Factorization of the Reconstruction Problem in Circular Cone-Beam Tomography and its Use for Stability Analysis

In this article, we propose a novel factorization of the circular cone-beam (CB) reconstruction problem into a set of independent 2D inversion problems. This factorization is established in the context of modern two-step Hilbert reconstruction methods by combining the ideas of an empirically derived CB inversion approach with a firm and exact theory. We were able to accurately discretize these 2D inversion problems, which allows a detailed investigation of CB reconstruction by using the singular value decomposition and also allows efficient iterative reconstruction approaches. The introduced theory is applied for preliminary studies of the stability of circular CB tomography assuming a short object. We analyzed, how the radius of the circular scan affects the stability and investigated the effect of an additional linear scan onto the condition of the problem. Numerical results are presented for a disc phantom.