Information theoretic analysis of hyperspectral imaging systems with applications to fluorescence microscopy

We present a general stochastic model for hyperspectral imaging data and derive analytical expressions for the Fisher information matrix for the underlying spectral unmixing problem. We investigate the linear mixing model as a special case and define a linear unmixing performance bound by using the Cramer-Rao inequality. As an application, we consider fluorescence imaging and show how the performance bound provides a spectral resolution limit that predicts how accurately a pair of spectrally similar fluorescent labels can be spectrally unmixed. We also report a novel result that shows how the spectral resolution limit can be overcome by exploiting the phenomenon of anti-Stokes shift fluorescence. In addition, we investigate how photon statistics, channel addition and channel splitting affect the performance bound. Finally by using the performance bound as a benchmark, we compare the performance of the least squares and the maximum likelihood estimators for spectral unmixing. For the imaging conditions tested here, our analysis shows that both estimators are unbiased and that the standard deviation of the maximum likelihood estimator is consistently closer to the performance bound than that of the least squares estimator. The results presented here are based on broad assumptions regarding the underlying data model and are applicable to hyperspectral data acquired with point detectors, sCMOS, CCD and EMCCD imaging detectors.