Mathematical Modeling for Tomography in Domains with Reflecting Obstacles

TL;DR

This paper introduces new numerical methods for tomography in domains with reflecting obstacles, significantly improving accuracy over classical methods by leveraging Lambertian and specular reflection models.

Contribution

The work develops novel algorithms for tomography with reflecting obstacles, enhancing accuracy and efficiency, and reducing the number of equations needed in linear systems.

Findings

Lambertian reflection improves accuracy by an order of magnitude.

Specular reflection enhances accuracy by approximately three times.

New algorithms are efficient and applicable to various algebraic tomographic methods.

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 unbroken 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 unbroken 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. The new method from this work for reducing the number of equations in tomography linear systems is applicable to improving the performance of a wide class of algebraic tomographic reconstruction methods.