Grangeat-Type and Katsevich-Type Algorithms for Cone-Beam CT

Cone-beam image reconstruction algorithms are in rapid development for major biomedical and industrial applications. In this report, we primarily focus on those algorithms that allow exact and efficient reconstruction and have potential for dynamic studies, which are recently developed Grangeat-type and Katsevich-type algorithms. This preference is due to the needs for quantitative and functional CT/micro-CT applications. Last year, Lee and Wang developed Grangeat-type half-scan cone-beam algorithms in the circular and helical scanning cases to solve the short object problem. In both the circular and helical half-scan cases, the boundaries between regions of different sample redundancies are first determined. Then, corresponding weighting functions are formulated for evaluation at various characteristic point. It was demonstrated that the Grangeat-type half-scan reconstruction clearly outperformed the Feldkamp-type half-scan reconstruction in terms of intensity dropping artifacts. In 2001, Katsevich derived the first theoretically exact reconstruction formula for the spiral cone-beam geometry in the filtered backprojection format. The limitations of this formula include a large detector window and a small radius of the object to be reconstructed. Last year, Katsevich improved his first formula remarkably. The new formula imposes little restriction on the size of the patient, and assumes a smaller detector array than the old formula. Recently, Katsevich generalized his method from the spiral scanning case to other trajectories, and proved that the earlier two formulas are special cases of his general formula. There are important needs to improve current Grangeat-type and Katsevich-type algorithms for dynamic volumetric imaging in the long object cone-beam geometry.