Chord-based image reconstruction in cone-beam CT with a curved detector Nianming Zuo National Laboratory of Pattern Recognition, Institute of Automation, The Chinese Academy of Sciences, Beijing 100080, China Dan Xia and Yu Zou Department of Radiology, The University of Chicago, Chicago, Illinois 60637 Tianzi Jiang National Laboratory of Pattern Recognition, Institute of Automation, The Chinese Academy of Sciences, Beijing 100080, China Xiao-Chuan Pan a Department of Radiology, The University of Chicago, Chicago, Illinois 60637 Received 7 September 2005; revised 22 June 2006; accepted for publication 25 July 2006; published 25 September 2006 Modern computed tomography CT scanners use cone-beam configurations for increasing volume coverage, improving x-ray-tube utilization, and yielding isotropic spatial resolution. Recently, there have been significant developments in theory and algorithms for exact image reconstruction from cone-beam projections. In particular, algorithms have been proposed for image reconstruction on chords; and advantages over the existing algorithms offered by the chord-based algorithms include the high flexibility of exact image reconstruction for general scanning trajectories and the capability of exact reconstruction of images within a region of interest from truncated data. These chord-based algorithms have been developed only for flat-panel detectors. Many cone-beam CT scanners em- ploy curved detectors for important practical considerations. Therefore, in this work, we have derived chord-based algorithms for a curved detector so that they can be applied to reconstructing images directly from data acquired by use of a CT scanner with a curved detector. We have also conducted preliminary numerical studies to demonstrate and evaluate the reconstruction properties of the derived chord-based algorithms for curved detectors. © 2006 American Association of Physicists in Medicine. DOI: 10.1118/1.2337270 Key words: computed tomography, cone-beam, curved detector, chords, image reconstruction, noise property I. INTRODUCTION Cone-beam configurations are becoming widely adopted in modern computed tomography CT systems for increasing volume coverage, improving x-ray-tube utilization, and yielding isotropic spatial resolution. In the past few years, significant breakthroughs have been made in theory and al- gorithms for exact image reconstruction from cone-beam projections 1–4 acquired with a helical scanning trajectory. Unlike the previously proposed Radon-transform-based algorithms, 5–8 these new algorithms 1–4 invoke only one- dimensional 1D filtration of the data derivative and recon- struct images directly from data without converting them into the Radon transform of the object function. In particular, Zou and Pan 3,4 proposed a formula for image reconstruction on PI-lines 8,9 in helical cone-beam scans. Based upon this formula, the backprojection-filtration BPF algorithm 3,4 and the filtered-backprojection FBP algorithm 10 have been de- veloped for image reconstruction on PI-lines from helical cone-beam data. Recently, successful effort has been devoted to generalize the BPF algorithm 11–15 and the FBP algorithm 14,16 to reconstruct images from data acquired with general cone-beam trajectories. Algorithms for image recon- struction on the M-lines were also developed. 12,17 One of the important features of the BPF algorithm is that it can exactly reconstruct an image within a region of interest ROI from projection data containing both longitudinal and transverse truncations. 12,18,19 On the other hand, the FBP- based algorithms 2,10 cannot be applied to reconstructing ex- act ROI images from transversely truncated data because the algorithms invoke, at each view, 1D filtering that requires full knowledge of data. Most recently, a new algorithm 14,20 was developed, which, like the existing FBP algorithms, in- vokes 1D filtering of the data derivative before its back- projection to the image space. However, because the data filtering can be carried out over a line segment of finite length on the detector, this algorithm, like the BPF algo- rithm, is capable of reconstructing exactly ROI images from data containing both longitudinal and transverse truncations. Therefore, in an attempt to differentiate it from the existing FBP-based algorithms, this algorithm has been referred to as the minimum-data FBP MDFBP algorithm. 20 Many CT scanners use curved detectors for minimizing the scanner size and reducing the centrifugal force induced by the high speed rotation of the detector and x-ray tube. Katsevich’s FBP algorithm for a curved detector was developed. 21 The chord-based BPF, MDFBP, and FBP algo- rithms were developed originally for a flat-panel detector, 3,20 3743 3743 Med. Phys. 33 „10…, October 2006 0094-2405/2006/33„10…/3743/15/$23.00 © 2006 Am. Assoc. Phys. Med.