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According to the standard paradigm, the strong and compact luminosity of active galactic nuclei (AGN) is due to multi-temperature black body emission originating from an accretion disk formed around a supermassive black hole. This central…
X-ray reverberation echoes are assumed to be produced in the strongly distorted spacetime around accreting supermassive black holes. This signal allows us to spatially map the geometry of the inner accretion flow - a region which cannot yet…
In matrix recovery from random linear measurements, one is interested in recovering an unknown $M$-by-$N$ matrix $X_0$ from $n<MN$ measurements $y_i=Tr(A_i^T X_0)$ where each $A_i$ is an $M$-by-$N$ measurement matrix with i.i.d random…
Deep Convolutional Neural Networks (CNNs) are widely employed in modern computer vision algorithms, where the input image is convolved iteratively by many kernels to extract the knowledge behind it. However, with the depth of convolutional…
Machine-learning (ML) algorithms will play a crucial role in studying the large datasets delivered by new facilities over the next decade and beyond. Here, we investigate the capabilities and limits of such methods in finding galaxies with…
X-ray absorption spectroscopy is a crucial experimental technique for elucidating the mechanisms of structural degradation in battery materials. However, extracting information from the measured spectrum is challenging without high-quality…
Optimization of strongly non-linear tightly coupled feeds attached to antennas is a challenging problem from a purely computational perspective. One can imagine that an optimization would (a) need to be in the time domain, and (b) has to be…
We consider the problem of recovering linear image $Bx$ of a signal $x$ known to belong to a given convex compact set ${\cal X}$ from indirect observation $\omega=Ax+\xi$ of $x$ corrupted by random noise $\xi$ with finite covariance matrix.…
In this paper we present new optimization strategies for the reconstruction of X-ray images of solar flares by means of the data collected by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). The imaging concept of the…
Kernel ridge regression (KRR) is a widely used nonparametric method due to its strong theoretical guarantees and computational convenience. However, standard KRR does not distinguish between linear and nonlinear components in the signal,…
Ultrafast scattering using X-rays or electrons is an emerging method to obtain structure dynamics at the atomic length and time scales. However, directly resolving in real-space atomic motions is inherently limited by the finite detector…
In computational optics, numerical modeling of diffraction between arbitrary planes offers unparalleled flexibility. However, existing methods suffer from the trade-off between computational accuracy and efficiency. To resolve this dilemma,…
Observations suggest that accretion discs in many X-ray binaries are likely flared. An outer edge of the disc intercepts radiation from the central X-ray source. Part of that radiation is absorbed and reemitted in the optical/UV spectral…
Image reconstruction in Magnetic Resonance Imaging (MRI) is fundamentally a linear inverse problem, such that the image can be recovered via explicit pseudoinversion of the encoding matrix by solving $\textbf{data} = \textbf{Encode} \times…
Variable X-ray absorption has been observed in active galactic nuclei (AGN) on several time scales. Observations allow us to identify the absorber with clouds associated either with the clumpy torus (parsec scales, long timescales) or with…
The size and structure of the dusty circumnuclear torus in active galactic nuclei (AGN) can be investigated by analyzing the temporal response of the torus's infrared (IR) dust emission to variations in the AGN ultraviolet/optical…
The UV-X continuum, the X-ray spectral features, and the variability in these bands provide powerful tools for studying the innermost regions of AGNs from which we gain an insight into the accretion process. In this chapter the discussion…
The X-ray spectra of Active Galactic Nuclei (AGN) are complex and vary rapidly in time as seen in recent observations. Magnetic flares above the accretion disk can account for the extreme variability of AGN. They also explain the observed…
We introduce a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$ - $\Omega$ a…
In this paper we study the topic of signal restoration using complexity regularization, quantifying the compression bit-cost of the signal estimate. While complexity-regularized restoration is an established concept, solid practical methods…