Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization

• Published in: Physics in medicine & biology Vol. 53; no. 17; pp. 4777 - 4807
• Main Authors: Sidky, Emil Y, Pan, Xiaochuan
• Format: Journal Article
• Language: English
• Published: England IOP Publishing 07.09.2008
• Subjects: Algorithms; Computer Simulation; Cone-Beam Computed Tomography - methods; Humans; Image Processing, Computer-Assisted - methods; Imaging, Three-Dimensional - methods; Models, Statistical; Models, Theoretical; Phantoms, Imaging; Radiographic Image Interpretation, Computer-Assisted - methods; Software; Tomography Scanners, X-Ray Computed; X-Rays
• ISSN: 0031-9155; 1361-6560
• DOI: 10.1088/0031-9155/53/17/021

An iterative algorithm, based on recent work in compressive sensing, is developed for volume image reconstruction from a circular cone-beam scan. The algorithm minimizes the total variation (TV) of the image subject to the constraint that the estimated projection data is within a specified tolerance of the available data and that the values of the volume image are non-negative. The constraints are enforced by the use of projection onto convex sets (POCS) and the TV objective is minimized by steepest descent with an adaptive step-size. The algorithm is referred to as adaptive-steepest-descent-POCS (ASD-POCS). It appears to be robust against cone-beam artifacts, and may be particularly useful when the angular range is limited or when the angular sampling rate is low. The ASD-POCS algorithm is tested with the Defrise disk and jaw computerized phantoms. Some comparisons are performed with the POCS and expectation-maximization (EM) algorithms. Although the algorithm is presented in the context of circular cone-beam image reconstruction, it can also be applied to scanning geometries involving other x-ray source trajectories.