Non-negative Matrix Factorization using Partial Prior Knowledge for Radiation Dosimetry

Hyperspectral unmixing aims at decomposing a given signal into its spectral signatures and its associated fractional abundances. To improve the accuracy of this decomposition, algorithms have included different assumptions depending on the application. The goal of this study is to develop a new unmixing algorithm that can be applied for the calibration of multi-point scintillation dosimeters used in the field of radiation therapy. This new algorithm is based on a non-negative matrix factorization. It incorporates a partial prior knowledge on both the abundances and the endmembers of a given signal. It is shown herein that, following a precise calibration routine, it is possible to use partial prior information about the fractional abundances, as well as on the endmembers, in order to perform a simplified yet precise calibration of these dosimeters. Validation and characterization of this algorithm is made using both simulations and experiments. The experimental validation shows an improvement in accuracy compared to previous algorithms with a mean spectral angle distance (SAD) on the estimated endmembers of 0.0766, leading to an average error of $(0.25 \pm 0.73)$ % on dose measurements.