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.<
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