Related papers: Reconstructing images of gravitational lenses with…
In a previous paper, we outlined a new Bayesian method for inferring the properties of extended gravitational lenses, given data in the form of resolved images. This method holds the most promise for optimally extracting information from…
Image de-blurring is important in many cases of imaging a real scene or object by a camera. This project focuses on de-blurring an image distorted by an out-of-focus blur through a simulation study. A pseudo-inverse filter is first explored…
The weak gravitational lensing formalism can be extended to the strong lensing regime by integrating a nonlinear version of the geodesic deviation equation. The resulting "roulette" expansion generalises the notion of convergence, shear and…
We propose a method for recovering the two-dimensional gravitational potential of galaxy clusters which combines data from weak and strong gravitational lensing. A first estimate of the potential from weak lensing is improved at the…
The transition of the binary gravitational lens from the equal mass case to small (planetary) mass ratios q is studied. It is shown how the limit of a (pure shear) Chang-Refsdal lens is approached, under what conditions the Chang-Refsdal…
These lecture notes for a graduate class present the regularization theory for linear and nonlinear ill-posed operator equations in Hilbert spaces. Covered are the general framework of regularization methods and their analysis via spectral…
The problem of object restoration in the case of spatially incoherent illumination is considered. A regularized solution to the inverse problem is obtained through a probabilistic approach, and a numerical algorithm based on the statistical…
In the context of strong gravitational lensing, the magnification of image is of crucial importance to constrain various lens models. For several commonly used quadruple lens models, the magnification invariants, defined as the sum of the…
Gravitational lensing of background compact objects like active galactic nuclei and quasars, by extended intermediate mass lenses such as globular clusters and and dark matter clumps with masses 10^5 - 10^8 M_sun, is considered. It is shown…
This paper explores features of an idealized mathematical machine (algorithm) that would be capable of reconstructing the gravitational nature (the multipolar structure or spacetime metric) of a compact object, by observing gravitational…
Several approaches exist to model gravitational lens systems. In this study, we apply global optimization methods to find the optimal set of lens parameters using a genetic algorithm. We treat the full optimization procedure as a two-step…
We show how observations of multiply-imaged quasars at high redshift can be used as a probe of dark matter clumps (subhalos with masses ~ 10^9 solar masses) within the virialized extent of more massive lensing halos. A large abundance of…
In this work, we consider the inverse problem of reconstructing the internal structure of an object from limited x-ray projections. We use a Gaussian process prior to model the target function and estimate its (hyper)parameters from…
Modeling strong gravitational lenses in order to quantify the distortions in the images of background sources and to reconstruct the mass density in the foreground lenses has been a difficult computational challenge. As the quality of…
In this work we present relensing, a package written in python whose goal is to model galaxy clusters from gravitational lensing. With relensing we extend the amount of software available, which provides the scientific community with a wide…
Gravitational lensing is the phenomenon arising when light rays are deflected by the mass between the source and the observer. Largely magnified and highly distorted images of background galaxies are formed by these angular deflections if…
The observables in a strong gravitational lens are usually just the image positions and sometimes the flux ratios. We develop a new and simple algorithm which allows a set of models to be fitted exactly to the observations. Taking our cue…
We study the influence of analytical regularization used in the generalized function (distribution) space to the Tikhonov regularization procedure utilized in the different versions of Moore-Penrose's inversion. By introducing a new…
This contribution deals with image restoration in optical systems with coherent illumination, which is an important topic in astronomy, coherent microscopy and radar imaging. Such optical systems suffer from wavefront distortions, which are…
The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds…