Mathematical Modeling and Solution of the Tomography Problem in Domains with Reflecting Obstacles

TL;DR

This paper introduces advanced numerical methods for solving tomography problems in domains with reflecting obstacles, significantly improving accuracy over classical methods and providing efficient algorithms for implementation.

Contribution

It presents novel numerical algorithms for tomography with reflecting obstacles, demonstrating substantial accuracy improvements for Lambertian and specular reflections.

Findings

Lambertian reflection improves accuracy by an order of magnitude

Specular reflection improves accuracy by about three times

New algorithms enhance software implementation efficiency

Abstract

This work develops new numerical methods for the solution of the tomography problem in domains with reflecting obstacles. We compare the solution's performance for Lambertian reflection, for classical tomography with ubroken rays and for specular reflection. Our numerical method using Lambertian reflection improves the solution's accuracy by an order of magnitude compared to classical tomography with ubroken rays and for tomography in the presence of a specularly reflecting obstacle the numerical method improves the solution's accuracy approximately by a factor of three times. We present efficient new algorithms for the solution's software implementation and analyze the solution's performance and effectiveness.