The R2 research thrust is responsible for the development of mathematical techniques for extracting relevant information from the signals collected by subsurface sensing mechanisms. The goal is to identify common mathematical structures and develop general approaches that are applicable across diverse application domains. The work under this thrust is described under four areas, representing distinct problem classes and information extraction strategies. Each of the areas is developing algorithms that are broadly applicable across different applications in these problem classes. The four areas are R2A Multi-View Tomography (MVT), R2B Localized Probing and Mosaicing (LPM), R2C Multi-Spectral Discrimination (MSD), and R2D Image Understanding and Sensor Fusion (IUSF).