ABSTRACT
This chapter provides a brief introduction to the topic of 3D image reconstruction in x-ray cone-beam computed tomography (CBCT). The topic represents an area of significant activity in research, commercial development, and clinical application since the first practical algorithm for 3D filtered backprojection (FBP) derived in 1984, referred to hereafter as the Feldkamp-DavisKress (FDK) algorithm.1 The numerous developments in 3D image reconstruction in the ensuing three decades are as follows:
• FDK algorithm for 3D FBP1 • Grangeat’s derivation of a well-posed inversion of the 3D
radon transform2 • Clinical application of 3D FBP on multidetector CT
(MDCT) scanners • Use of flat-panel detectors (FPDs) for CBCT in applica-
• FBP-like reconstruction techniques for general (noncircular) trajectories6,7
• Katsevich’s derivation of exact reconstruction in helical CBCT8
• A variety of iterative, statistical, and model-based reconstruction methods developed to provide higher-quality reconstruction at lower dose, from sparse projection data sets, and/or with better utilization of prior information9-13
• Application of iterative reconstruction techniques on clinical MDCT scanners
This cursory list only scratches the surface of a vast and vibrant area of medical imaging research, and a single chapter can do little more than provide a summary introduction of a few key principles. The sections below are organized along three broad strokes: (1) a review of the FDK algorithm (Section 13.2) and variations thereof (Sections 13.3 and 13.4); (2) an introduction to the principles and specific techniques for 3D reconstruction from noncircular trajectories (Section 13.5); and (3) a brief introduction to iterative reconstruction methods, including algebraic, likelihood-based, and compressive sensing techniques (Section 13.6). Considering the depth and breadth of such topics,
13.3 System Geometry and Geometric Calibration ....................................................................181 13.4 “Offset-Detector” Geometry for Increased Lateral FOV ...................................................183 13.5 Beyond Feldkamp: Reconstruction from Noncircular Source-Detector Trajectories ....184 13.6 Iterative Reconstruction .........................................................................................................185
