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In this paper the filtering of partially observed diffusions, with discrete-time observations, is considered. It is assumed that only biased approximations of the diffusion can be obtained, for choice of an accuracy parameter indexed by…
Wavelet coefficients are estimated recursively at progressively coarser scales recursively. As a result, the estimation is prone to multiplicative propagation of truncation errors due to quantization and round-off at each stage. Yet, the…
We present a general method for the error analysis of spatial modulation (SM) systems over correlated and uncorrelated Rayleigh and Rician fading channels. The proposed method, making use of the properties of proper complex random variables…
Empirical work often uses treatment assigned following geographic boundaries. When the effects of treatment cross over borders, classical difference-in-differences estimation produces biased estimates for the average treatment effect. In…
We present analytical approximations for calculating the scattering, absorption and escape of nonionizing photons from a spherically symmetric two-phase clumpy medium, with either a central point source of isotropic radiation, a uniform…
The probability distribution of the reflection coefficient for light reflected from a one-dimensional random amplifying medium with {\it cross-correlated} spatial disorder in the real and the imaginary parts of the refractive index is…
We introduce a new approach for measuring both the effective medium and the transport properties of light propagation in heterogeneous media. Our method utilizes the conceptual equivalence of frequency variation with a change in the…
Nonlinear effects in pulse propagation through a medium consisting of four-level double-$\Lambda$-type systems are studied theoretically. We apply three continous-wave driving fields and a pulsed probe field such that they form a closed…
Properly modeling and predicting the scattering response of a metasurface is a particularly challenging task. This has been shown to be especially difficult if the metasurface supports both local and nonlocal interactions, in the form of…
The previous research proves that the random laser emission reflects not only the scattering properties but also the absorption properties. The random laser is therefore considered a potential tool for optical properties sensing. Although…
This paper derives physically meaningful boundary conditions for fractional diffusion equations, using a mass balance approach. Numerical solutions are presented, and theoretical properties are reviewed, including well-posedness and steady…
Imaging through diffusive media is a challenging problem, where the existing solutions heavily rely on digital computers to reconstruct distorted images. We provide a detailed analysis of a computer-free, all-optical imaging method for…
From the earth's crust to the human brain, remitted waves are used for sensing and imaging in a diverse range of diffusive media. Separating the source and detector increases the penetration depth of remitted light, yet rapidly decreases…
Focusing waves inside inhomogeneous media is a fundamental problem for imaging. Spatial variations of wave velocity can strongly distort propagating wavefronts and degrade image quality. Adaptive focusing can compensate for such aberration,…
Considering light transport in disordered media, the medium is often treated as an effective medium requiring accurate evaluation of an effective refractive index. Because of its simplicity, the Maxwell-Garnett (MG) mixing rule is widely…
This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using…
Asymptotic radiative transfer (ART), like diffusion theory, assumes the angular intensity distribution incident at a boundary is identical with that in the depth of the scattering medium. However, the asymptotic intensity profile and…
In this study, we develop a saturation-dependent treatment of dispersion in porous media using concepts from critical path analysis, cluster statistics of percolation, and fractal scaling of percolation clusters. We calculate spatial solute…
We present an analysis of enhanced wave transmission through random media with mirror symmetry about a reflecting barrier. The mathematical model is the acoustic wave equation and we consider two setups, where the wave propagation is along…
This paper deals with the problem of outliers in high frequency observation data from diffusion processes. Robust estimation methods are needed because the inclusion of outliers can lead to incorrect statistical inference even in the…