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In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape…
We present a novel, blind, single image deblurring method that utilizes information regarding blur kernels. Our model solves the deblurring problem by dividing it into two successive tasks: (1) blur kernel estimation and (2) sharp image…
The problem of restoration of the source brightness distribution from an analysis of the stellar and AGNs microlensing light curves is investigated. In case of microlensing of stars by a point-mass lens as well as for caustic crossing…
The problem of reconstructing an object from the measurements of the light it scatters is common in numerous imaging applications. While the most popular formulations of the problem are based on linearizing the object-light relationship,…
We introduce a continuous domain framework for the recovery of points on a surface in high dimensional space, represented as the zero-level set of a bandlimited function. We show that the exponential maps of the points on the surface…
Continuum and emission-line variability of active galactic nuclei provides a powerful probe of microarcsecond scale structures in the central regions of these sources. In this contribution, we review basic concepts and methodologies used in…
We construct the rest-frame 2--10 keV intrinsic X-ray luminosity function of Active Galactic Nuclei (AGNs) from a combination of X-ray surveys from the all-sky Swift BAT survey to the Chandra Deep Field-South. We use ~3200 AGNs in our…
In most adaptive signal processing applications, system linearity is assumed and adaptive linear filters are thus used. The traditional class of supervised adaptive filters rely on error-correction learning for their adaptive capability.…
Kernel methods for solving partial differential equations on surfaces have the advantage that those methods work intrinsically on the surface and yield high approximation rates if the solution to the partial differential equation is smooth…
We consider the problem of recovering the superposition of $R$ distinct complex exponential functions from compressed non-uniform time-domain samples. Total Variation (TV) minimization or atomic norm minimization was proposed in the…
X-ray interaction with matter is an energy-dependent process that is contingent on the atomic structure of the constituent material elements. The most advanced models to capture this relationship currently rely on Monte Carlo (MC)…
Paganin's method for image reconstruction in propagation-based phase-contrast X-ray imaging and tomography has enjoyed broad acceptance in recent years, with over one thousand publications citing its use. The present paper discusses…
We present a probabilistic cross-correlation approach to estimate time delays in the context of reverberation mapping (RM) of Active Galactic Nuclei (AGN). We reformulate the traditional interpolated cross-correlation method as a…
We propose and study a row-and-column affine measurement scheme for low-rank matrix recovery. Each measurement is a linear combination of elements in one row or one column of a matrix $X$. This setting arises naturally in applications from…
This paper establishes a kernel-based framework for reconstructing data on manifolds, tailored to fit the dynamic-(d)MRI-data recovery problem. The proposed methodology exploits simple tangent-space geometries of manifolds in reproducing…
Continuum reverberation mapping of AGN can provide new insight into the nature and geometry of the accretion flow. Some of the X-rays from the central corona irradiating the disc are absorbed, increasing the local disc temperature. This…
We note that the solution of accretion disk dynamics for an initial delta-function mass distribution gives a light curve that fits both the rise and the decay pattern of the outburst light curves of black-hole soft X-ray transients (BSXTs)…
When imaging through a semi-reflective medium such as glass, the reflection of another scene can often be found in the captured images. It degrades the quality of the images and affects their subsequent analyses. In this paper, a novel deep…
Reverberation mapping (RM) is a widely-used method for probing the physics of broad-line regions (BLRs) in active galactic nuclei (AGNs). There are increasing preliminary evidences that the RM behaviors of broad emission lines are…
Accreting black holes show characteristic reflection features in their X-ray spectrum, including an iron K$\alpha$ line, resulting from hard X-ray continuum photons illuminating the accretion disk. The reverberation lag resulting from the…