On the Uniqueness of the Inverse Source Problem for Linear Particle Transport Theory

Abstract

Inverse source problems for time-independent linear transport with data from invasive and noninvasive detectors are analyzed. The former inverse problem is proven to have a unique solution, while for the latter we construct counterexamples that prove that the problem is underdetermined for the general case of anisotropic sources and prove that it has a unique solution for isotropic sources and scattering. Using duality we propose and analyze a general class of inverse source algorithms. The emphasis is on establishing new inversion techniques and in proving uniqueness or nonuniqueness as well as to find, when possible, ways to regularize the inverse source problem.

Keywords:

• Particle transport
• Inverse problems
• Radon transform
• Nonradiating sources
• Regularization

One of the authors (RS) thanks Lahbib Bourhrara for helpful discussions and for suggesting the example in Eq. (2) and Mustapha Mokhtar-Kharroubi and Rémi Sentis for their advice.