Attenuation-Corrected Fluorescence Spectra Unmixing for Spectroscopy and Microscopy

In fluorescence measurements, light is often absorbed and scattered by a sample both for excitation and emission, resulting in the measured spectra to be distorted. Conventional linear unmixing methods computationally separate overlapping spectra but do not account for these effects. We propose a new algorithm for fluorescence unmixing that accounts for the attenuation-related distortion effect on fluorescence spectra. Using a matrix representation, we derive forward measurement formation and a corresponding inverse method; the unmixing algorithm is based on nonnegative matrix factorization. We also demonstrate how this method can be extended to a higher-dimensional tensor form, which is useful for unmixing overlapping spectra observed under the attenuation effect in spectral imaging microscopy. We evaluate the proposed methods in simulation and experiments and show that it outperforms a conventional, linear unmixing method when absorption and scattering contributes to the measured signals, as in deep tissue imaging.