Comparative study of one-step and two-step quantitative fluorescence photoacoustic tomography

Fluorescence optical tomography (FOT) is a well-known imaging technique, where fluorescent biological markers are injected to tag targeted tissues (tumors, proteins), and the absorption coefficient of fluorophore is reconstructed to provide contrast-enhanced images. Conventional FOT is known to have lack of stability to noise and shallow imaging depth due to strong optical scattering in biological tissue. Photoacoustic tomography (PAT) has been previously proposed to combine with FOT to resolve this issue. We propose a fully nonlinear one-step reconstruction in a diffuse-approximation modeled fluorescence photoacoustic tomographic (FPAT) setting, where the absorption coefficient of exogenous fluorophore is recovered directly from the photoacoustic data. Computational validations in two dimensions in single- and dual-grid reconstruction settings using full as well as partial data have been provided in support of the proposed algorithm. One-step schemes are particularly useful with respect to dual representations of field (optical and pressure) variables and optical parameters, especially in limited-data settings, which effectively help in constraining the optimization search space. We have compared the results of one- and two-step FPAT schemes and concluded that the one-step reconstructions are superior as compared with the corresponding two-step reconstructions. To the best of our knowledge, these are the first comparisons of one-step and two-step reconstructions in FPAT.