Linear Spectral Unmixing Algorithms for Abundance Fraction Estimation in Spectroscopy

Fluorescence spectroscopy is commonly used in modern biological and chemical studies, especially for cellular and molecular analysis. Since the measured fluorescence spectrum is the sum of the spectrum of each fluorophore in a sample, a reliable separation of fluorescent labels is the key to the successful analysis of the sample. A technique known as linear spectral unmixing is often used to linearly decompose the measured fluorescence spectrum into a set of constituent fluorescence spectra with abundance fractions. Various algorithms have been developed for linear spectral unmixing. In this work, we implement the existing linear unmixing algorithms and compare their results to discuss their strengths and drawbacks. Furthermore, we apply optimization methods to the linear unmixing problem and evaluate their performance to demonstrate their capabilities of solving the linear unmixing problem. Finally, we denoise noisy fluorescence emission spectra and examine how noise may affect the performance of the algorithms.