Abstract
Using filtered backprojection (FBP) and an analytic continuation approach, we prove that exact interior reconstruction is possible and unique from truncated limited-angle projection data, if we assume a prior knowledge on a subregion or subvolume within an object to be reconstructed. Our results show that (i) the interior region-of-interest (ROI) problem and interior volume-of-interest (VOI) problem can be exactly reconstructed from a limited-angle scan of the ROI/VOI and a 180 degree PI-scan of the subregion or subvolume and (ii) the whole object function can be exactly reconstructed from nontruncated projections from a limited-angle scan. These results improve the classical theory of Hamaker et al. (1980).
Highlights
The importance of performing exact image reconstruction from the minimum amount of data has been recognized for a long time
A recent milestone is the two-step Hilbert transform method developed by Noo et al [2] in 2004 In their framework, an object image on a PIline/chord can be exactly reconstructed if the intersection between the chord and the object is completely covered by a field of view (FOV)
Inspired by the tremendous biomedical implications including local cardiac CT at minimum dose, local dental CT with high accuracy, CT guided procedures, and nano-CT using analytic continuation we recently proved that the interior problem can be exactly and stably solved if a subregion in an ROI/VOI in the FOV is known [4,5,6,7] from fan-beam/cone-beam projection datasets, while the conventional wisdom that the interior problem does not have a unique solution [8] remains correct
Summary
The importance of performing exact image reconstruction from the minimum amount of data has been recognized for a long time. A recent milestone is the two-step Hilbert transform method developed by Noo et al [2] in 2004 In their framework, an object image on a PIline/chord can be exactly reconstructed if the intersection between the chord and the object is completely covered by a field of view (FOV). Inspired by the tremendous biomedical implications including local cardiac CT at minimum dose, local dental CT with high accuracy, CT guided procedures, and nano-CT using analytic continuation we recently proved that the interior problem can be exactly and stably solved if a subregion in an ROI/VOI in the FOV is known [4,5,6,7] from fan-beam/cone-beam projection datasets, while the conventional wisdom that the interior problem does not have a unique solution [8] remains correct. We will discuss relevant ideas and conclude the paper
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