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The need for tomographic reconstruction from sparse measurements arises when the measurement process is potentially harmful, needs to be rapid, or is uneconomical. In such cases, prior information from previous longitudinal scans of the…
Motivated by single-particle cryo-electron microscopy, multi-reference alignment (MRA) models the task of recovering an unknown signal from multiple noisy observations corrupted by random rotations. The standard approach,…
Optical interferometers provide multiple wavelength measurements. In order to fully exploit the spectral and spatial resolution of these instruments, new algorithms for image reconstruction have to be developed. Early attempts to deal with…
Usual Structure-from-Motion (SfM) techniques require at least trifocal overlaps to calibrate cameras and reconstruct a scene. We consider here scenarios of reduced image sets with little overlap, possibly as low as two images at most seeing…
Current and future radio interferometric arrays such as LOFAR and SKA are characterized by a paradox. Their large number of receptors (up to millions) allow theoretically unprecedented high imaging resolution. In the same time, the ultra…
Tomographic reconstruction of a binary image from few projections is considered. A novel {\em heuristic} algorithm is proposed, the central element of which is a nonlinear transformation $\psi(p)=\log(p/(1-p))$ of the probability $p$ that a…
Here we present new joint reconstruction and regularization techniques inspired by ideas in microlocal analysis and lambda tomography, for the simultaneous reconstruction of the attenuation coefficient and electron density from X-ray…
Magnetic Resonance Imaging (MRI) is a crucial medical imaging technology for the screening and diagnosis of frequently occurring cancers. However image quality may suffer by long acquisition times for MRIs due to patient motion, as well as…
The inversion of linear systems is a fundamental step in many inverse problems. Computational challenges exist when trying to invert large linear systems, where limited computing resources mean that only part of the system can be kept in…
Single molecule fluorescence microscopy is a powerful technique for uncovering detailed information about biological systems, both in vitro and in vivo. In such experiments, the inherently low signal to noise ratios mean that accurate…
Sparse-view 3D CT reconstruction aims to recover volumetric structures from a limited number of 2D X-ray projections. Existing feedforward methods are constrained by the scarcity of large-scale training datasets and the absence of direct…
Four-dimensional scanning transmission electron microscopy (4D-STEM) of local atomic diffraction patterns is emerging as a powerful technique for probing intricate details of atomic structure and atomic electric fields. However, efficient…
Even though image signals are typically defined on a regular two-dimensional grid, there also exist many scenarios where this is not the case and the amplitude of the image signal only is available for a non-regular subset of pixel…
When a single molecule is detected in a wide-field microscope, the image approximates the point spread function of the system. However, as the distribution of molecules becomes denser and their images begin to coincide, existing solutions…
Reconstructing the unknown spectrum of a given X-ray source is a common problem in a wide range of X-ray imaging tasks. For high-energy sources, transmission measurements are mostly used to recover the X-ray spectrum, as a solution to an…
An inverse elastic source problem with sparse measurements is of concern. A generic mathematical framework is proposed which incorporates a low- dimensional manifold regularization in the conventional source reconstruction algorithms…
The application that motivates this paper is molecular imaging at the atomic level. When discretized at sub-atomic distances, the volume is inherently sparse. Noiseless measurements from an imaging technology can be modeled by convolution…
We propose a solution to the image deconvolution problem where the convolution kernel or point spread function (PSF) is assumed to be only partially known. Small perturbations generated from the model are exploited to produce a few…
We study unique recovery of cosparse signals from limited-angle tomographic measurements of two- and three-dimensional domains. Admissible signals belong to the union of subspaces defined by all cosupports of maximal cardinality $\ell$ with…
We demonstrate a novel approach to the reconstruction of scanning probe x-ray diffraction tomography data with anisotropic poly crystalline samples. The method involves reconstructing a voxel map containing an orientation distribution…