An extended completeness condition for exact cone-beam reconstruction and its application

The completeness condition is an important concept that specifies the capability of exact image reconstruction from a set of cone-beam projections. Unfortunately, the existing completeness conditions associated with Tuy´s (1983), Smith´s (1985), and Grangeat´s (1991) inversion formulae are too restrictive in various situations where some projections are partially measured. The authors derive an extended completeness condition that improves the existing results. The new condition is a direct consequence of a reconstruction algorithm that is in the form of space-variant filtering followed by cone-beam backprojection. The new condition is less restrictive compared with the existing ones and provides an effective means to incorporate partially measured projections into image reconstruction