Related papers: Dynamic angular synchronization under smoothness c…
Given an undirected measurement graph $G = ([n], E)$, the classical angular synchronization problem consists of recovering unknown angles $\theta_1,\dots,\theta_n$ from a collection of noisy pairwise measurements of the form $(\theta_i -…
The angular synchronization problem is to obtain an accurate estimation (up to a constant additive phase) for a set of unknown angles $\theta_1,...,\theta_n$ from $m$ noisy measurements of their offsets $\theta_i-\theta_j \mod 2\pi$. Of…
The angular synchronization problem of estimating a set of unknown angles from their known noisy pairwise differences arises in various applications. It can be reformulated as a optimization problem on graphs involving the graph Laplacian…
We consider the problem of joint learning of multiple linear dynamical systems. This has received significant attention recently under different types of assumptions on the model parameters. The setting we consider involves a collection of…
The problem of synchronization over a group $\mathcal{G}$ aims to estimate a collection of group elements $G^*_1, \dots, G^*_n \in \mathcal{G}$ based on noisy observations of a subset of all pairwise ratios of the form $G^*_i {G^*_j}^{-1}$.…
Maximum likelihood estimation problems are, in general, intractable optimization problems. As a result, it is common to approximate the maximum likelihood estimator (MLE) using convex relaxations. In some cases, the relaxation is tight: it…
The synchronization problem over the special orthogonal group $SO(d)$ consists of estimating a set of unknown rotations $R_1,R_2,...,R_n$ from noisy measurements of a subset of their pairwise ratios $R_{i}^{-1}R_{j}$. The problem has found…
In this paper, we investigate an inverse random source problem concerned with recovering the strength of a random, uncorrelated acoustic source from correlation measurements of emitted time-harmonic acoustic waves. Such problems arise in…
We propose a novel formulation for phase synchronization -- the statistical problem of jointly estimating alignment angles from noisy pairwise comparisons -- as a nonconvex optimization problem that enforces consistency among the pairwise…
We consider the problem of tensor completion with graphs serving as side information to represent interrelationships among variables. Existing approaches suffer from several limitations: (1) they are often task-specific and lack generality…
We propose a distributed algorithm for time synchronization in mobile wireless sensor networks. Each node can employ the algorithm to estimate the global time based on its local clock time. The problem of time synchronization is formulated…
This paper addresses the problem of synchronizing orthogonal matrices over directed graphs. For synchronized transformations (or matrices), composite transformations over loops equal the identity. We formulate the synchronization problem as…
We consider a class of stochastic smooth convex optimization problems under rather general assumptions on the noise in the stochastic gradient observation. As opposed to the classical problem setting in which the variance of noise is…
Many important geometric estimation problems take the form of synchronization over the special Euclidean group: estimate the values of a set of poses given a set of relative measurements between them. This problem is typically formulated as…
We interpret steady linear statistical inverse problems as artificial dynamic systems with white noise and introduce a stochastic differential equation (SDE) system where the inverse of the ending time $T$ naturally plays the role of the…
We study the phase synchronization problem with noisy measurements $Y=z^*z^{*H}+\sigma W\in\mathbb{C}^{n\times n}$, where $z^*$ is an $n$-dimensional complex unit-modulus vector and $W$ is a complex-valued Gaussian random matrix. It is…
Group synchronization refers to estimating a collection of group elements from the noisy pairwise measurements. Such a nonconvex problem has received much attention from numerous scientific fields including computer vision, robotics, and…
Many geometric estimation problems take the form of synchronization over the special Euclidean group: estimate the values of a set of poses given noisy measurements of a subset of their pairwise relative transforms. This problem is…
We consider $\mathbb{Z}_2$-synchronization on the Euclidean lattice. Every vertex of $\mathbb{Z}^d$ is assigned an independent symmetric random sign $\theta_u$, and for every edge $(u,v)$ of the lattice, one observes the product…
Under a smart grid paradigm, there has been an increase in sensor installations to enhance situational awareness. The measurements from these sensors can be leveraged for real-time monitoring, control, and protection. However, these…