Complementary data fusion for limited-angle tomography

Ambiguity in the solution of inverse problems arises when data are insufficient to define a unique solution (i.e., the problem is ill-posed). Data fusion has the potential to reduce this ambiguity by using other sensory data that complement the original data. This paper examines the application of data fusion to limited-angle computed tomography (CT) to resolve ambiguity. While CT in its conventional form is ill-posed with a small null space, limited-angle CT has a much larger null space. Structures that lie primarily in the null space of the limited-angle Radon transform are particularly prone to ambiguity. We describe a novel constraint-based data fusion system that fuses spatial support and ultrasound measurements with x-ray data. The ensuing problem is less ambiguous, has a reduced null space, and permits accurate reconstruction of a sandwich structure where otherwise impossible.