Evaluation of Unmixing Methods for the Separation of Quantum Dot Sources

Quantum Dots (QDs) are semiconductor crystals with nanometer dimensions, which have fluorescence properties that can be adjusted through controlling their diameter. Under ultraviolet light excitation, these nanocrystals re-emit photons in the visible spectrum, with a wavelength ranging from red to blue as their size diminishes. We created an experiment to evaluate unmixing methods for hyperspectral images. The wells of a matrix [3x3] were filled with individual or up to three of five QDs. The matrix was imaged by a hyperspectral system (Photon Etc., Montréal, QC, CA) and a data “cube” of 512 rows x 512 columns x 63 wavelengths was generated. For unmixing, we tested three approaches: Independent Component Analysis (ICA), Bayesian Positive Source Separation (BPSS) and our new Consensus Non-negative Matrix Factorization (CNFM) method. For each of these methods, we assessed the ability to separate the different sources from both spectral and spatial localization points of view. In this situation, we showed that BPSS and CNMF model estimates were very close to the original design of our experiment and were better than the ICA results. However, the time needed for the BPSS model to converge is substantially higher than CNMF. In addition, we show how the CNMF coefficients can be used to provide reasonable bounds for the number of sources, a key issue for unmixing methods, and allow for an effective segmentation of the spatial signal.