相关论文: Radio Interferometric Calibration Using a Riemanni…

Full polarimetric radio interferometric calibration is performed by estimating 2 by 2 Jones matrices representing instrumental and propagation effects. The solutions obtained in this way differ from the true solutions by a 2 by 2 unitary…

In the context of next generation radio telescopes, like the Square Kilometre Array, the efficient processing of large-scale datasets is extremely important. Convex optimisation tasks under the compressive sensing framework have recently…

We propose a new Riemannian geometry for fixed-rank matrices that is specifically tailored to the low-rank matrix completion problem. Exploiting the degree of freedom of a quotient space, we tune the metric on our search space to the…

The increased sensitivity of future radio telescopes will result in requirements for higher dynamic range within the image as well as better resolution and immunity to interference. In this paper we propose a new matrix formulation of the…

Next-generation radio interferometers like the Square Kilometer Array have the potential to unlock scientific discoveries thanks to their unprecedented angular resolution and sensitivity. One key to unlocking their potential resides in…

In this paper, we design unimodular waveforms with good correlation properties for multi-input multi-output (MIMO) radar systems. Specifically, first, we analyze the geometric properties of the unimodular constraint in the fourth-order…

The integrated inertial system, typically integrating an IMU and an exteroceptive sensor such as radar, LiDAR, and camera, has been widely accepted and applied in modern robotic applications for ego-motion estimation, motion control, or…

[abridged] The International LOFAR Telescope is an interferometer with stations spread across Europe. With baselines of up to ~2,000 km, LOFAR has the unique capability of achieving sub-arcsecond resolution at frequencies below 200 MHz,…

We propose an inexact optimization algorithm on Riemannian manifolds, motivated by quadratic discrimination tasks in high-dimensional, low-sample-size (HDLSS) imaging settings. In such applications, gradient evaluations are often biased due…

The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this…

Rotation group $\mathcal{SO}(d)$ synchronization is an important inverse problem and has attracted intense attention from numerous application fields such as graph realization, computer vision, and robotics. In this paper, we focus on the…

We consider the problem of reconstructing an embedding of a compact connected Riemannian manifold in a Euclidean space up to an almost isometry, given the information on intrinsic distances between points from its ``sufficiently large''…

We examine a wide class of stochastic approximation algorithms for solving (stochastic) nonlinear problems on Riemannian manifolds. Such algorithms arise naturally in the study of Riemannian optimization, game theory and optimal transport,…

Programmable linear optical interferometers are important for classical and quantum information technologies, as well as for building hardware-accelerated artificial neural networks. Recent results showed the possibility of constructing…

The indicator matrix plays an important role in machine learning, but optimizing it is an NP-hard problem. We propose a new relaxation of the indicator matrix and prove that this relaxation forms a manifold, which we call the Relaxed…

We reformulate the gain correction problem of the radio interferometry as an optimization problem with regularization, which is solved efficiently with an iterative algorithm. Combining this new method with our previously proposed imaging…

We propose a Riemannian version of Nesterov's Accelerated Gradient algorithm (RAGD), and show that for geodesically smooth and strongly convex problems, within a neighborhood of the minimizer whose radius depends on the condition number as…

Euclidean representations distort data with intrinsic non-Euclidean structure. While Riemannian representation learning offers a solution by embedding data onto matching manifolds, it typically relies on an encoder to estimate densities on…

Recent work has successfully achieved sub-arcsecond wide-field imaging with high-band observations from the Low Frequency Array (LOFAR). However, the scalability of this work remains limited due to the need for manual intervention, poor…

Riemannian optimization uses local methods to solve optimization problems whose constraint set is a smooth manifold. A linear step along some descent direction usually leaves the constraints, and hence retraction maps are used to…