Algorithms for constrained linear unmixing with application to the hyperspectral analysis of fluorophore mixtures

In this paper, we describe the use of linear unmixing algorithms to spatially and spectrally separate fluorescence emission signals from fluorophores having highly overlapping emission spectra. Hyperspectral image data for mixtures of Nile Blue and HIDC Iodide in a methanol/polymer matrix were obtained using the Information-efficient Spectral Imaging sensor (ISIS) operated in its Hadamard Transform mode. The data were analyzed with a combination of Principal Components Analysis (PCA), orthogonal rotation, and equality and non-negativity constrained least squares methods. The analysis provided estimates of the pure-component fluorescence emission spectra and the spatial distributions of the fluorophores. In addition, spatially varying interferences from the background and laser excitation were identified and separated. A major finding resulting from this work is that the pure-component spectral estimates are very insensitive to the initial estimates supplied to the alternating least squares procedures. In fact, random number starting points reliably gave solutions that were effectively equivalent to those obtained when measured pure-component spectra were used as the-initial estimates. While our proximate application is evaluating the possibility of multivariate quantitation of DNA microarrays, the results of this study should be generally applicable to hyperspectral imagery typical of remote sensing spectrometers.