Image reconstruction in peripheral and central regions-of-interest and data redundancy

Algorithms have been developed for image reconstruction within a region-of-interest (ROI) from fan-beam data less than that required for reconstructing the entire image. However, these algorithms do not admit truncated data. In this work, we investigate exact ROI-image reconstruction from fan-beam data containing truncations by use of the so-called fan-beam backprojection-filtration (BPF) algorithm. We also generalize the fan-beam BPF algorithm to exploit redundant information inherent in the truncated fan-beam data. Because the parallel-beam scan can be interpreted as a special case of the fan-beam scan, based upon the fan-beam BPF algorithm, we derive a parallel-beam BPF algorithm for exactly reconstructing ROI images from truncated parallel-beam data. Furthermore, we investigate image reconstruction within two types of distinctive ROIs, which are referred to as the peripheral and central ROIs, respectively, from fan-beam data containing truncations and discuss their potential clinical applications. The results can readily be generalized to reconstructing 3D ROI images from data acquired in circular and helical cone-beam scan. They can also be extended to address ROI-image-reconstruction problems in parallel-, fan-, and cone-beam scans with general trajectories. The work not only has significant implications for clinical and animal-imaging applications of CT, but also may find applications in other imaging modalities.