Purpose: Helical cone-beam CT can be used for rapid volumetric imaging with high longitudinal resolution and for efficient utilization of X-ray power. Non-iterative algorithms have been developed for accurate image reconstruction in helical cone-beam CT. In the last year or so, an exact algorithm that is based upon the filtered backprojection (FBP) was developed by Katsevich. This algorithm appears to be particularly attractive because of its computational efficiency and numerical stability. In this work, we generalize Katsevich's cone-beam algorithm so that it can reconstruct accurate images from a smaller amount of data than does the current FBP-based algorithms require.
Methods and Materials: The Tam region on a detector panel is bounded by the cone-beam projection of the lower and upper turns of a helix. It has been shown that the data within the Tam region contain complete information for reconstruction of exact images. Exact FBP-based algorithms can reconstruct accurate images of long- and/or short-objects from data acquired in helical cone-beam configuration. These existing FBP-based algorithms, however, require data about 20% more than the minimum amount of data within the Tam region that has been proved theoretically to be sufficient for exact image reconstruction. In this work, we reveal an observation that the projection filtration in Katsevich's algorithm can be performed along any lines on the detector panel. Based upon this critical observation, we developed exact algorithms to reconstruct images from data within the Tam region on the detector panel. In particular, we develop a new strategy that performs the data filtration along the lines tangential to the boundary of the Tam region, thus ensuring that only the data within the Tam region are required and leading to a considerable reduction of data required for exact image reconstruction.
Results: We have implemented the proposed algorithms and performed numerical studies. The Shepp-Logan and other phantoms were used in our numerical studies. Results in these computer-simulation studies confirm that accurate images can be reconstructed by use of our proposed exact FBP-based algorithm.
Conclusion: Our proposed algorithms can reconstruct accurate images from the minimum amount of data within the Tam region, thus requiring a considerably less amount of data than do the existing algorithms. The practical implication of the proposed algorithms is that they can lead to significantly reduced radiation dosage that would be delivered to patients in CT imaging.
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