Optimal estimator for tomographic fluorescence lifetime multiplexing.

We use the model resolution matrix to analytically derive an optimal Bayesian estimator for multiparameter inverse problems that simultaneously minimizes inter-parameter cross talk and the total reconstruction error. Application of this estimator to time-domain diffuse fluorescence imaging shows that the optimal estimator for lifetime multiplexing is identical to a previously developed asymptotic time-domain (ATD) approach, except for the inclusion of a diagonal regularization term containing decay amplitude uncertainties. We show that, while the optimal estimator and ATD provide zero cross talk, the optimal estimator provides lower reconstruction error, while ATD results in superior relative quantitation. The framework presented here is generally applicable to other multiplexing problems where the simultaneous and accurate relative quantitation of multiple parameters is of interest.