Related papers: Orthogonal Group Synchronization with Incomplete M…
Given the noisy pairwise measurements among a set of unknown group elements, how to recover them efficiently and robustly? This problem, known as group synchronization, has drawn tremendous attention in the scientific community. In this…
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 $G^*_i {G^*_j}^{-1}$.…
Group synchronization is the problem of determining reliable global estimates from noisy local measurements on networks. The typical task for group synchronization is to assign elements of a group to the nodes of a graph in a way that…
An estimation problem of fundamental interest is that of phase synchronization, in which the goal is to recover a collection of phases using noisy measurements of relative phases. It is known that in the Gaussian noise setting, the maximum…
This paper proposes a Generalized Power Method (GPM) to tackle the problem of community detection and group synchronization simultaneously in a direct non-convex manner. Under the stochastic group block model (SGBM), theoretical analysis…
Group synchronization asks to recover group elements from their pairwise measurements. It has found numerous applications across various scientific disciplines. In this work, we focus on orthogonal and permutation group synchronization…
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 -…
Group synchronization aims to recover the group elements from their noisy pairwise measurements. It has found many applications in community detection, clock synchronization, and joint alignment problem. This paper focuses on the orthogonal…
Orthogonal Matching Pursuit (OMP) has been a powerful method in sparse signal recovery and approximation. However, OMP suffers computational issues when the signal has a large number of non-zeros. This paper advances OMP and its extension…
Given multiple point clouds, how to find the rigid transform (rotation, reflection, and shifting) such that these point clouds are well aligned? This problem, known as the generalized orthogonal Procrustes problem (GOPP), has found numerous…
The generalized orthogonal Procrustes problem (GOPP) plays a fundamental role in several scientific disciplines including statistics, imaging science and computer vision. Despite its tremendous practical importance, it is generally an…
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 study the statistical estimation problem of orthogonal group synchronization and rotation group synchronization. The model is $Y_{ij} = Z_i^* Z_j^{*T} + \sigma W_{ij}\in\mathbb{R}^{d\times d}$ where $W_{ij}$ is a Gaussian random matrix…
Finding group elements from noisy measurements of their pairwise ratios is also known as the group synchronization problem, first introduced in the context of the group SO(2) of planar rotations, whose usefulness has been demonstrated…
In Group Synchronization, one attempts to find a collection of unknown group elements from noisy measurements of their pairwise differences. Several important problems in vision and data analysis reduce to group synchronization over various…
We study the performance of the spectral method for the phase synchronization problem with additive Gaussian noises and incomplete data. The spectral method utilizes the leading eigenvector of the data matrix followed by a normalization…
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…
Group synchronization arises when two or more synchronization patterns coexist in a network formed of oscillators of different types, with the systems in each group synchronizing on the same time-evolution, but systems in different groups…
We consider the group testing problem, in which one seeks to identify a subset of defective items within a larger set of items based on a number of noisy tests. While matching achievability and converse bounds are known in several cases of…
We investigate group-level synchronization between oscillator groups induced by common noise in the absence of inter-group coupling. Each group receives a common noise shared by all its oscillators and independent local noise inputs to…