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In this paper we propose a method of proving impossibility results based on applying strong data-processing inequalities to estimate mutual information between sets of variables forming certain Markov random fields. The end result is that…
Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process…
Reconstructing continuous signals from a small number of discrete samples is a fundamental problem across science and engineering. In practice, we are often interested in signals with 'simple' Fourier structure, such as bandlimited,…
This work studies the problem of estimating a two-dimensional superposition of point sources or spikes from samples of their convolution with a Gaussian kernel. Our results show that minimizing a continuous counterpart of the $\ell_1$ norm…
In this thesis, we re-assess some aspects of axionic electrodynamics by coupling non-linear electromagnetic effects to axion physics. We present a number of motivations to justify the coupling of the axion to the photon in terms of a…
This paper addresses the problem of distributed coding of images whose correlation is driven by the motion of objects or positioning of the vision sensors. It concentrates on the problem where images are encoded with compressed linear…
We propose a new space-variant regularization term for variational image restoration based on the assumption that the gradient magnitudes of the target image distribute locally according to a half-Generalized Gaussian distribution. This…
Causal structure learning from observational data remains a non-trivial task due to various factors such as finite sampling, unobserved confounding factors, and measurement errors. Constraint-based and score-based methods tend to suffer…
A generic computational imaging setup is considered which assumes sequential illumination of a semi-transparent object by an arbitrary set of structured illumination patterns. For each incident illumination pattern, all transmitted light is…
Maxima of the linear density field form a point process that can be used to understand the spatial distribution of virialized halos that collapsed from initially overdense regions. However, owing to the peak constraint, clustering…
Gravitational waves astronomy has opened a new opportunity to study the Universe. Full exploitation of this window can especially be provided by combining data coming from gravitational waves experiments with luminous tracers of the Large…
We show that in a spontaneously broken effective gauge field theory, quantized in a general background $R_\xi$-gauge, also the background fields undergo a non-linear (albeit background-gauge invariant) field redefinition induced by…
These days we live in a world with a permanent electromagnetic field. This raises many questions about our health and the deployment of new equipment. The problem is that these fields remain difficult to visualize easily, which only some…
Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the…
The problem of light waves interaction with charged particles becomes more and more complex starting with the case of plane waves, where the analytical solution is well known, to more natural, though more complicated situations which…
Motivated by applications in mathematical biology concerning randomly alternating motion of micro-organisms, we analyze a generalized integrated telegraph process. The random times between consecutive velocity reversals are…
Structured light concerns the control of light in its spatial degrees of freedom (amplitude, phase and polarization), and has proven instrumental in many applications. The creation of structured light usually involves the conversion of a…
We demonstrate experimentally a new technique to control the bandwidth and the type of frequency correlations (correlation, anticorrelation, and even uncorrelation) of entangled photons generated by spontaneous parametric downconversion.…
We generalize the invariant imbedding theory of the wave propagation and derive new invariant imbedding equations for the propagation of arbitrary number of coupled waves of any kind in arbitrarily-inhomogeneous stratified media, where the…
The adiabatic connection fluctuation-dissipation theorem with the random phase approximation (RPA) has recently been applied with success to obtain correlation energies of a variety of chemical and solid state systems. The main merit of…