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Transmission electron microscopes use electrons with wavelengths of a few picometers, potentially capable of imaging individual atoms in solids at a resolution ultimately set by the intrinsic size of an atom. Unfortunately, due to…
A new set of discrete ordinates is proposed for one-dimensional radiative transfer in spheres with central symmetry. The set is structured with un-normalized circular functions. This resulted in a conservative and closed set of discrete…
Image restoration aims to recover high-quality images from degraded observations. When the degradation process is known, the recovery problem can be formulated as an inverse problem, and in a Bayesian context, the goal is to sample a clean…
In this paper we perform quantitative reconstruction of the electric susceptibility and the Gr\"uneisen parameter of a non-magnetic linear dielectric medium using measurement of a multi-modal photoacoustic and optical coherence tomography…
Electron ptychography describes a family of algorithms which are used to enable the reconstruction of complex specimen transmission functions of a sample in order to obtain both phase and amplitude information, as applied within the realms…
Diffraction tomography is a widely used inverse scattering technique for quantitative imaging of weakly scattering media. In its conventional formulation, diffraction tomography assumes monochromatic plane wave illumination. This…
We introduce ICE-TIDE, a method for cryogenic electron tomography (cryo-ET) that simultaneously aligns observations and reconstructs a high-resolution volume. The alignment of tilt series in cryo-ET is a major problem limiting the…
The Discrete Fourier Transform (DFT) underpins the solution to many inverse problems commonly possessing missing or un-measured frequency information. This incomplete coverage of Fourier space always produces systematic artefacts called…
We present a new digital holographic microscope (DHM) with a low coherent source for the quantitative imaging of smooth and optically rough objects. The experimental design of the microscope uses an in-line experimental geometry based on…
This article presents a method to perform diffraction tomography in a standard microscope that includes an LED array for illumination. After acquiring a sequence of intensity-only images of a thick sample, a ptychography-based…
We propose a general methodology for efficient statistical reconstruction of a quantum state through collection and analysis of photon counting statistics. Our approach includes both strict quantitative criteria for adequacy and…
Discrete tomography is concerned with the reconstruction of images that are defined on a discrete set of lattice points from their projections in several directions. The range of values that can be assigned to each lattice point is…
Fourier ptychography microscopy (FPM) is a new computational imaging technique that can provide gigapixel images with both high resolution and a wide field of view (FOV). However, time consuming of the data-acquisition process is a critical…
Cryo-electron microscopy (EM) single particle reconstruction is an entirely general technique for 3D structure determination of macromolecular complexes. However, because the images are taken at low electron dose, it is extremely hard to…
How, in principle, could one solve the atomic structure of a quasicrystal, modeled as a random tiling decorated by atoms, and what techniques are available to do it? One path is to solve the phase problem first, obtaining the density in a…
It has been a general trend to develop low-voltage electron microscopes due to their high imaging contrast of the sample and low radiation damage. Atom-resolved transmission electron microscopes with voltages as low as 15-40 kV have been…
In the process of performing image super-resolution processing, the processing of complex localized information can have a significant impact on the quality of the image generated. Fractal features can capture the rich details of both micro…
We consider the problem of reconstructing a nanocrystal at atomic resolution from electron microscopy images taken at a few tilt angles. A popular reconstruction approach called discrete tomography confines the atom locations to a coarse…
Optical diffraction tomography is an indispensable tool for studying objects in three-dimensions due to its ability to accurately reconstruct scattering objects. Until now this technique has been limited to coherent light because spatial…
This article provides an exposition of recent methodologies for nonparametric analysis of digital observations on images and other non-Euclidean objects. Fr\'echet means of distributions on metric spaces, such as manifolds and stratified…