Reconstruction from Sparsely Sampled Data by ART with Interpolated Rays

After a brief discussion of the algebraic reconstruction techniques (ART), we introduce the attenuation problem in positron emission tomography (PET). We anticipate that a generalization of ART, the so-called cyclic subgradient projection (CSP) method, may be useful for solving this problem. This, however, has not been successfully realized, due to the fact that data collected by our proposed stationary PET detector ring are too sparsely sampled. That this is, in fact, a major problem is demonstrated by showing that ordinary ART produces reconstructions with unacceptably strong artifacts even on perfect (no attenuation) data collected according to the PET geometry. We demonstrate that the source of this artifact is the sparse sampling, and we propose the use of interpolated rays to overcome the problem. This approach is successful, as is illustrated by showing reconstructions from sparsely sampled data by ART with interpolated rays.