148 citations · 567 across the 75 of their papers we have counts for
38 papers · 1 filter
Orbit recovery under the rigid motions group
Amnon Balanov, Tamir Bendory, Dan Edidin
We study the orbit recovery problem under the rigid-motion group SE(n), where the objective is to reconstruct an unknown signal from multiple noisy observations subjected to unknow…
A transversality theorem for semi-algebraic sets with application to signal recovery from the second moment and cryo-EM
Tamir Bendory, Nadav Dym, Dan Edidin +1
Semi-algebraic priors are ubiquitous in signal processing and machine learning. Prevalent examples include a) linear models where the signal lies in a low-dimensional subspace; b)…
Detection and Recovery of Hidden Submatrices
Marom Dadon, Wasim Huleihel, Tamir Bendory
In this paper, we study the problems of detection and recovery of hidden submatrices with elevated means inside a large Gaussian random matrix. We consider two different structures…
Finite alphabet phase retrieval
Tamir Bendory, Dan Edidin, Ivan Gonzalez
We consider the finite alphabet phase retrieval problem: recovering a signal whose entries lie in a small alphabet of possible values from its Fourier magnitudes. This problem aris…
The sample complexity of sparse multi-reference alignment and single-particle cryo-electron microscopy
Tamir Bendory, Dan Edidin
Multi-reference alignment (MRA) is the problem of recovering a signal from its multiple noisy copies, each acted upon by a random group element. MRA is mainly motivated by single-p…
On the Role of Channel Capacity in Learning Gaussian Mixture Models
Elad Romanov, Tamir Bendory, Or Ordentlich
This paper studies the sample complexity of learning the unknown centers of a balanced Gaussian mixture model (GMM) in with spherical covariance matrix $σ^2\math…
Near-optimal bounds for signal recovery from blind phaseless periodic short-time Fourier transform
Tamir Bendory, Chi-yu Cheng, Dan Edidin
We study the problem of recovering a signal from samples of its phaseless periodic short-time Fourier transform (STFT): the magnitude of the Fourier transform of…
Sparse multi-reference alignment: sample complexity and computational hardness
Tamir Bendory, Oscar Mickelin, Amit Singer
Motivated by the problem of determining the atomic structure of macromolecules using single-particle cryo-electron microscopy (cryo-EM), we study the sample and computational compl…
Dihedral multi-reference alignment
Tamir Bendory, Dan Edidin, William Leeb +1
We study the dihedral multi-reference alignment problem of estimating the orbit of a signal from multiple noisy observations of the signal, acted on by random elements of the dihed…
Signal recovery from a few linear measurements of its high-order spectra
Tamir Bendory, Dan Edidin, Shay Kreymer
The -th order spectrum is a polynomial of degree in the entries of a signal , which is invariant under circular shifts of the signal. For , this p…
Multi-reference alignment in high dimensions: sample complexity and phase transition
Elad Romanov, Tamir Bendory, Or Ordentlich
Multi-reference alignment entails estimating a signal in from its circularly-shifted and noisy copies. This problem has been studied thoroughly in recent years, focu…
Super-resolution multi-reference alignment
Tamir Bendory, Ariel Jaffe, William Leeb +2
We study super-resolution multi-reference alignment, the problem of estimating a signal from many circularly shifted, down-sampled, and noisy observations. We focus on the low SNR…
Toward a mathematical theory of the crystallographic phase retrieval problem
Tamir Bendory, Dan Edidin
Motivated by the X-ray crystallography technology to determine the atomic structure of biological molecules, we study the crystallographic phase retrieval problem, arguably the lea…
A note on Douglas-Rachford, gradients, and phase retrieval
Eitan Levin, Tamir Bendory
The properties of gradient techniques for the phase retrieval problem have received a considerable attention in recent years. In almost all applications, however, the phase retriev…
Single-particle cryo-electron microscopy: Mathematical theory, computational challenges, and opportunities
Tamir Bendory, Alberto Bartesaghi, Amit Singer
In recent years, an abundance of new molecular structures have been elucidated using cryo-electron microscopy (cryo-EM), largely due to advances in hardware technology and data pro…
Multi-target Detection with an Arbitrary Spacing Distribution
Ti-Yen Lan, Tamir Bendory, Nicolas Boumal +1
Motivated by the structure reconstruction problem in single-particle cryo-electron microscopy, we consider the multi-target detection model, where multiple copies of a target signa…
Multi-target detection with application to cryo-electron microscopy
Tamir Bendory, Nicolas Boumal, William Leeb +2
We consider the multi-target detection problem of recovering a set of signals that appear multiple times at unknown locations in a noisy measurement. In the low noise regime, one c…
Toward single particle reconstruction without particle picking: Breaking the detection limit
Tamir Bendory, Nicolas Boumal, William Leeb +2
Single-particle cryo-electron microscopy (cryo-EM) has recently joined X-ray crystallography and NMR spectroscopy as a high-resolution structural method to resolve biological macro…
Blind Phaseless Short-Time Fourier Transform Recovery
Tamir Bendory, Dan Edidin, Yonina C. Eldar
The problem of recovering a pair of signals from their blind phaseless short-time Fourier transform measurements arises in several important phase retrieval applications, including…
Stable Super-Resolution of Images: A Theoretical Study
Armin Eftekhari, Tamir Bendory, Gongguo Tang
We study the ubiquitous super-resolution problem, in which one aims at localizing positive point sources in an image, blurred by the point spread function of the imaging device. To…
Multireference Alignment is Easier with an Aperiodic Translation Distribution
Emmanuel Abbe, Tamir Bendory, William Leeb +3
In the multireference alignment model, a signal is observed by the action of a random circular translation and the addition of Gaussian noise. The goal is to recover the signal's o…
Heterogeneous multireference alignment: a single pass approach
Nicolas Boumal, Tamir Bendory, Roy R. Lederman +1
Multireference alignment (MRA) is the problem of estimating a signal from many noisy and cyclically shifted copies of itself. In this paper, we consider an extension called heterog…
On Signal Reconstruction from FROG Measurements
Tamir Bendory, Dan Edidin, Yonina C. Eldar
Phase retrieval refers to recovering a signal from its Fourier magnitude. This problem arises naturally in many scientific applications, such as ultra-short laser pulse characteriz…
Benchmark problems for phase retrieval
Veit Elser, Ti-Yen Lan, Tamir Bendory
In recent years, the mathematical and algorithmic aspects of the phase retrieval problem have received considerable attention. Many papers in this area mention crystallography as a…