Ultrasound Modulated Bioluminescence Tomography With A Single Optical Measurement

TL;DR

This paper introduces a novel method for ultrasound modulated bioluminescence tomography that reconstructs sources using only a single optical measurement, leveraging new inversion formulas with proven convergence.

Contribution

The paper presents two new inversion formulas based on Neumann series and Fredholm theory for UMBLT, enabling source reconstruction from a single optical measurement.

Findings

Successful reconstruction of continuous sources

Effective handling of discontinuous sources

Robustness to noise in numerical experiments

Abstract

Ultrasound modulated bioluminescence tomography (UMBLT) is an imaging method which can be formulated as a hybrid inverse source problem. In the regime where light propagation is modeled by a radiative transfer equation, previous approaches to this problem require large numbers of optical measurements [10]. Here we propose an alternative solution for this inverse problem which requires only a single optical measurement in order to reconstruct the isotropic source. Specifically, we derive two inversion formulae based on Neumann series and Fredholm theory respectively, and prove their convergence under sufficient conditions. The resulting numerical algorithms are implemented and experimented to reconstruct both continuous and discontinuous sources in the presence of noise.