Related papers: Backward Propagation
The inverse problem of backward diffusion is known to be ill-posed and highly unstable. Backward diffusion processes appear naturally in image enhancement and deblurring applications. It is therefore greatly desirable to establish a…
We discuss here the direct and inverse problems for wave propagation in a waveguide with rough internal surface and arbitrary mean shape. The high degree of multiple scattering inside the waveguide poses significant challenges both for the…
We present a preconditioning method for the multi-dimensional Helmholtz equation with smoothly varying coefficient. The method is based on a frame of functions, that approximately separates components associated with different singular…
The recent results presented in arXiv:2202.05608 have led to significant developments in achieving stable approximations of Helmholtz solutions by plane wave superposition. The study shows that the numerical instability and ill-conditioning…
Diffraction tomography is a noninvasive technique that estimates the refractive indices of unknown objects and involves an inverse-scattering problem governed by the wave equation. Recent works have shown the benefit of nonlinear models of…
This paper describes how to propagate wavefields for arbitrary numbers of traditional time steps in a single step, called a superstep. We show how to construct operators that accomplish this task for finite-difference time domain schemes,…
Tomographic image reconstruction can be mapped to a problem of finding solutions to a large system of linear equations which maximize a function that includes \textit{a priori} knowledge regarding features of typical images such as…
We investigate light propagation through materials with periodically modulated gain/loss profile in both transverse and longitudinal directions, i.e. in material with two-dimensional modulation in space. We predict effects of…
In the context of providing a mathematical framework for the propagation of ultrasound waves in a random multiscale medium, we consider the scattering of classical waves (modeled by a divergence form scalar Helmholtz equation) by a bounded…
Backflow is a counter-intuitive phenomenon in which a forward propagating quantum particle propagates locally backwards. The actual counter-propagation property associated with this delicate interference phenomenon has not been observed to…
Rescattering electrons offer great potential as probes of molecular properties on ultrafast timescales. The most famous example is molecular tomography, in which high harmonic spectra of oriented molecules are mapped to ``tomographic…
Presented is a novel way to combine snapshot compressive imaging and lateral shearing interferometry in order to capture the spatio-spectral phase of an ultrashort laser pulse in a single shot. A deep unrolling algorithm is utilised for the…
Recent theoretical and experimental advances have shed light on the existence of so-called `perfectly transmitting' wavefronts with transmission coefficients close to 1 in strongly backscattering random media. These perfectly transmitting…
Airy beams are solutions to the paraxial Helmholtz equation known for exhibiting shape invariance along their self-accelerated propagation in free space. These two properties are associated with the fact that they are not square integrable,…
A backward-wave slab based on a capacitively and inductively loaded three-dimensional transmission-line network is designed in such a way that impedance-matching with free space is obtained. To enable field propagation from free space to…
Diffuse scattering of electromagnetic waves from natural and artificial surfaces has been extensively studied in various disciplines, including radio wave propagation, and several diffuse scattering models based on different approaches have…
Inferring electromagnetic propagation characteristics within the marine atmospheric boundary layer (MABL) from data in real time is crucial for modern maritime navigation and communications. The propagation of electromagnetic waves is well…
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,…
A version of the so-called "convexification" numerical method for a coefficient inverse scattering problem for the 3D Hemholtz equation is developed analytically and tested numerically. Backscattering data are used, which result from a…
Medical ultrasound provides images which are the spatial map of the tissue echogenicity. Unfortunately, an ultrasound image is a low-quality version of the expected Tissue Reflectivity Function (TRF) mainly due to the non-ideal Point Spread…