The Spatial LASSO with Applications to Unmixing Hyperspectral Biomedical Images

Hyperspectral imaging (HSI) is a spectroscopic method which uses densely sampled measurements along the electromagnetic spectrum to identify the unique molecular composition of an object. Traditionally HSI has been associated with remote sensing type applications, but recently has found increased use in biomedicine, from investigations at the cellular to the tissue level. One of the main challenges in the analysis of HSI is estimating the proportions, also called abundance fractions of each of the molecular signatures. While there is great promise for HSI in the area of biomedicine, large variability in the measurements and artifacts related to the instrumentation have slown adoption into more widespread practice. In this paper we propose a novel regularization and variable selection method called the spatial LASSO (SPLASSO). The SPLASSO incorporates spatial information via a graph Laplacian based penalty to help improve the model estimation process for multivariate response data. We show the strong performance of this approach on a benchmark HSI data set with considerable improvement in predictive accuracy over the standard LASSO.