Multiplexed fluorescence tomography with spectral and temporal data: demixing with intrinsic regularization

We consider the joint use of spectral and temporal data for multiplexed fluorescence molecular tomography to enable high-throughput imaging of multiple fluorescent targets in bulk tissue. This is a challenging problem due to the narrow near-infrared diagnostic window and relatively broad emission spectra of common fluorophores, and the distortion ("redshift") that the fluorophore signals undergo as they propagate through tissue. We show through a Cramér-Rao lower bound analysis that demixing with spectral-temporal data could result in an order of magnitude improvement in performance over either modality alone. To cope with the resulting large data set, we propose a novel two-stage algorithm that decouples the demixing and tomographic reconstruction operations. In this work we concentrate on the demixing stage. We introduce an approach which incorporates ideas from sparse subspace clustering and compressed sensing and does not require a regularization parameter. We report on simulations in which we simultaneously demixed four fluorophores with closely overlapping spectral and temporal profiles in a 25 mm diameter cross-sectional area with a root-mean-square error of less than 3% per fluorophore, as well as on studies of sensitivity of the method to model mismatch.