Memory-efficient self-supervised learning of null space projection operators

Abstract

Many imaging systems can be described by a linear operator that maps object properties to a collection of discrete measurements. The null space of such an imaging operator represents the set of object components that are effectively invisible to the imaging system. The ability to extract the object components that lie within the null space of an imaging operator allows one to analyze and optimize not only the measurement capabilities of the system itself, but also its associated reconstruction methods. An orthogonal null space projection operator (ONPO), which maps any object to its corresponding null space component, offers this ability. However, existing methods for producing an ONPO are limited by high memory requirements. In this work, we develop a novel learning-based method for calculating an ONPO. Numerical results show that our method can produce an accurate ONPO using less memory than existing methods, enabling the characterization of the null spaces of larger imaging operators than previously possible.