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Scanning Electron Microscopy (SEM) is critical in nanotechnology, materials science, and biological imaging due to its high spatial resolution and depth of focus. Signal-to-noise ratio (SNR) is an essential parameter in SEM because it…
Serial section electron microscopy (ssEM) is a widely used technique for obtaining volumetric information of biological tissues at nanometer scale. However, accurate 3D reconstructions of identified cellular structures and volumetric…
The group synchronization problem involves estimating a collection of group elements from noisy measurements of their pairwise ratios. This task is a key component in many computational problems, including the molecular reconstruction…
X-ray single particle imaging involves the measurement of a large number of noisy diffraction patterns of isolated objects in random orientations. The missing information about these patterns is then computationally recovered in order to…
Recording atomic-resolution transmission electron microscopy (TEM) images is becoming increasingly routine. A new bottleneck is then analyzing this information, which often involves time-consuming manual structural identification. We have…
While electron microscopy offers crucial atomic-resolution insights into structure-property relationships, radiation damage severely limits its use on beam-sensitive materials like proteins and 2D materials. To overcome this challenge, we…
Macromolecules change their shape (conformation) in the process of carrying out their functions. The imaging by cryo-electron microscopy of rapidly-frozen, individual copies of macromolecules (single particles) is a powerful and general…
This work studies the sample complexity of the multi-target detection (MTD) problem, which involves recovering a signal from a noisy measurement containing multiple instances of a target signal in unknown locations, each transformed by a…
A major limitation of two-dimensional scanning electron microscopy (SEM) in imaging porous membranes is its inability to resolve three-dimensional pore architecture and interconnectivity, which are critical factors governing membrane…
We study a class of orbit recovery problems in which we observe independent copies of an unknown element of $\mathbb{R}^p$, each linearly acted upon by a random element of some group (such as $\mathbb{Z}/p$ or $\mathrm{SO}(3)$) and then…
Motivated by applications to single-particle cryo-electron microscopy (cryo-EM), we study several problems of function estimation in a high noise regime, where samples are observed after random rotation and possible linear projection of the…
Electron Cryo-Tomography (ECT) enables 3D visualization of macromolecule structure inside single cells. Macromolecule classification approaches based on convolutional neural networks (CNN) were developed to separate millions of…
The multi-reference alignment (MRA) problem entails estimating an image from multiple noisy and rotated copies of itself. If the noise level is low, one can reconstruct the image by estimating the missing rotations, aligning the images, and…
Central to the application of many multi-view geometry algorithms is the extraction of matching points between multiple viewpoints, enabling classical tasks such as camera pose estimation and 3D reconstruction. Many approaches that…
Microstructure reconstruction is an important cornerstone to the inverse materials design concept. In this work, a general algorithm is developed to reconstruct a three-dimensional microstructure from given descriptors. Based on…
Cryogenic electron tomography is a technique for imaging biological samples in 3D. A microscope collects a series of 2D projections of the sample, and the goal is to reconstruct the 3D density of the sample called the tomogram.…
Transmission electron microscopy (TEM) is a powerful imaging tool that has found broad application in materials science, nanoscience and biology(1-3). With the introduction of aberration-corrected electron lenses, both the spatial…
We introduce the EMC algorithm for reconstructing a particle's 3D diffraction intensity from very many photon shot-noise limited 2D measurements, when the particle orientation in each measurement is unknown. The algorithm combines a…
Increasing interest in three-dimensional nanostructures adds impetus to electron microscopy techniques capable of imaging at or below the nanoscale in three dimensions. We present a reconstruction algorithm that takes as input a focal…
We consider the two-dimensional multi-target detection problem of recovering a target image from a noisy measurement that contains multiple copies of the image, each randomly rotated and translated. Motivated by the structure reconstruction…