Dr. Barnes and graduate student members of his research teams pursue research in the areas of image and video-driven data mining with applications in medical imaging, remote sensing, genomics, and in mobile telecommunications/multimedia applications. Some of these teams are making advances in synthetic aperture image formation algorithms. His research teams have focused on direct sum successive approximation signal processing structures. These research activities have expanded the frontiers of residual vector quantization and power- and bandwidth-constrained communications. This research is both theoretical and applied, with proven applications in areas of data compression, communications, and pattern recognition. Channel coding duals of direct sum structures are leading into research areas of a group theory description of lattice-like structures that retain all significant group properties, but where a closure constraint is relaxed: enabling increased power efficiency in bandlimited communications. Using the theoretical foundation of direct sum successive approximation source coding, Dr. Barnes’ research teams are also working in the areas of pattern recognition, database management system engineering and human-system interfaces. Dr. Barnes has acquired funding to develop applications of this technology in the areas of medical imaging and remote sensing. Dr. Barnes, working with Ph.D. candidate Jehanzeb Burki, has pushed the state-of-the-art in SAR image formation processing by developing an interpolation-free OMEGA-K SAR algorithm. The research philosophy of Dr. Barnes and his research team members is to work jointly with others in cross-disciplines to solve challenging, multi-faceted, basic and applied problems.