A theoretical framework of regional cone-beam tomography

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Abstract
Intuitively, if only part of an object is to be reconstructed, the information required to perform the reconstruction should be less than that required to perform global reconstruction (global reconstruction is assumed by every published reconstruction formula with closed format). The reduction of input information will hopefully lead to the simplification of data collection, and reduction of implementation cost. Motivated by this, the author has explored three basic issues of regional cone-beam tomography: 1) a completeness condition for regional reconstruction, 2) an estimation formula, and 3) a convergence condition. The analysis of the first issue yields requirements for artifact free reconstruction, and a convenient criterion for source curve design. The closed format of the estimation formula developed in this paper enables efficient analysis. Last, the discussion of the third issue facilitates guidelines for selecting an appropriate interpolation technique for discrete input data.

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