# Method of moments for 3D single particle ab initio modeling with non-uniform distribution of viewing angles

@article{Sharon2020MethodOM, title={Method of moments for 3D single particle ab initio modeling with non-uniform distribution of viewing angles}, author={Nir Sharon and Joe Kileel and Yuehaw Khoo and Boris Landa and Amit Singer}, journal={Inverse Problems}, year={2020}, volume={36} }

Single-particle reconstruction in cryo-electron microscopy (cryo-EM) is an increasingly popular technique for determining the 3D structure of a molecule from several noisy 2D projections images taken at unknown viewing angles. Most reconstruction algorithms require a low-resolution initialization for the 3D structure, which is the goal of ab initio modeling. Suggested by Zvi Kam in 1980, the method of moments (MoM) offers one approach, wherein low-order statistics of the 2D images are computed…

## 29 Citations

### Toward single particle reconstruction without particle picking: Breaking the detection limit

- MathematicsbioRxiv
- 2018

This paper contends that the structure could, in principle, be reconstructed directly from the micrographs, without intermediate detection, and as a result, even small molecules should be within reach for cryo-EM.

### Autocorrelation analysis for cryo-EM with sparsity constraints: Improved sample complexity and projection-based algorithms

- Computer Science
- 2022

It is proved that molecular structures modeled as sums of idealized point masses are uniquely determined by the second-order autocorrelation of their projection images, implying that the sample complexity is proportional to the square of the variance of the noise.

### Computational Methods for Single-Particle Cryo-EM

- Chemistry
- 2020

Computational methods for structure determination by single-particle cryo-EM and their guiding principles from statistical inference, machine learning, and signal processing that also play a significant role in many other data science applications are discussed.

### Learning to recover orientations from projections in single-particle cryo-EM

- Computer ScienceArXiv
- 2021

The proposed method offers a novel learning-based take on orientation recovery in SPA, and demonstrates that orientations can be accurately recovered from projections that are shifted and corrupted with a high level of noise.

### The sample complexity of sparse multi-reference alignment and single-particle cryo-electron microscopy

- Computer Science
- 2022

The second moment of the MRA and cryo-EM models is analyzed, showing that in both models the second moment determines the signal up to a set of unitary matrices, whose dimension is governed by the decomposition of the space of signals into irreducible representations of the group.

### Orthogonal Matrix Retrieval with Spatial Consensus for 3D Unknown-View Tomography

- Computer ScienceArXiv
- 2022

This work proposes to jointly recover the density map and the orthogonal matrices by requiring that they be mutually consistent, and designs an easy-to-compute initial density map which effectively mitigates the non-convexity of the reconstruction problem.

### Fast Principal Component Analysis for Cryo-EM Images

- Computer ScienceArXiv
- 2022

A fast method for estimating a compressed representa- tion of the 2-D covariance matrix of noisy cryo-electron microscopy projection images that enables fast PCA computation and is based on a new algorithm for expanding ages in the Fourier-Bessel basis.

### Denoiser-based projections for 2-D super-resolution multi-reference alignment

- Computer Science, Mathematics
- 2022

This work builds on recent advances in image processing, and harness the power of denoisers as priors of images, and design two computational frameworks to estimate the image: projected expectation-maximization and projected method of moments.

### 3D Unknown View Tomography Via Rotation Invariants

- Mathematics, Computer ScienceICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
- 2020

The method obviates the need to recover the projection angles by extracting a set of rotation-invariant features from the noisy projection data by reconstructing the density map through a constrained nonconvex optimization.

### Motion Detection in Diffraction Tomography by Common Circle Methods

- MathematicsArXiv
- 2022

The method of common lines is a well-established reconstruction technique in cryogenic electron microscopy (cryo-EM), which can be used to extract the relative orientations of an object in…

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