Related papers: Numerical algorithms of the radiative transport eq…
In this paper, the photon stationary transport equation has been extended from $\mathbb{R}^3$ to $\mathbb{C}^3$. A solution of the inverse problem is obtained on a hyper-sphere and a hyper-cylinder as X-ray and Radon transform,…
We present a numerical method to solve the optimal transport problem with a quadratic cost when the source and target measures are periodic probability densities. This method is based on a numerical resolution of the corresponding…
Optical diffraction tomography is an indispensable tool for studying objects in three-dimensions due to its ability to accurately reconstruct scattering objects. Until now this technique has been limited to coherent light because spatial…
This note carries three purposes involving our latest advances on the radial basis function (RBF) approach. First, we will introduce a new scheme employing the boundary knot method (BKM) to nonlinear convection-diffusion problem. It is…
Functional lifting methods provide a tool for approximating solutions of difficult non-convex problems by embedding them into a larger space. In this work, we investigate a mathematically rigorous formulation based on embedding into the…
When solving the time-dependent radiative transport equation (RTE), implicit time discretization is often employed for its robustness and stability. This results in a sequence of steady-state RTEs with identical cross-sections but varying…
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…
Radio-frequency (RF) tomographic imaging is a promising technique for inferring multi-dimensional physical space by processing RF signals traversed across a region of interest. However, conventional RF tomography schemes are generally based…
We derive radiative transport equations for solutions of a Schr\"odinger equation in a periodic structure with small random inhomogeneities. We use systematically the Wigner transform and the Bloch wave expansion. The streaming part of the…
Deep learning-based image restoration methods generally struggle with faithfully preserving the structures of the original image. In this work, we propose a novel Residual-Conditioned Optimal Transport (RCOT) approach, which models image…
The low-rank approximation is a complexity reduction technique to approximate a tensor or a matrix with a reduced rank, which has been applied to the simulation of high dimensional problems to reduce the memory required and computational…
The radiative transfer equation (RTE) for polarized light accepts a convenient exponential solution when the absorption matrix commutes with its integral. We characterize some of the matrix depth variations which are compatible with the…
We consider radiation transport theory applied to non-dispersive but refractive media. This setting is used to discuss Minkowski's and Abraham's electromagnetic momentum, and to derive conservation equations independent of the choice of…
We present an optomechanical system as a paradigm of three-mode teleportation network. Quantum state transfer among optical and vibrational modes becomes possible by exploiting correlations established by radiation pressure.
A generic computational imaging setup is considered which assumes sequential illumination of a semi-transparent object by an arbitrary set of structured illumination patterns. For each incident illumination pattern, all transmitted light is…
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…
We report a new computational method based on the recursive Green's function technique for calculation of light propagation in photonic crystal structures. The advantage of this method in comparison to the conventional finite-difference…
We consider the classical integral equation reformulation of the radiative transport equation (RTE) in a heterogeneous medium, assuming isotropic scattering. We prove an estimate for the norm of the integral operator in this formulation…
In this work, we prove rigorous error estimates for a hybrid method introduced in [15] for solving the time-dependent radiation transport equation (RTE). The method relies on a splitting of the kinetic distribution function for the…
In this paper we present a novel method for the numerical solution of linear transport equations, which is based on ridgelets. Such equations arise for instance in radiative transfer or in phase contrast imaging. Due to the fact that…