相关论文: Single pixel X-ray transform and related inverse p…

Any even function defined on 2-sphere is reconstructed from its integrals over big circles by means of the classical Funk formula. For the non-geodesic Funk transform on the sphere of arbitrary dimension, there is the explicit inversion…

Single-pixel imaging has emerged as a key technique in fluorescence microscopy, where fast acquisition and reconstruction are crucial. In this context, images are reconstructed from linearly compressed measurements. In practice, total…

We present a compact, diffuser-assisted, single-pixel computational camera. A rotating ground glass diffuser is adopted, in preference to a commonly used digital micro-mirror device (DMD), to encode a two-dimensional (2D) image into…

We consider the statistical inverse problem of recovering a function $f: M \to \mathbb R$, where $M$ is a smooth compact Riemannian manifold with boundary, from measurements of general $X$-ray transforms $I_a(f)$ of $f$, corrupted by…

We present new models for illuminated accretion disks, their structure and reprocessed emission. We consider the effects of incident X-rays on the surface of an accretion disk by solving simultaneously the equations of radiative transfer,…

A unique inversion of the exponential X-ray transform of some class of symmetric 2-tensor field in a two dimensional strictly convex set is considered. The approach to inversion is based on the Cauchy problem for a Beltrami-like equation…

Schemes for X-ray imaging single protein molecules using new x-ray sources, like x-ray free electron lasers (XFELs), require processing many frames of data that are obtained by taking temporally short snapshots of identical molecules, each…

Conformal transformation optics provides a simple scheme for manipulating light rays with inhomogeneous isotropic dielectrics. However, there is usually discontinuity for refractive index profile at branch cuts of different virtual Riemann…

The advent of nonlinear X-ray processes like sum-frequency generation and four-wave mixing raises the possibility of non-linear X-ray imaging, combining the high-resolution and elemental specificity of X-ray imaging with the state…

The Compton camera is a promising alternative to the Anger camera for imaging gamma radiation, with the potential to significantly increase the sensitivity of SPECT. Two-dimensional Compton camera image reconstruction can be implemented by…

Single particle diffraction imaging experiments at free-electron lasers (FEL) have a great potential for structure determination of reproducible biological specimens that can not be crystallized. One of the challenges in processing the data…

The cone-beam transform consists of integrating a function defined on the three-dimensional space along every ray that starts on a certain scanning set. Based on Grangeat's formula, Louis [2016, Inverse Problems 32 115005] states…

We present a comprehensive analysis of the the nonlinear optical Kerr effect in graphene. We directly solve the S-matrix element to calculate the absorption rate, utilizing the Volkov-Keldysh- type crystal wave functions. We then convert to…

Limited-angle computerized tomography stands for one of the most difficult challenges in imaging. Although it opens the way to faster data acquisition in industry and less dangerous scans in medicine, standard approaches, such as the…

The ill-posed problem of phase retrieval in optics, using one or more intensity measurements, has a multitude of applications using electromagnetic or matter waves. Many phase retrieval algorithms are computed on pixel arrays using discrete…

X-ray imaging is an invaluable tool for noninvasive analysis in many fields ranging from basic science to medicine and security. The development of low-dose large area imaging solutions still represents an important challenge for various…

If $d$ is a boundary defining function for the Euclidean unit disk and $I$ denotes the geodesic X-ray transform, for $\gamma\in (-1,1)$, we study the singularly-weighted X-ray transforms $I_m d^\gamma$ acting on symmetric $m$-tensors. For…

Image reconstruction in X ray tomography consists in determining an object from its projections. In many applications such as non destructive testing, we look for an image who has a constant value inside a region (default) and another…

This paper presents an uncalibrated deep neural network framework for the photometric stereo problem. For training models to solve the problem, existing neural network-based methods either require exact light directions or ground-truth…

Both in the plane and in space, we invert the nonlinear Ullman transformation for 3 points and 3 orthographic cameras. While Ullman's theorem assures a unique reconstruction modulo a reflection for 3 cameras and 4 points, we find a locally…