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We study the multi-reference alignment (MRA) problem of recovering a signal from noisy observations acted on by unknown random circular shifts. While the information-theoretic limits of MRA are well characterized in many settings, the…

Signal Processing · Electrical Eng. & Systems 2026-02-12 Amnon Balanov , Wasim Huleihel , Tamir Bendory

In recent years, there is a growing need for processing methods aimed at extracting useful information from large datasets. In many cases the challenge is to discover a low-dimensional structure in the data, often concealed by the existence…

Statistics Theory · Mathematics 2019-06-05 Yariv Aizenbud , Boris Landa , Yoel Shkolnisky

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 orbit by accessing multiple independent observations. Of…

Information Theory · Computer Science 2018-11-06 Emmanuel Abbe , Tamir Bendory , William Leeb , João Pereira , Nir Sharon , Amit Singer

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 regime, and show that a signal in $\mathbb{R}^M$ is uniquely…

Information Theory · Computer Science 2020-11-10 Tamir Bendory , Ariel Jaffe , William Leeb , Nir Sharon , Amit Singer

We propose a nonlinear, wavelet based signal representation that is translation invariant and robust to both additive noise and random dilations. Motivated by the multi-reference alignment problem and generalizations thereof, we analyze the…

Signal Processing · Electrical Eng. & Systems 2020-07-14 Matthew Hirn , Anna Little

Accurate spectral analysis of high-energy astrophysical sources often relies on comparing observed data to incident spectral models convolved with the instrument response. However, for Gamma-Ray Bursts and other high-energy transient events…

This paper studies the application of the generalized method of moments (GMM) to multi-reference alignment (MRA): the problem of estimating a signal from its circularly-translated and noisy copies. We begin by proving that the GMM estimator…

Signal Processing · Electrical Eng. & Systems 2022-04-06 Asaf Abas , Tamir Bendory , Nir Sharon

We propose a novel algorithm for image reconstruction in radio interferometry. The ill-posed inverse problem associated with the incomplete Fourier sampling identified by the visibility measurements is regularized by the assumption of…

Instrumentation and Methods for Astrophysics · Physics 2012-10-12 R. E. Carrillo , J. D. McEwen , Y. Wiaux

The Multi-Reference Alignment (MRA) problem aims at the recovery of an unknown signal from repeated observations under the latent action of a group of cyclic isometries, in the presence of additive noise of high intensity $\sigma$. It is a…

Statistics Theory · Mathematics 2023-12-14 Subhro Ghosh , Soumendu Sundar Mukherjee , Jing Bin Pan

The estimation of the frequencies of multiple superimposed exponentials in noise is an important research problem due to its various applications from engineering to chemistry. In this paper, we propose an efficient and accurate algorithm…

Numerical Analysis · Mathematics 2016-05-05 Shanglin Ye , Elias Aboutanios

From molecular imaging to wireless communications, the ability to align and reconstruct signals from multiple misaligned observations is crucial for system performance. We study the problem of multi-reference alignment (MRA), which arises…

Machine Learning · Computer Science 2025-11-06 Rob Romijnders , Gabriele Cesa , Christos Louizos , Kumar Pratik , Arash Behboodi

This paper presents a novel approach for estimating the modes of an observed non-stationary mixture signal. A link is first established between the short-time Fourier transform and the sparse sampling theory, where the observations are…

Numerical Analysis · Mathematics 2022-12-23 Quentin Legros , Dominique Fourer

Multiple rotation averaging is an essential task for structure from motion, mapping, and robot navigation. The task is to estimate the absolute orientations of several cameras given some of their noisy relative orientation measurements. The…

Computer Vision and Pattern Recognition · Computer Science 2020-07-29 Pulak Purkait , Tat-Jun Chin , Ian Reid

High-dimensional matrix regression has been studied in various aspects, such as statistical properties, computational efficiency and application to specific instances including multivariate regression, system identification and matrix…

Statistics Theory · Mathematics 2024-03-06 Xin Li , Dongya Wu

Phase-rectified signal averaging (PRSA) is a widely used algorithm to analyze nonstationary biomedical time series. The method operates by identifying hinge points in the time series according to prescribed rules, extracting segments…

Statistics Theory · Mathematics 2025-11-04 Jiro Akahori , Joseph Najnudel , Hau-Tieng Wu , Ju-Yi Yen

Multi-reference alignment entails estimating a signal in $\mathbb{R}^L$ from its circularly-shifted and noisy copies. This problem has been studied thoroughly in recent years, focusing on the finite-dimensional setting (fixed $L$).…

Information Theory · Computer Science 2021-10-01 Elad Romanov , Tamir Bendory , Or Ordentlich

We introduce a new rotationally invariant viewing angle classification method for identifying, among a large number of Cryo-EM projection images, similar views without prior knowledge of the molecule. Our rotationally invariant features are…

Biomolecules · Quantitative Biology 2014-03-19 Zhizhen Zhao , Amit Singer

Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivariate signals is usually carried out by analyzing two separate…

Methodology · Statistics 2016-09-09 Julien Flamant , Nicolas Le Bihan , Pierre Chainais

The growing role of data-driven approaches to scientific discovery has unveiled a large class of models that involve latent transformations with a rigid algebraic constraint. Three-dimensional molecule reconstruction in Cryo-Electron…

Information Theory · Computer Science 2019-06-04 Amelia Perry , Jonathan Weed , Afonso S. Bandeira , Philippe Rigollet , Amit Singer

In this work, we consider the problem of multi-pitch estimation, i.e., identifying super-imposed truncated harmonic series from noisy measurements. We phrase this as recovering a harmonically-structured measure on the unit circle, where the…

Signal Processing · Electrical Eng. & Systems 2025-08-05 Anton Björkman , Filip Elvander