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We aim to improve cluster lens modeling and source reconstruction by utilizing the full information in giant, caustic-crossing arcs lensed by galaxy clusters. Lens models are generally constrained using image positions and assuming point…
Uncompressed clinical data from modern positron emission tomography (PET) scanners are very large, exceeding 350 million data points (projection bins). The last decades have seen tremendous advancements in mathematical imaging tools many of…
Dense image matching is a fundamental low-level problem in Computer Vision, which has received tremendous attention from both discrete and continuous optimization communities. The goal of this paper is to combine the advantages of discrete…
In imaging modalities recording diffraction data, the original image can be reconstructed assuming known phases. When phases are unknown, oversampling and a constraint on the support region in the original object can be used to solve a…
Limited view tomographic reconstruction aims to reconstruct a tomographic image from a limited number of sinogram or projection views arising from sparse view or limited angle acquisitions that reduce radiation dose or shorten scanning…
In this paper we analyze several inexact fast augmented Lagrangian methods for solving linearly constrained convex optimization problems. Mainly, our methods rely on the combination of excessive-gap-like smoothing technique developed in…
A simple, yet general, formalism for the optimized linear combination of astrophysical images is constructed and demonstrated. The formalism allows the user to combine multiple undersampled images to provide oversampled output at high…
Much research has been devoted to the problem of restoring Poissonian images, namely for medical and astronomical applications. However, the restoration of these images using state-of-the-art regularizers (such as those based on multiscale…
Future searches for biomarkers on habitable exoplanets will rely on telescope instruments that achieve extremely high contrast at small planet-to-star angular separations. Coronagraphy is a promising starlight suppression technique,…
We present a new method for numerical propagation through Lyot-style coronagraphs using finite occulting masks. Standard methods for coronagraphic simulations involve Fast Fourier Transforms (FFT) of very large arrays, and computing power…
Inhomogeneities in the refractive index of a biological sample can introduce phase aberrationsin microscopy systems, severely impairing the quality of images. Adaptive optics can be employed to correct for phase aberrations and improve…
A major science goal of future, large-aperture, optical space telescopes is to directly image and spectroscopically analyze reflected light from potentially habitable exoplanets. To accomplish this, the optical system must suppress…
Optimization problems with convex quadratic cost and polyhedral constraints are ubiquitous in signal processing, automatic control and decision-making. We consider here an enlarged problem class that allows to encode logical conditions and…
Recent developments in image acquisition literature have miniaturized the confocal laser endomicroscopes to improve usability and flexibility of the apparatus in actual clinical settings. However, miniaturized devices collect less light and…
Phase-Induced Amplitude Apodization Complex Mask Coronagraphs (PIAACMC) offer high-contrast performance at a small inner-working angle ($\approx$ 1 $\lambda$/D) with high planet throughput ($>$ 70%). The complex mask is a multi-zone,…
We propose a framework for modeling and solving low-rank optimization problems to certifiable optimality. We introduce symmetric projection matrices that satisfy $Y^2=Y$, the matrix analog of binary variables that satisfy $z^2=z$, to model…
Anderson Acceleration (AA) is a method to accelerate the convergence of fixed point iterations for nonlinear, algebraic systems of equations. Due to the requirement of solving a least squares problem at each iteration and a reliance on…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
Though modern microscopes have an autofocusing system to ensure optimal focus, out-of-focus images can still occur when cells within the medium are not all in the same focal plane, affecting the image quality for medical diagnosis and…
Context. Proxima Cen b is the prime target for the search of life around a nearby exoplanet by characterizing its atmosphere in reflected light. Due to the very high star/companion contrast (<1E-6), High Dispersion Coronagraphy is the most…