Publications related to Optimal image alignment with random projections of manifolds: algorithm and geometric analysis

Convex optimization in sums of Banach spaces

We characterize the solution of a broad class of convex optimization problems that address the reconstruction of a function from a finite number of linear measurements. The underlying hypothesis is that the solution is decomposable as a finite sum of compo ...

2021

Shrinking Scale Equidistribution for Monochromatic Random Waves on Compact Manifolds

Matthew De Courcy-Ireland

We prove equidistribution at shrinking scales for the monochromatic ensemble on a compact Riemannian manifold of any dimension. This ensemble on an arbitrary manifold takes a slowly growing spectral window in order to synthesize a random function. With hig ...

OXFORD UNIV PRESS2021

A Multi-Agent Primal-Dual Strategy for Composite Optimization over Distributed Features

Ali H. Sayed, Sulaiman A S A E Alghunaim, Ming Yan

This work studies multi-agent sharing optimization problems with the objective function being the sum of smooth local functions plus a convex (possibly non-smooth) function coupling all agents. This scenario arises in many machine learning and engineering ...

IEEE2020

Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

Nicolas Henri Bernard Flammarion

We consider minimizing a nonconvex, smooth function

f

on a Riemannian manifold

\mathcal{M}

. We show that a perturbed version of Riemannian gradient descent algorithm converges to a second-order stationary point (and hence is able to escape saddle point ...

2019

Configuration Spaces Of Products

Kathryn Hess Bellwald

We show that the configuration spaces of a product of parallelizable manifolds may be recovered from those of the factors as the Boardman-Vogt tensor product of right modules over the operads of little cubes of the appropriate dimension. We also discuss an ...

2019

Scalable Low-rank Matrix and Tensor Decomposition on Graphs

Nauman Shahid

In many signal processing, machine learning and computer vision applications, one often has to deal with high dimensional and big datasets such as images, videos, web content, etc. The data can come in various forms, such as univariate or multivariate time ...

EPFL2017

A Fourier dimensionality reduction model for big data interferometric imaging

Jean-Philippe Thiran, Yves Wiaux, Rafael Eduardo Carrillo Rangel, Vijay Kartik

Data dimensionality reduction in radio interferometry can provide savings of computational resources for image reconstruction through reduced memory footprints and lighter computations per iteration, which is important for the scalability of imaging method ...

Oxford Univ Press2017

The tropical momentum map: a classification of toric log symplectic manifolds

Tudor Ratiu

We give a generalization of toric symplectic geometry to Poisson manifolds which are symplectic away from a collection of hypersurfaces forming a normal crossing configuration. We introduce the tropical momentum map, which takes values in a generalization ...

Springer Verlag2017

Time synchronization of consumer cameras on Micro Aerial Vehicles

Jan Skaloud, Martin Rehak

This article discusses the problem of time registration between navigation and imaging components on Micro Aerial Vehicles (MAVs). Accurate mapping with MAVs is gaining importance in applications such as corridor mapping, road and pipeline inspections or m ...

Elsevier2017

Riemannian Optimization for Solving High-Dimensional Problems with Low-Rank Tensor Structure

Michael Maximilian Steinlechner

In this thesis, we present a Riemannian framework for the solution of high-dimensional optimization problems with an underlying low-rank tensor structure. Here, the high-dimensionality refers to the size of the search space, while the cost function is scal ...

EPFL2016

Optimal image alignment with random projections of manifolds: algorithm and geometric analysis

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Convex optimization in sums of Banach spaces

Shrinking Scale Equidistribution for Monochromatic Random Waves on Compact Manifolds

A Multi-Agent Primal-Dual Strategy for Composite Optimization over Distributed Features

Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

Configuration Spaces Of Products

Scalable Low-rank Matrix and Tensor Decomposition on Graphs

A Fourier dimensionality reduction model for big data interferometric imaging

The tropical momentum map: a classification of toric log symplectic manifolds

Time synchronization of consumer cameras on Micro Aerial Vehicles

Riemannian Optimization for Solving High-Dimensional Problems with Low-Rank Tensor Structure

Convex optimization in sums of Banach spaces

Scalable Low-rank Matrix and Tensor Decomposition on Graphs

A Fourier dimensionality reduction model for big data interferometric imaging

Riemannian Optimization for Solving High-Dimensional Problems with Low-Rank Tensor Structure

Configuration Spaces Of Products

Time synchronization of consumer cameras on Micro Aerial Vehicles

Shrinking Scale Equidistribution for Monochromatic Random Waves on Compact Manifolds

A Multi-Agent Primal-Dual Strategy for Composite Optimization over Distributed Features

Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

The tropical momentum map: a classification of toric log symplectic manifolds