Related papers: Exact Hidden Paths in Noisy High Dimensional Path …
In this paper, we consider inverse shape problems coming from diffuse optical tomography and inverse scattering. In both problems, our goal is to reconstruct small volume interior regions from measured data on the exterior surface of an…
Many models for sparse regression typically assume that the covariates are known completely, and without noise. Particularly in high-dimensional applications, this is often not the case. This paper develops efficient OMP-like algorithms to…
This work presents new methods and algorithms for tracking the shape and trajectory of moving reflecting obstacles with broken rays, or rays reflecting at an obstacle. While in tomography the focus of the reconstruction method is to recover…
In this paper, practically computable low-order approximations of potentially high-dimensional differential equations driven by geometric rough paths are proposed and investigated. In particular, equations are studied that cover the linear…
Accurate depth information is essential for many computer vision applications. Yet, no available dataset recording method allows for fully dense accurate depth estimation in a large scale dynamic environment. In this paper, we introduce…
We consider the phase retrieval problem of reconstructing a $n$-dimensional real or complex signal $\mathbf{X}^{\star}$ from $m$ (possibly noisy) observations $Y_\mu = | \sum_{i=1}^n \Phi_{\mu i} X^{\star}_i/\sqrt{n}|$, for a large class of…
With the rise of the Internet of Things, strategies for effectively processing big data are essential for discovering meaningul insights. The time series datasets produced by groups of interconnected devices contain valuable underlying…
The paper suggests a method of recovering missing values for sequences, including sequences with a multidimensional index, based on optimal approximation by processes featuring spectrum degeneracy. The problem is considered in the pathwise…
In this paper, we propose a new global geometry constraint for depth completion. By assuming depth maps often lay on low dimensional subspaces, a dense depth map can be approximated by a weighted sum of full-resolution principal depth…
Discrete optimal transport solvers do not scale well on dense large problems since they do not explicitly exploit the geometric structure of the cost function. In analogy to continuous optimal transport we provide a framework to verify…
Implicit neural representations have shown promising potential for the 3D scene reconstruction. Recent work applies it to autonomous 3D reconstruction by learning information gain for view path planning. Effective as it is, the computation…
Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to $\infty$, one recovers the constrained solution. In the exact…
We present an essentially exact numerical method for modelling flux qubit chains subject to charge and flux noise. We define an essentially exact method as one that introduces errors that are completely controlled such that they can be made…
We develop a multidimensional version of Gradient-MUSIC for estimating the frequencies of a nonharmonic signal from noisy samples. The guiding principle is that frequency recovery should be based only on the signal subspace determined by…
This work is concerned with the following fundamental question in scientific machine learning: Can deep-learning-based methods solve noise-free inverse problems to near-perfect accuracy? Positive evidence is provided for the first time,…
Geometry reconstruction of textureless, non-Lambertian objects under unknown natural illumination (i.e., in the wild) remains challenging as correspondences cannot be established and the reflectance cannot be expressed in simple analytical…
The rapid developing area of compressed sensing suggests that a sparse vector lying in an arbitrary high dimensional space can be accurately recovered from only a small set of non-adaptive linear measurements. Under appropriate conditions…
Paths in a given network are a generalised form of time-serial chains in many real-world applications, such as trajectories and Internet flows. Differentially private trajectory publishing concerns publishing path information that is usable…
An important open problem in robotic planning is the autonomous generation of 3D inspection paths -- that is, planning the best path to move a robot along in order to inspect a target structure. We recently suggested a new method for…
Unstructured environments are difficult for autonomous driving. This is because various unknown obstacles are lied in drivable space without lanes, and its width and curvature change widely. In such complex environments, searching for a…