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Found 40 papers, 18 papers with code
Moment-based metrics for molecules computable from cryo-EM images
Further, we introduce a metric between a stack of projection images and a molecular structure, which is invariant to rotations and reflections and does not require performing 3-D reconstruction.
Alignment of Density Maps in Wasserstein Distance
In this paper we propose an algorithm for aligning three-dimensional objects when represented as density maps, motivated by applications in cryogenic electron microscopy.
A stochastic approximate expectation-maximization for structure determination directly from cryo-EM micrographs
A single-particle cryo-electron microscopy (cryo-EM) measurement, called a micrograph, consists of multiple two-dimensional tomographic projections of a three-dimensional molecular structure at unknown locations, taken under unknown viewing directions.
Fast expansion into harmonics on the disk: a steerable basis with fast radial convolutions
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) on the disk.
A Molecular Prior Distribution for Bayesian Inference Based on Wilson Statistics
Furthermore, it improves the resolution of estimates on the problems considered for a wide range of SNR and produces Fourier Shell Correlation curves that are insensitive to masking effects.
Ab-initio Contrast Estimation and Denoising of Cryo-EM Images
We show that the contrast variability can be derived from the 2-D covariance matrix and we apply the existing Covariance Wiener Filtering (CWF) framework to estimate it.
An approximate expectation-maximization for two-dimensional multi-target detection
We consider the two-dimensional multi-target detection (MTD) problem of estimating a target image from a noisy measurement that contains multiple copies of the image, each randomly rotated and translated.
Multi-target detection with rotations
We demonstrate that, regardless of the level of noise, our technique can be used to recover the target image when the measurement is sufficiently large.
Manifold learning with arbitrary norms
Manifold learning methods play a prominent role in nonlinear dimensionality reduction and other tasks involving high-dimensional data sets with low intrinsic dimensionality.
Wasserstein K-Means for Clustering Tomographic Projections
Motivated by the 2D class averaging problem in single-particle cryo-electron microscopy (cryo-EM), we present a k-means algorithm based on a rotationally-invariant Wasserstein metric for images.
Product Manifold Learning
Mathematically, if the parameter space of each continuous independent motion is a manifold, then their combination is known as a product manifold.
NMR Assignment through Linear Programming
Nuclear Magnetic Resonance (NMR) Spectroscopy is the second most used technique (after X-ray crystallography) for structural determination of proteins.
Image recovery from rotational and translational invariants
We introduce a framework for recovering an image from its rotationally and translationally invariant features based on autocorrelation analysis.
Earthmover-based manifold learning for analyzing molecular conformation spaces
In this paper, we propose a novel approach for manifold learning that combines the Earthmover's distance (EMD) with the diffusion maps method for dimensionality reduction.
Bias and variance reduction and denoising for CTF Estimation
Our method is based on the multi-taper method for power spectral density estimation, which aims to reduce the bias and variance of the estimator.
Hyper-Molecules: on the Representation and Recovery of Dynamical Structures, with Application to Flexible Macro-Molecular Structures in Cryo-EM
We introduce the ``hyper-molecule'' framework for modeling structures across different states of heterogeneous molecules, including continuums of states.
Cryo-EM reconstruction of continuous heterogeneity by Laplacian spectral volumes
An important challenge in cryo-EM is the reconstruction of non-rigid molecules with parts that move and deform.
Steerable $e$PCA: Rotationally Invariant Exponential Family PCA
The second is steerable PCA, a fast and accurate procedure for including all planar rotations for PCA.
Heterogeneous multireference alignment for images with application to 2-D classification in single particle reconstruction
In this problem, the goal is to estimate a (typically small) set of target images from a (typically large) collection of observations.
APPLE Picker: Automatic Particle Picking, a Low-Effort Cryo-EM Framework
Selecting particles from the micrographs is difficult especially for small particles with low contrast.
Anisotropic twicing for single particle reconstruction using autocorrelation analysis
The missing phase problem in X-ray crystallography is commonly solved using the technique of molecular replacement, which borrows phases from a previously solved homologous structure, and appends them to the measured Fourier magnitudes of the diffraction patterns of the unknown structure.
Continuously heterogeneous hyper-objects in cryo-EM and 3-D movies of many temporal dimensions
One of the great opportunities in cryo-EM is to recover the structure of macromolecules in heterogeneous samples, where multiple types or multiple conformations are mixed together.
A New Rank Constraint on Multi-view Fundamental Matrices, and its Application to Camera Location Recovery
We show that in general, with the selection of proper scale factors, a matrix formed by stacking fundamental matrices between pairs of images has rank 6.
A Survey of Structure from Motion
The structure from motion (SfM) problem in computer vision is the problem of recovering the three-dimensional ($3$D) structure of a stationary scene from a set of projective measurements, represented as a collection of two-dimensional ($2$D) images, via estimation of motion of the cameras corresponding to these images.
$e$PCA: High Dimensional Exponential Family PCA
We develop $e$PCA (exponential family PCA), a new methodology for PCA on exponential family distributions.
Methodology
Mahalanobis Distance for Class Averaging of Cryo-EM Images
Single particle reconstruction (SPR) from cryo-electron microscopy (EM) is a technique in which the 3D structure of a molecule needs to be determined from its contrast transfer function (CTF) affected, noisy 2D projection images taken at unknown viewing directions.
A Representation Theory Perspective on Simultaneous Alignment and Classification
One of the difficulties in 3D reconstruction of molecules from images in single particle Cryo-Electron Microscopy (Cryo-EM), in addition to high levels of noise and unknown image orientations, is heterogeneity in samples: in many cases, the samples contain a mixture of molecules, or multiple conformations of one molecule.
Denoising and Covariance Estimation of Single Particle Cryo-EM Images
In CWF, the covariance matrix of the projection images is used within the classical Wiener filtering framework for solving the image restoration deconvolution problem.
Non-unique games over compact groups and orientation estimation in cryo-EM
Let $\mathcal{G}$ be a compact group and let $f_{ij} \in L^2(\mathcal{G})$.
Covariance estimation using conjugate gradient for 3D classification in Cryo-EM
Classifying structural variability in noisy projections of biological macromolecules is a central problem in Cryo-EM.
Fast Steerable Principal Component Analysis
Cryo-electron microscopy nowadays often requires the analysis of hundreds of thousands of 2D images as large as a few hundred pixels in each direction.
Orthogonal Matrix Retrieval in Cryo-Electron Microscopy
In single particle reconstruction (SPR) from cryo-electron microscopy (cryo-EM), the 3D structure of a molecule needs to be determined from its 2D projection images taken at unknown viewing directions.
Robust Camera Location Estimation by Convex Programming
$3$D structure recovery from a collection of $2$D images requires the estimation of the camera locations and orientations, i. e. the camera motion.
Open problem: Tightness of maximum likelihood semidefinite relaxations
We have observed an interesting, yet unexplained, phenomenon: Semidefinite programming (SDP) based relaxations of maximum likelihood estimators (MLE) tend to be tight in recovery problems with noisy data, even when MLE cannot exactly recover the ground truth.
Stable Camera Motion Estimation Using Convex Programming
We further identify the implications of parallel rigidity theory for the location estimation problem to be well-posed, and prove exact (in the noiseless case) and stable location recovery results.
Rotationally Invariant Image Representation for Viewing Direction Classification in Cryo-EM
Our pipeline for viewing angle classification and alignment is experimentally shown to be faster and more accurate than reference-free alignment with rotationally invariant K-means clustering, MSA/MRA 2D classification, and their modern approximations.
Global registration of multiple point clouds using semidefinite programming
We empirically demonstrate that (a) unlike the spectral relaxation, the relaxation gap is mostly zero for the semidefinite program (i. e., we are able to solve the original non-convex least-squares problem) up to a certain noise threshold, and (b) the semidefinite program performs significantly better than spectral and manifold-optimization methods, particularly at large noise levels.
Spectral Convergence of the connection Laplacian from random samples
We prove that the eigenvectors and eigenvalues of these Laplacians converge in the limit of infinitely many independent random samples.
Orientation Determination from Cryo-EM images Using Least Unsquared Deviation
An approximation to the least squares global self consistency error was obtained using convex relaxation by semidefinite programming.
Vector Diffusion Maps and the Connection Laplacian
We introduce {\em vector diffusion maps} (VDM), a new mathematical framework for organizing and analyzing massive high dimensional data sets, images and shapes.
