Related papers: Integer-ambiguity resolution in astronomy and geod…
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$…
We consider approximation algorithms for covering integer programs of the form min $\langle c, x \rangle $ over $x \in \mathbb{N}^n $ subject to $A x \geq b $ and $x \leq d$; where $A \in \mathbb{R}_{\geq 0}^{m \times n}$, $b \in…
Linear programming (LP) decoding approximates maximum-likelihood (ML) decoding of a linear block code by relaxing the equivalent ML integer programming (IP) problem into a more easily solved LP problem. The LP problem is defined by a set of…
We study the computational complexity certification of inexact gradient augmented Lagrangian methods for solving convex optimization problems with complicated constraints. We solve the augmented Lagrangian dual problem that arises from the…
We develop techniques to solve ill-posed inverse problems on the sphere by sparse regularisation, exploiting sparsity in both axisymmetric and directional scale-discretised wavelet space. Denoising, inpainting, and deconvolution problems,…
Inverse optimization is the problem of determining the values of missing input parameters for an associated forward problem that are closest to given estimates and that will make a given target vector optimal. This study is concerned with…
The problem of tensor completion has applications in healthcare, computer vision, and other domains. However, past approaches to tensor completion have faced a tension in that they either have polynomial-time computation but require…
The $L_{\infty}$ star discrepancy is a measure for the regularity of a finite set of points taken from $[0,1)^d$. Low discrepancy point sets are highly relevant for Quasi-Monte Carlo methods in numerical integration and several other…
Finding fast yet accurate numerical solutions to the Helmholtz equation remains a challenging task. The pollution error (i.e. the discrepancy between the numerical and analytical wave number k) requires the mesh resolution to be kept fine…
A common problem in applied mathematics is to find a function in a Hilbert space with prescribed best approximations from a finite number of closed vector subspaces. In the present paper we study the question of the existence of solutions…
We report a computational study of cutting plane algorithms for multi-stage stochastic mixed-integer programming models with the following cuts: (i) Benders', (ii) Integer L-shaped, and (iii) Lagrangian cuts. We first show that Integer…
Traditional lost-in-space algorithms, such as those implemented in astrometry.net, solve for spacecraft orientation by matching observed star fields to celestial catalogs using geometric asterisms alone. In this work, we propose a novel…
We present a method, called matching synthesis, for decoding quantum codes that produces an enhanced assignment of errors from an ensemble of decoders. We apply matching synthesis to develop a decoder named Libra, and show in simulations…
We introduce a class of specially structured linear programming (LP) problems, which has favorable modeling capability for important application problems in different areas such as optimal transport, discrete tomography and economics. To…
Objective: This review aims to explore the potential and challenges of using Natural Language Processing (NLP) to detect, correct, and mitigate medically inaccurate information, including errors, misinformation, and hallucination. By…
Due to the sheer complexity of the Laser Interferometer Space Antenna (LISA) space mission, data gaps arising from instrumental irregularities and/or scheduled maintenance are unavoidable. Focusing on merger-dominated massive black hole…
Ill-posed linear inverse problems (ILIP), such as restoration and reconstruction, are a core topic of signal/image processing. A standard approach to deal with ILIP uses a constrained optimization problem, where a regularization function is…
We study three problems that involve identifying homogeneous halfspaces under Gaussian distributions: agnostic learning, one-sided reliable learning, and fairness auditing. In each of these problems, we are given labeled examples…
This paper presents a novel formulation and solution of orbit determination over finite time horizons as a learning problem. We present an approach to orbit determination under very broad conditions that are satisfied for n-body problems.…
A simple, yet general, formalism for the optimized linear combination of astrophysical images is constructed and demonstrated. The formalism allows the user to combine multiple undersampled images to provide oversampled output at high…