Degrees of freedom for projection imaging

This paper presents the use of the gramian as an aid in defining the degrees of freedom (DOF) in projection imaging systems. The gramian is developed for a general continuous-discrete imaging model and is then applied to the specific case of projection imaging. The theoretical development shows the general structure of the gramian to be quite well behaved and indicates where redundant data are achieved and the best ways of increasing the degrees of freedom with a minimum sample increase. The experimental development shows these inherent limitations on gramians up to 32 768 by 32 768 and is experimentally confirmed by reconstructing a series of projection images.