Related papers: Maximum likelihood for high-noise group orbit esti…
We study a class of orbit recovery problems in which we observe independent copies of an unknown element of $\mathbb{R}^p$, each linearly acted upon by a random element of some group (such as $\mathbb{Z}/p$ or $\mathrm{SO}(3)$) and then…
Orbit recovery problems are a class of problems that often arise in practice and various forms. In these problems, we aim to estimate an unknown function after being distorted by a group action and observed via a known operator. Typically,…
In cryo-electron microscopy (cryo-EM), a microscope generates a top view of a sample of randomly-oriented copies of a molecule. The problem of single particle reconstruction (SPR) from cryo-EM is to use the resulting set of noisy 2D…
Single-particle cryo-electron microscopy (cryo-EM) is an emerging imaging modality capable of visualizing proteins and macro-molecular complexes at near-atomic resolution. The low electron-doses used to prevent sample radiation damage,…
We study maximum likelihood estimation (MLE) in the generalized group orbit recovery model, where each observation is generated by applying a random group action and a known, fixed linear operator to an unknown signal, followed by additive…
Motivated by the task of 2-D classification in single particle reconstruction by cryo-electron microscopy (cryo-EM), we consider the problem of heterogeneous multireference alignment of images. In this problem, the goal is to estimate a…
The computational pipelines of single-particle cryo-electron microscopy (cryo-EM) and cryo-electron tomography (cryo-ET) include an early particle-picking stage, in which a micrograph or tomogram is scanned to extract candidate particles,…
A single-particle cryo-electron microscopy (cryo-EM) measurement, called a micrograph, consists of multiple two-dimensional tomographic projections of a three-dimensional (3-D) molecular structure at unknown locations, taken under unknown…
Determining the three-dimensional structure of proteins and protein complexes at atomic resolution is a fundamental task in structural biology. Over the last decade, remarkable progress has been made using "single particle" cryo-electron…
Motivated by single-particle cryo-electron microscopy, multi-reference alignment (MRA) models the task of recovering an unknown signal from multiple noisy observations corrupted by random rotations. The standard approach,…
Cryo-Electron Microscopy (Cryo-EM) is a Nobel prize-winning technology for determining the 3D structure of particles at near-atomic resolution. A fundamental step in the recovering of the 3D single-particle structure is to align its 2D…
We study the connection between exceptional points (EPs) and optimal parameter estimation, in a simple system consisting of two counter-propagating traveling wave modes in a microring resonator. The unknown parameter to be estimated is the…
Electron cryomicroscopy (cryo-EM) is a technique in structural biology used to reconstruct accurate volumetric maps of molecules. One step of the cryo-EM pipeline involves solving an inverse-problem. This inverse-problem, referred to as…
In this paper we study the formal algebraic structure underlying the intrinsic classification algorithm, recently introduced by Hadani, Shkolnisky, Singer and Zhao, for classifying noisy projection images of similar viewing directions in…
We study the recovery of an unknown three-dimensional band-limited signal from multiple noisy observations that are randomly rotated by latent elements of SO(3), where the rotations are drawn from an unknown, non-uniform distribution.…
The group synchronization problem involves estimating a collection of group elements from noisy measurements of their pairwise ratios. This task is a key component in many computational problems, including the molecular reconstruction…
In this work we study orbit recovery over $SO(3)$, where the goal is to recover a function on the sphere from noisy, randomly rotated copies of it. We assume that the function is a linear combination of low-degree spherical harmonics. This…
Cryo-electron microscopy (Cryo-EM) enables high-resolution imaging of biomolecules, but structural heterogeneity remains a major challenge in 3D reconstruction. Traditional methods assume a discrete set of conformations, limiting their…
Cryo-electron microscopy (cryo-EM) has recently become a premier method for obtaining high-resolution structures of biological macromolecules. However, it is limited to biomolecular samples with low conformational heterogeneity, where all…
In single-particle cryo-electron microscopy (cryo-EM), the efficient determination of orientation parameters for 2D projection images poses a significant challenge yet is crucial for reconstructing 3D structures. This task is complicated by…