Related papers: Paraxial diffusion-field retrieval
In this article we propose a generalization of the theory of diffusion approximation for random ODE to a nonlinear system of random Schr\"{o}dinger equations. This system arises in the study of pulse propagation in randomly birefringent…
In this paper, we extend the paraxial conical refraction model to the case of the partially coherent light using the unified optical coherence theory. We demonstrate the decomposition of conical refraction correlation functions into…
We study some non-parabolic diffusion problems in one-space dimension, where the diffusion flux exhibits forward and backward nature of the Perona-Malik, H\"ollig or non-Fourier type. Classical weak solutions to such problems are…
A standard inverse problem is to determine a source which is supported in an unknown domain $D$ from external boundary measurements. Here we consider the case of a time-dependent situation where the source is equal to unity in an unknown…
Galaxies are biased tracers of the underlying cosmic web, which is dominated by dark matter components that cannot be directly observed. The relationship between dark matter density fields and galaxy distributions can be sensitive to…
Optical fields with rich and well-developed spatio-temporal structure, including ultra-short structured light pulses, are essentially non-monochromatic and contain a continuous spectrum of monochromatic constituents. However, some…
Image deblurring is an ill-posed problem with multiple plausible solutions for a given input image. However, most existing methods produce a deterministic estimate of the clean image and are trained to minimize pixel-level distortion. These…
X-ray diffusive dark-field imaging, which allows spatially unresolved microstructure to be mapped across a sample, is an increasingly popular tool in an array of settings. Here, we present a new algorithm for phase and dark-field computed…
We show that radiation from complex and inherently random but correlated wave sources can be modelled efficiently by using an approach based on the Wigner distribution function. Our method exploits the connection between correlation…
Image reconstruction based on indirect, noisy, or incomplete data remains an important yet challenging task. While methods such as compressive sensing have demonstrated high-resolution image recovery in various settings, there remain issues…
This dissertation is concerned with understanding and analyzing some of the effects of diffraction in the near field. The contributions of homogeneous and of evanescent waves to two-dimensional near-field diffraction patterns of scalar…
Previous raw image-based low-light image enhancement methods predominantly relied on feed-forward neural networks to learn deterministic mappings from low-light to normally-exposed images. However, they failed to capture critical…
Diffusion models have emerged as a key pillar of foundation models in visual domains. One of their critical applications is to universally solve different downstream inverse tasks via a single diffusion prior without re-training for each…
Dark-field X-ray imaging visualizes structural inhomogeneities through small-angle scattering, but existing directional methods are confined to the micrometer scale. While recent advances have extended dark-field capabilities to nanoscale…
At radio wavelengths, scattering in the interstellar medium distorts the appearance of astronomical sources. Averaged over a scattering ensemble, the result is a blurred image of the source. However, Narayan & Goodman (1989) and Goodman &…
A semi-analytical computational algorithm to model the wavefield generated by paraxial diffraction of a class of Laguerre-Gauss beams by sharp-edge elliptic apertures is here developed. Thanks to such a powerful computational tool, some…
Aliasing artifacts in renderings produced by Neural Radiance Field (NeRF) is a long-standing but complex issue in the field of 3D implicit representation, which arises from a multitude of intricate causes and was mitigated by designing more…
By using operator techniques, we solve the paraxial wave equation for a field given by the multiplication of a Gaussian function and an entire function. The latter possesses a unique property, being an eigenfunction of the {\it…
This paper deals with a novel nonlinear coupled nonlocal reaction-diffusion system proposed for image restoration, characterized by the advantages of preserving low gray level features and textures.The gray level indicator in the proposed…
This work concerns the asymptotic analysis of high-frequency wave propagation in randomly layered media with fast variations and long-range correlations. The analysis takes place in the 3D physical space and weak-coupling regime. The role…