Related papers: Paraxial Sharp-Edge Diffraction: A General Computa…
The Fraunhofer diffraction of quantum particles from materials with sharp electron-density edges or symmetric bond structures is ubiquitous. In contrast, diffraction from atoms with characteristic asymptotically-diffused electron…
A unified method for three-dimensional reconstruction of objects from transmission images collected at multiple illumination directions is described. The method may be applicable to experimental conditions relevant to absorption-based,…
We address the inverse problem of recovering a degeneracy point within the diffusion coefficient of a one-dimensional complex parabolic equation by observing the normal derivative at one point of the boundary. The strongly degenerate case…
De-diffraction (DD), a new procedure to totally cancel diffraction effects from wave-fields is presented, whereby the full field from an aperture is utilized and a truncated geometrical field is obtained, allowing infinitely sharp focusing…
We present some classical and weighted Poincar\'e inequalities for some one-dimensional probability measures. This work is the one-dimensional counterpart of a recent study achieved by the authors for a class of spherically symmetric…
Tomography is the three-dimensional reconstruction of an object from images taken at different angles. The term classical tomography is used, when the imaging beam travels in straight lines through the object. This assumption is valid for…
We analyze multi-bounce propagation of light in an unknown hidden volume and demonstrate that the reflected light contains sufficient information to recover the 3D structure of the hidden scene. We formulate the forward and inverse theory…
Diffraction tomography aims to recover an object's scattering potential from measured wave fields. In the classical setting, the object is illuminated by plane waves from many directions, and the Fourier diffraction theorem provides a…
Purpose: To develop an algorithm for robust partial Fourier (PF) reconstruction applicable to diffusion-weighted (DW) images with non-smooth phase variations. Methods: Based on an unrolled proximal splitting algorithm, a neural network…
By suitably generalizing the Fourier constraint projection in the difference map phasing algorithm, an object can be reconstructed from its diffraction pattern even when the latter has been incoherently averaged over a discrete group of…
We introduce a statistical extension of the classic Poisson Surface Reconstruction algorithm for recovering shapes from 3D point clouds. Instead of outputting an implicit function, we represent the reconstructed shape as a modified Gaussian…
We consider Taylor dispersion for tracer particles in micro-fluidic planar channels with strong confinement. In this context, the channel walls modify the local diffusivity tensor and also interactions between the tracer particles and the…
We propose a method based on sinc series approximations for computing the Rayleigh-Sommerfeld and Fresnel diffraction integrals of optics. The diffraction integrals are given in terms of a convolution, and our proposed numerical approach is…
We present the development of extended diffraction tomography, a new approach to the solution of the linear seismic waveform inversion problem. This method has several appealing features, such as the use of arbitrary depth-dependent…
We introduce an accurate and efficient method for a class of nonlocal potential evaluations with free boundary condition, including the 3D/2D Coulomb, 2D Poisson and 3D dipolar potentials. Our method is based on a Gaussian-sum approximation…
Photothermal imaging is a powerful noncontact and nondestructive technique for subsurface inspection of composite materials, yet its performance is fundamentally limited by the diffusive and irreversible nature of heat transport, leading to…
The surface current method known in the theory of electromagnetic waves diffraction is generalized to be applied for the problems of diffraction radiation generated by a charged particle moving nearby an ideally-conducting screen in vacuum.…
Diffusion models have recently shown remarkable results in magnetic resonance imaging reconstruction. However, the employed networks typically are black-box estimators of the (smoothed) prior score with tens of millions of parameters,…
We demonstrate a method for filtering images defined on curved surfaces embedded in 3D. Applications are noise removal and the creation of artistic effects. Our approach relies on in-surface diffusion: we formulate Weickert's edge/coherence…
We study nonparametric Bayesian models for reversible multi-dimensional diffusions with periodic drift. For continuous observation paths, reversibility is exploited to prove a general posterior contraction rate theorem for the drift…