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Alternating projection onto convex sets (POCS) provides an iterative procedure to find a signal that satisfies two or more convex constraints when the sets intersect. For nonintersecting constraints, the method of simultaneous projections…
We consider the problem of signal reconstruction for computed tomography (CT) under a nonlinear forward model that accounts for exponential signal attenuation, a polychromatic X-ray source, general measurement noise (e.g., Poisson shot…
Uniqueness of solution is proved for any ptychographic scheme with a random masks under a minimum overlap condition and local geometric convergence analysis is given for the alternating projection (AP) and Douglas-Rachford (DR) algorithms.…
Photoacoustic tomography is an emerging medical imaging technology whose primary aim is to map the high-contrast optical properties of biological tissues by leveraging high-resolution ultrasound measurements. Mathematically, this can be…
Ptychography is a lensless imaging method that allows for wavefront sensing and phase-sensitive microscopy from a set of diffraction patterns. Recently, it has been shown that the optimization task in ptychography can be achieved via…
Tilting planar samples for multi-zone-axes observation is a routine procedure in electron microscopy. However, this process invariably introduces optical path differences in the electron beam across different sample positions, significantly…
Conventional tomographic reconstruction algorithms assume that one has obtained pure projection images, involving no within-specimen diffraction effects nor multiple scattering. Advances in x-ray nanotomography are leading towards the…
In tomographic reconstruction, the goal is to reconstruct an unknown object from a collection of line integrals. Given a complete sampling of such line integrals for various angles and directions, explicit inverse formulas exist to…
Imaging of biological cells and tissues often relies on fluorescent labels, which offer high contrast with molecular specificity. The use of exogenous labeling agents, however, may alter the normal physiology of the bio-specimens.…
Ever brighter light sources, fast parallel detectors, and advances in phase retrieval methods, have made ptychography a practical and popular imaging technique. Compared to previous techniques, ptychography provides superior robustness and…
This paper presents a variational based approach to fusing hyperspectral and multispectral images. The fusion process is formulated as an inverse problem whose solution is the target image assumed to live in a much lower dimensional…
Ptychography provides highly efficient imaging in scanning transmission electron microscopy (STEM), but questions have remained over its applicability to strongly scattering samples such as those most commonly seen in materialsscience.…
Plasma diagnostics often employ computerized tomography to estimate emissivity profiles from a finite, and often limited, number of line-integrated measurements. Decades of algorithmic refinement have brought considerable improvements, and…
Many signal processing algorithms break the target signal into overlapping segments (also called windows, or patches), process them separately, and then stitch them back into place to produce a unified output. At the overlaps, the final…
Prior panorama stitching approaches heavily rely on pairwise feature correspondences and are unable to leverage geometric consistency across multiple views. This leads to severe distortion and misalignment, especially in challenging scenes…
Existing approaches to image reconstruction in photoacoustic computed tomography (PACT) with acoustically heterogeneous media are limited to weakly varying media, are computationally burdensome, and/or cannot effectively mitigate the…
Reconstructing medical images from partial measurements is an important inverse problem in Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). Existing solutions based on machine learning typically train a model to directly map…
X-ray tomography is capable of imaging the interior of objects in three dimensions non-invasively, with applications in biomedical imaging, materials science, electronic inspection, and other fields. The reconstruction process can be an…
We use convolutional neural networks to recover images optically down-sampled by $6.7\times$ using coherent aperture synthesis over a 16 camera array. Where conventional ptychography relies on scanning and oversampling, here we apply…
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…