assume or are considerably more efficient if the distances between the data points satisfy a metric. These algorithms include metric learning, clustering, and dimension reduction. As real data…
Curvilinear structures are present in various fields in image processing such as blood vessels in medical imaging or roads in remote sensing. Their detection is crucial for many applications. In this article, we propose an unsupervised…
As a confined thin sheet crumples, it spontaneously segments into flat facets delimited by a network of ridges. Despite the apparent disorder of this process, statistical properties of crumpled sheets exhibit striking reproducibility.…
This article proposes an efficient numerical method for solving nonlinear partial differential equations (PDEs) based on sparse Gaussian processes (SGPs). Gaussian processes (GPs) have been extensively studied for solving PDEs by…
We address the inverse problem of identifying nonlocal interaction potentials in nonlinear aggregation-diffusion equations from noisy discrete trajectory data. Our approach involves formulating and solving a regularized variational problem,…
The restoration lemma by Afek, Bremler-Barr, Kaplan, Cohen, and Merritt [Dist. Comp. '02] proves that, in an undirected unweighted graph, any replacement shortest path avoiding a failing edge can be expressed as the concatenation of two…
While recent feed-forward 3D reconstruction models accelerate 3D reconstruction by jointly inferring dense geometry and camera poses in a single pass, their reliance on dense attention imposes a quadratic complexity, creating a prohibitive…
The reconstruction of low-textured areas is a prominent research focus in multi-view stereo (MVS). In recent years, traditional MVS methods have performed exceptionally well in reconstructing low-textured areas by constructing plane models.…
Existing optimization-based methods for non-rigid registration typically minimize an alignment error metric based on the point-to-point or point-to-plane distance between corresponding point pairs on the source surface and target surface.…
Estimating subsurface dielectric properties is essential for applications ranging from environmental surveys of soils to nondestructive evaluation of concrete in infrastructure. Conventional wave inversion methods typically assume few…