Multi-Dimensional Inverse Scattering Transform 1-Time and 2-Space Problem

Application of FDTD and Dynamic Differential Evolution for Inverse Scattering Problem Time Domain Inverse Scattering

Abstract—This paper reports a two-dimensional time-domain inverse scattering algorithm based upon the finite-difference time domain method for determining the shape of a perfectly conducting cylinder. Finite difference time domain method (FDTD) is used to solve the scattering electromagnetic wave of a perfectly conducting cylinder. The inverse problem is resolved by an optimization approach and...

Finite-Dimensional Hilbert Space and The Linear Inverse Problem

Linear Vector Space. A Vector Space, X , is a collection of vectors, x ∈ X , over a field, F , of scalars. Any two vectors x, y ∈ X can be added to form x+y ∈ X where the operation “+” of vector addition is associative and commutative. The vector space X must contain an additive identity (the zero vector 0) and, for every vector x, an additive inverse −x. The required properties of vector addit...

One-dimensional inverse scattering problem for optical coherence tomography

Optical coherence tomography is a non-invasive imaging technique based on the use of light sources exhibiting a low degree of coherence. Low-coherence interferometric microscopes have been successful in producing internal images of thin pieces of biological tissue; typically samples of the order of 1 mm in depth have been imaged, with a resolution of the order of 10 μm in some portions of the s...

Space-Time Tradeoffs in the Inverse B-W Transform

Space-time radial basis function collocation method for one-dimensional advection-diffusion problem

The parabolic partial differential equation arises in many application of technologies. In this paper, we propose an approximate method for solution of the heat and advection-diffusion equations using Laguerre-Gaussians radial basis functions (LG-RBFs). The results of numerical experiments are compared with the other radial basis functions and the results of other schemes to confirm the validit...