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

Frequency conversion of single photons in a nonlinear crystal is theoretically discussed. Losses and noise are included within a Heisenberg-Langevin formalism for the propagating photon field. We calculate the first- and second-order…

We propose an encryption-decryption framework for validating diffraction intensity volumes reconstructed using single-particle imaging (SPI) with x-ray free-electron lasers (XFELs) when the ground truth volume is absent. This framework…

In a recent article the authors showed that the radiative Transfer equations with multiple frequencies and scattering can be formulated as a nonlinear integral system. In the present article, the formulation is extended to handle reflective…

Optical quantum nondemolition devices can provide essential tools for quantum information processing. Here, we describe several optical interferometers that signal the presence of a single photon in a particular input state without…

In recent years, image-scanning microscopy (ISM, also termed pixel-reassignment microscopy) has emerged as a technique that improves the resolution and signal-to-noise compared to confocal and widefield microscopy by employing a detector…

A well-characterised wavefront is important for many X-ray free-electron laser (XFEL) experiments, especially for single-particle imaging (SPI), where individual bio-molecules randomly sample a nanometer-region of highly-focused femtosecond…

Several novel imaging applications have lead recently to a variety of Radon type transforms, where integration is done over a family of conical surfaces. We call them \emph{cone transforms} (in 2D they are also called \emph{V-line} or…

We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…

The usually reported pixel resolution of single pixel imaging (SPI) varies between $32 \times 32$ and $256 \times 256$ pixels falling far below imaging standards with classical methods. Low resolution results from the trade-off between the…

Single Pixel (SP) imaging is now a reality in many applications, e.g., biomedical ultrathin endoscope and fluorescent spectroscopy. In this context, many schemes exist to improve the light throughput of these device, e.g., using structured…

This article surveys recent results aiming at obtaining refined mapping estimates for the X-ray transform on a Riemannian manifold with boundary, which leverage the condition that the boundary be strictly geodesically convex. These…

The Kustaanheimo-Stiefel (KS) transformation maps the non-linear and singular equations of motion of the three-dimensional Kepler problem to the linear and regular equations of a four-dimensional harmonic oscillator. It is used extensively…

We study iterative signal reconstruction in computed tomography (CT), wherein measurements are produced by a linear transformation of the unknown signal followed by an exponential nonlinear map. Approaches based on pre-processing the data…

Eliminating reflections caused by incident light interacting with reflective medium remains an ill-posed problem in the image restoration area. The primary challenge arises from the overlapping of reflection and transmission components in…

In many areas of physics, the Kramers-Kronig (KK) relations are used to extract information about the real part of the optical response of a medium from its imaginary counterpart. In this paper we discuss an alternative but mathematically…

We present a novel, blind, single image deblurring method that utilizes information regarding blur kernels. Our model solves the deblurring problem by dividing it into two successive tasks: (1) blur kernel estimation and (2) sharp image…

How can we perform a metrological task if only limited control over a quantum system is given? Here, we present systematic methods for conducting nonlinear quantum metrology in scenarios lacking a common reference frame. Our approach…

The problem of reconstruction of an unknown refractive index $k(x)$ of an inhomogeneous solid $P$ is considered. The refractive index is assumed to be a piecewise-H\"{o}lder function The original boundary value problem for the Helmholtz…

Enabled by x-ray free-electron lasers, nonlinear optical phenomena can be explored in the x-ray domain nowadays. Among the multitude of newly accessible processes, this theoretical study focuses parametric x-ray optical wavemixing for…

Dark-field X-ray imaging is a novel modality which visualises scattering from unresolved microstructure. Most dark-field imaging techniques rely on crystals or structured illumination, but recent work has shown that dark-field effects are…