Related papers: Numerical algorithms of the radiative transport eq…
Ultrasound Computed Tomography (USCT) has great potential for 3D quantitative imaging of acoustic breast tissue properties. Typical devices include high-frequency transducers, which makes tomography techniques based on numerical wave…
Case's method obtains solutions to the radiative transport equation as superpositions of elementary solutions when the specific intensity depends on one spatial variable. In this paper, we find elementary solutions when the specific…
The geometry of a light wavefront, evolving from a initial flat wavefront in the 3-space associated with a post-Newtonian relativistic spacetime, is studied numerically by means of the ray tracing method. For a discretization of the…
We introduce fractional Brownian motion processes (fBm) as an alternative model for the turbulent index of refraction. These processes allow to reconstruct most of the refractive index properties, but they are not differentiable. We…
In this article, we are concerned with the analysis on the numerical reconstruction of the spatial component in the source term of a time-fractional diffusion equation. This ill-posed problem is solved through a stabilized nonlinear…
We develop a new numerical scheme for solving the radiative transfer equation in a spherically symmetric system. This scheme does not rely on any kind of diffusion approximation and it is accurate for optically thin, thick, and intermediate…
An inverse scattering problem is formulated for reconstructing optical properties of biological tissues. A recursive linearization algorithm is used to solve the inverse scattering problem. We employed the idea of finite element boundary…
Resting-state functional Magnetic Resonance Imaging (fMRI) is a powerful imaging technique for studying functional development of the brain in utero. However, unpredictable and excessive movement of fetuses have limited its clinical…
We propose a supervised machine learning approach for boosting existing signal and image recovery methods and demonstrate its efficacy on example of image reconstruction in computed tomography. Our technique is based on a local nonlinear…
We consider an inverse source problem in the stationary radiative transport through an absorbing and scattering medium in two dimensions. Using the angularly resolved radiation measured on an arc of the boundary, we propose a numerical…
The radiative transfer equation (RTE) is a fundamental mathematical model to describe physical phenomena involving the propagation of radiation and its interactions with the host medium. Deterministic methods can produce accurate solutions…
Albeit the past intensive research, the governing equation of anomalous diffusion which is observed for the transport of particles underground is still an open problem. In this paper, as a governing equation, the advection-diffusion…
We consider an inverse problem for a radiative transport equation (RTE) in which boundary sources and measurements are restricted to a single subset $E$ of the boundary of the domain $\Omega$. We show that this problem can be solved…
The transport of energetic particles in a spatially varying magnetic field is described by the focused transport equation. In the past two versions of this equation were investigated. The more commonly used standard form described a…
It has been shown recently that the optimal fluctuation method -- essentially geometrical optics -- provides a valuable insight into large deviations of Brownian motion. Here we extend the geometrical optics formalism to two-sided,…
In this paper we study the application of a simplified method to solve the dynamic radiative transfer problem in expanding envelopes. The method, which requires a computational effort similar to that of the diffusion approximation, is based…
This paper introduces a mathematical approach that allows one to numerically solve the nonclassical transport equation in a deterministic fashion using classical numerical procedures. The nonclassical transport equation describes particle…
Lorentz transformation equations provide us a set of relations between the spacetime coordinates as observed from two different inertial frames. In case, one of the frames is moving with a uniform rectilinear acceleration we have Rindler's…
We present a numerical method for solving the time-independent thermal radiative transfer (TRT) equation or the neutron transport (NT) equation when the opacity or cross-section varies rapidly in energy (frequency). The approach is based on…
Transport-Based Morphometry (TBM) has emerged as a new framework for 3D medical image analysis. By embedding images into a transport domain via invertible transformations, TBM facilitates effective classification, regression, and other…