Near-source imaging with δ-SP_N approximation based fluorescence optical tomography

In a recent work, we developed the δ-SP_N approximation, a low-order approximation to the radiative transfer equation that provides improved estimates of fluence in the near source when directed sources and scattering are considered. In this work, we present reconstruction frameworks and a detailed numerical study to demonstrate the use of the δ-SP_N approximation for mesoscopic fluorescence optical tomography applications in reflectance-mode imaging in the near-source region. Comparisons are presented with the standard SP_N approximation to highlight the improvements afforded by the use of the δ-SP_N approximation. We investigate the effect of improved modeling using two different reconstruction schemes, namely, the regularizing Levenberg-Marquardt and a total-variation regularization scheme with measurement data obtained via Monte Carlo simulations over a wide range of test cases. With the δ-SP_N approximation, better localization, improved volume recovery, and consistent estimates across different reconstruction schemes are observed. The improvement is significant for test cases with two objects, shallow domain as well as oblique incidence scenarios, where the standard SP_N approximation consistently fails across both the reconstruction schemes.