arXiv subjects

Matt Walker

Publications and source records attributed to Matt Walker.

3 recordsLinked to original sources

arXiv2026

Bayesian Semi-Blind Deconvolution at Scale

Blind image deconvolution refers to the problem of simultaneously estimating the blur kernel and the true image from a set of observations when both the blur kernel and the true image are unknown. Sometimes, additional image and/or blur information is available and the term semi-blind deconvolution (SBD) is used. We consider a recently introduced Bayesian conjugate hierarchical model for SBD, formulated on an extended cyclic lattice to allow a computationally scalable Gibbs sampler. In this article, we extend this model to the general SBD problem, rewrite the previously proposed Gibbs sampler so that operations are performed in the Fourier domain whenever possible, and introduce a new marginal Hamiltonian Monte Carlo (HMC) blur update, obtained by analytically integrating the blur-image joint conditional over the image. The cyclic formulation combined with non-trivial linear algebra manipulations allows a Fourier-based, scalable HMC update, otherwise complicated by the rigid constraints of the SBD problem. Having determined the padding size in the cyclic embedding through a numerical experiment, we compare the mixing and exploration behaviour of the Gibbs and HMC blur updates on simulated data and on a real geophysical seismic imaging problem where we invert a grid with $300\times50$ nodes, corresponding to a posterior with approximately $80,000$ parameters.

stat.CO↗

arXiv2019

Relation Learning on Social Networks with Multi-Modal Graph Edge Variational Autoencoders

While node semantics have been extensively explored in social networks, little research attention has been paid to profile edge semantics, i.e., social relations. Ideal edge semantics should not only show that two users are connected, but also why they know each other and what they share in common. However, relations in social networks are often hard to profile, due to noisy multi-modal signals and limited user-generated ground-truth labels. In this work, we aim to develop a unified and principled framework that can profile user relations as edge semantics in social networks by integrating multi-modal signals in the presence of noisy and incomplete data. Our framework is also flexible towards limited or missing supervision. Specifically, we assume a latent distribution of multiple relations underlying each user link, and learn them with multi-modal graph edge variational autoencoders. We encode the network data with a graph convolutional network, and decode arbitrary signals with multiple reconstruction networks. Extensive experiments and case studies on two public DBLP author networks and two internal LinkedIn member networks demonstrate the superior effectiveness and efficiency of our proposed model.

cs.SI↗

arXiv2017

Theia: Faint objects in motion or the new astrometry frontier

In the context of the ESA M5 (medium mission) call we proposed a new satellite mission, Theia, based on relative astrometry and extreme precision to study the motion of very faint objects in the Universe. Theia is primarily designed to study the local dark matter properties, the existence of Earth-like exoplanets in our nearest star systems and the physics of compact objects. Furthermore, about 15 $\%$ of the mission time was dedicated to an open observatory for the wider community to propose complementary science cases. With its unique metrology system and "point and stare" strategy, Theia's precision would have reached the sub micro-arcsecond level. This is about 1000 times better than ESA/Gaia's accuracy for the brightest objects and represents a factor 10-30 improvement for the faintest stars (depending on the exact observational program). In the version submitted to ESA, we proposed an optical (350-1000nm) on-axis TMA telescope. Due to ESA Technology readiness level, the camera's focal plane would have been made of CCD detectors but we anticipated an upgrade with CMOS detectors. Photometric measurements would have been performed during slew time and stabilisation phases needed for reaching the required astrometric precision.

astro-ph.IM↗