Tensor decomposition of hyperspectral images to study autofluorescence in age-related macular degeneration

Autofluorescence is the emission of light by naturally occurring tissue components on the absorption of incident light. Autofluorescence within the eye is associated with several disorders, such as Age-related Macular Degeneration (AMD) which is a leading cause of central vision loss. Its pathogenesis is incompletely understood, but endogenous fluorophores in retinal tissue might play a role. Hyperspectral fluorescence microscopy of ex-vivo retinal tissue can be used to determine the fluorescence emission spectra of these fluorophores. Comparisons of spectra in healthy and diseased tissues can provide important insights into the pathogenesis of AMD. However, the spectrum from each pixel of the hyperspectral image is a superposition of spectra from multiple overlapping tissue components. As spectra cannot be negative, there is a need for a non-negative blind source separation model to isolate individual spectra. We propose a tensor formulation by leveraging multiple excitation wavelengths to excite the tissue sample. Arranging images from different excitation wavelengths as a tensor, a non-negative tensor decomposition can be performed to recover a provably unique low-rank model with factors representing emission and excitation spectra of these materials and corresponding abundance maps of autofluorescent substances in the tissue sample. We iteratively impute missing values common in fluorescence measurements using Expectation-Maximization and use L₂ regularization to reduce ill-posedness. Further, we present a framework for performing group hypothesis testing on hyperspectral images, finding significant differences in spectra between AMD and control groups in the peripheral macula. In the absence of ground truth, i.e. molecular identification of fluorophores, we provide a rigorous validation of chosen methods on both synthetic and real images where fluorescence spectra are known. These methodologies can be applied to the study of other pathologies presenting autofluorescence that can be captured by hyperspectral imaging.