His research is on the application of mathematics to problems in image processing. He is particularly interested in using partial differential equations and optimization models to enhance the resolution of images, whether they are barcodes scanned at the grocery stores or satellite photos taken by Earth-observing satellites. His research has been used by the manufacturers of barcode scanners, the National Geospatial Intelligence Agency, the Air Force Research Office, and Pixar Animation Studios. Professor Wittman teaches courses in calculus, differential equations, and mathematical modeling. He is the mentor for the Citadel Chess Club.