Amit Singer
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View article: Misspecified Maximum Likelihood Estimation for Non-Uniform Group Orbit Recovery
Misspecified Maximum Likelihood Estimation for Non-Uniform Group Orbit Recovery Open
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…
View article: Diagonally-Weighted Generalized Method of Moments Estimation for Gaussian Mixture Modeling
Diagonally-Weighted Generalized Method of Moments Estimation for Gaussian Mixture Modeling Open
Since Pearson [Philosophical Transactions of the Royal Society of London. A, 185 (1894), pp. 71-110] first applied the method of moments (MM) for modeling data as a mixture of one-dimensional Gaussians, moment-based estimation methods have…
View article: The Inaugural Flatiron Institute Cryo-EM Conformational Heterogeneity Challenge
The Inaugural Flatiron Institute Cryo-EM Conformational Heterogeneity Challenge Open
Despite the rise of single particle cryo-electron microscopy (cryo-EM) as a premier method for resolving macromolecular structures at atomic resolution, methods to address molecular heterogeneity in vitrified samples have yet to reach matu…
View article: Image-processing methods for electron microscopy of biological specimens
Image-processing methods for electron microscopy of biological specimens Open
The focused issue on Image-processing methods for electron microscopy of biological specimens is introduced. The virtual issue is available at https://journals.iucr.org/special_issues/2025/imageprocessing.
View article: Manifold learning in metric spaces
Manifold learning in metric spaces Open
Laplacian-based methods are popular for the dimensionality reduction of data lying in $\mathbb{R}^N$. Several theoretical results for these algorithms depend on the fact that the Euclidean distance locally approximates the geodesic distanc…
View article: Cryo-EM heterogeneity analysis using regularized covariance estimation and kernel regression
Cryo-EM heterogeneity analysis using regularized covariance estimation and kernel regression Open
Proteins and the complexes they form are central to nearly all cellular processes. Their flexibility, expressed through a continuum of states, provides a window into their biological functions. Cryogenic electron microscopy (cryo-EM) is an…
View article: Bayesian Perspective for Orientation Determination in Cryo-EM with Application to Structural Heterogeneity Analysis
Bayesian Perspective for Orientation Determination in Cryo-EM with Application to Structural Heterogeneity Analysis Open
Accurate orientation estimation is a crucial component of 3D molecular structure reconstruction, both in single-particle cryo-electron microscopy (cryo-EM) and in the increasingly popular field of cryo-electron tomography (cryo-ET). The do…
View article: Subspace method of moments for ab initio 3-D single-particle cryo-EM reconstruction
Subspace method of moments for ab initio 3-D single-particle cryo-EM reconstruction Open
Cryo-electron microscopy (cryo-EM) is a widely used technique for recovering the 3-D structure of biological molecules from a large number of experimentally generated noisy 2-D tomographic projection images of the 3-D structure, taken from…
View article: Fast expansion into harmonics on the ball
Fast expansion into harmonics on the ball Open
We devise fast and provably accurate algorithms to transform between an $N\times N \times N$ Cartesian voxel representation of a three-dimensional function and its expansion into the {ball harmonics}, that is, the eigenbasis of the Dirichl…
View article: Moment-based metrics for molecules computable from cryo-EM images
Moment-based metrics for molecules computable from cryo-EM images Open
Single particle cryogenic electron microscopy (cryo-EM) is an imaging technique capable of recovering the high-resolution 3-D structure of biological macromolecules from many noisy and randomly oriented projection images. One notable appro…
View article: Moment-based metrics for molecules computable from cryogenic electron microscopy images
Moment-based metrics for molecules computable from cryogenic electron microscopy images Open
Single-particle cryogenic electron microscopy (cryo-EM) is an imaging technique capable of recovering the high-resolution three-dimensional (3D) structure of biological macromolecules from many noisy and randomly oriented projection images…
View article: Self Fourier shell correlation: properties and application to cryo-ET
Self Fourier shell correlation: properties and application to cryo-ET Open
The Fourier shell correlation (FSC) is a measure of the similarity between two signals computed over corresponding shells in the frequency domain and has broad applications in microscopy. In structural biology, the FSC is ubiquitous in met…
View article: Cryo-EM Heterogeneity Analysis using Regularized Covariance Estimation and Kernel Regression
Cryo-EM Heterogeneity Analysis using Regularized Covariance Estimation and Kernel Regression Open
Proteins and the complexes they form are central to nearly all cellular processes. Their flexibility, expressed through a continuum of states, provides a window into their biological functions. Cryogenic electron microscopy (cryo-EM) is an…
View article: Fast Expansion into Harmonics on the Disk: A Steerable Basis with Fast Radial Convolutions
Fast Expansion into Harmonics on the Disk: A Steerable Basis with Fast Radial Convolutions Open
We present a fast and numerically accurate method for expanding digitized images representing functions on [-1, 1]2 supported on the disk in the harmonics (Dirichlet Laplacian eigenfunctions) on the disk. Our method, which …
View article: Toward Single Particle Reconstruction without Particle Picking: Breaking the Detection Limit
Toward Single Particle Reconstruction without Particle Picking: Breaking the Detection Limit Open
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 macromolecules. In a cryo-EM experiment, the microscope produces…
View article: Alignment of Density Maps in Wasserstein Distance
Alignment of Density Maps in Wasserstein Distance Open
In this paper we propose an algorithm for aligning three-dimensional objects when represented as density maps, motivated by applications in cryogenic electron microscopy. The algorithm is based on minimizing the 1-Wasserstein distance betw…
View article: Autocorrelation analysis for cryo-EM with sparsity constraints: Improved sample complexity and projection-based algorithms
Autocorrelation analysis for cryo-EM with sparsity constraints: Improved sample complexity and projection-based algorithms Open
The number of noisy images required for molecular reconstruction in single-particle cryoelectron microscopy (cryo-EM) is governed by the autocorrelations of the observed, randomly oriented, noisy projection images. In this work, we conside…
View article: Quantitatively Visualizing Bipartite Datasets
Quantitatively Visualizing Bipartite Datasets Open
As experiments continue to increase in size and scope, a fundamental challenge of subsequent analyses is to recast the wealth of information into an intuitive and readily interpretable form. Often, each measurement conveys only the relatio…
View article: Expectation-maximization for structure determination directly from cryo-EM micrographs
Expectation-maximization for structure determination directly from cryo-EM micrographs Open
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 …
View article: Fast principal component analysis for cryo-electron microscopy images
Fast principal component analysis for cryo-electron microscopy images Open
Principal component analysis (PCA) plays an important role in the analysis of cryo-electron microscopy (cryo-EM) images for various tasks such as classification, denoising, compression, and ab initio modeling. We introduce a fast method fo…
View article: Fast Principal Component Analysis for Cryo-EM Images
Fast Principal Component Analysis for Cryo-EM Images Open
Principal component analysis (PCA) plays an important role in the analysis of cryo-EM images for various tasks such as classification, denoising, compression, and ab-initio modeling. We introduce a fast method for estimating a compressed r…
View article: Representing Steerable Bases for cryo-EM in ASPIRE
Representing Steerable Bases for cryo-EM in ASPIRE Open
An introduction to the mathematical problem of cryo-electron microscopy (cryo-EM) is given, along with an overview of ASPIRE, an open-source Python package for processing cryo-EM image data. ASPIRE uses unique Fourier-Bessel basis represen…
View article: Multi-target detection with rotations
Multi-target detection with rotations Open
We consider the multi-target detection problem of estimating a two-dimensional target image from a large noisy measurement image that contains many randomly rotated and translated copies of the target image. Motivated by single-particle cr…
View article: Autocorrelation analysis for cryo-EM with sparsity constraints: Improved sample complexity and projection-based algorithms
Autocorrelation analysis for cryo-EM with sparsity constraints: Improved sample complexity and projection-based algorithms Open
The number of noisy images required for molecular reconstruction in single-particle cryo-electron microscopy (cryo-EM) is governed by the autocorrelations of the observed, randomly-oriented, noisy projection images. In this work, we consid…
View article: Fast expansion into harmonics on the disk: a steerable basis with fast radial convolutions
Fast expansion into harmonics on the disk: a steerable basis with fast radial convolutions Open
We present a fast and numerically accurate method for expanding digitized $L \times L$ images representing functions on $[-1,1]^2$ supported on the disk $\{x \in \mathbb{R}^2 : |x|<1\}$ in the harmonics (Dirichlet Laplacian eigenfunctions)…
View article: Quantitatively visualizing bipartite datasets
Quantitatively visualizing bipartite datasets Open
As experiments continue to increase in size and scope, a fundamental challenge of subsequent analyses is to recast the wealth of information into an intuitive and readily-interpretable form. Often, each measurement only conveys the relatio…
View article: Random conical tilt reconstruction without particle picking in cryo-electron microscopy
Random conical tilt reconstruction without particle picking in cryo-electron microscopy Open
A method is proposed to reconstruct the 3D molecular structure from micrographs collected at just one sample tilt angle in the random conical tilt scheme in cryo-electron microscopy. The method uses autocorrelation analysis on the microgra…