Related papers: Inversion of the Abel equation for toroidal densit…
We study the backward scatterings of plane waves by reciprocal scatterers and reveal that $n$-fold ($n\geq3$) rotation symmetry is sufficient to secure invariant backscattering for arbitrarily-polarized incident plane waves. It is further…
We present a flexible and efficient method to construct triaxial dynamical models of galaxies with a central black hole, using Schwarzschild's orbital superposition approach. Our method is general and can deal with realistic luminosity…
The established way of looking at special relativity is based on Einstein postulates: the principle of relativity and the constancy of the velocity of light. In the most general geometric approach to the theory of special relativity, the…
Weak gravitational lensing surveys have the potential to directly probe mass density fluctuation in the universe. Recent studies have shown that it is possible to model the statistics of the convergence field at small angular scales by…
An expression is obtained on the basis of phase perturbation theory for the contribution to the mean differential reflection coefficient from the in-plane co-polarized component of the light scattered diffusely from a two-dimensional…
The work develops further the theory of the following inversion problem, which plays the central role in the rapidly developing area of thermoacoustic tomography and has intimate connections with PDEs and integral geometry: {\it Reconstruct…
In this paper a novel contour integral method is proposed for linear convection-diffusion equations. The method is based on the inversion of the Laplace transform and makes use of a contour given by an elliptic arc joined symmetrically to…
In this paper, a new model is proposed for the inverse random source scattering problem of the Helmholtz equation with attenuation. The source is assumed to be driven by a fractional Gaussian field whose covariance is represented by a…
Two-dimensional radiative transfer is employed to obtain the broad-band infrared spectrum of active galaxies. In the models we vary the geometry and size of the obscuring medium, the surface density, the opacity and the grain size…
We establish results for the injectivity and injectivity modulo gauge of certain inverse source problems in transport on a simply connected domain with variable index of refraction inducing a 'simple geometry'. The model given by radiative…
Arbitrary distributions of radiant exposure may be written by transversely scanning a single known spatially-random screen that is normally illuminated by spatially but not necessarily temporally uniform radiation or matter wave fields. The…
We obtain the ratio of semiclassical partition functions for the extension under mixed flux of the minimal surfaces subtending a circumference and a line in Euclidean $AdS_{3}\times S^{3}\times T^{4}$. We reduce the problem to the…
The emergence of neural and Gaussian-based radiance field methods has led to considerable advancements in novel view synthesis and 3D object reconstruction. Nonetheless, specular reflection and refraction continue to pose significant…
We introduce the concept of the inverse prism as the dual of the conventional prism and deduce from this duality an implementation of it based on temporal discontinuity and spatial dispersion provided by anisotropy. Moreover, we show that…
Spatially incoherent light sources, such as spontaneously emitting atoms, naively require Maxwell's equations to be solved many times to obtain the total emission, which becomes computationally intractable in conjunction with large-scale…
Weak gravitational lensing is the slight distortion of galaxy shapes caused primarily by the gravitational effects of dark matter in the universe. In our work, we seek to invert the weak lensing signal from 2D telescope images to…
3D Gaussian Splatting shows great potential in reconstructing photo-realistic 3D scenes. However, these methods typically bake illumination into their representations, limiting their use for physically-based rendering and scene editing.…
We present a method to reconstruct the dielectric susceptibility (scattering potential) of an inhomogeneous scattering medium, based on the solution to the inverse scattering problem with internal sources. We employ the theory of…
The concept of turnaround surface in an accelerating universe is generalized to arbitrarily large deviations from spherical symmetry, to close the gap between the idealized theoretical literature and the real world observed by astronomers.…
Diffusion models can generate a variety of high-quality images by modeling complex data distributions. Trained diffusion models can also be very effective image priors for solving inverse problems. Most of the existing diffusion-based…