Validating the LASSO algorithm by unmixing spectral signatures in multicolor phantoms

As hyperspectral imaging (HSI) sees increased implementation into the biological and medical elds it becomes increasingly important that the algorithms being used to analyze the corresponding output be validated. While certainly important under any circumstance, as this technology begins to see a transition from benchtop to bedside ensuring that the measurements being given to medical professionals are accurate and reproducible is critical. In order to address these issues work has been done in generating a collection of datasets which could act as a test bed for algorithms validation. Using a microarray spot printer a collection of three food color dyes, acid red 1 (AR), brilliant blue R (BBR) and erioglaucine (EG) are mixed together at dierent concentrations in varying proportions at dierent locations on a microarray chip. With the concentration and mixture proportions known at each location, using HSI an algorithm should in principle, based on estimates of abundances, be able to determine the concentrations and proportions of each dye at each location on the chip. These types of data are particularly important in the context of medical measurements as the resulting estimated abundances will be used to make critical decisions which can have a serious impact on an individual's health. In this paper we present a novel algorithm for processing and analyzing HSI data based on the LASSO algorithm (similar to "basis pursuit"). The LASSO is a statistical method for simultaneously performing model estimation and variable selection. In the context of estimating abundances in an HSI scene these so called "sparse" representations provided by the LASSO are appropriate as not every pixel will be expected to contain every endmember. The algorithm we present takes the general framework of the LASSO algorithm a step further and incorporates the rich spatial information which is available in HSI to further improve the estimates of abundance. We show our algorithm's improvement over the standard LASSO using the dye mixture data as the test bed.