Cone-beam mammo-computed tomography from data along two tilting arcs Kai Zeng, a Hengyong Yu, b Laurie L. Fajardo, c and Ge Wang d CT/Micro-CT Laboratory, Department of Radiology, University of Iowa, Iowa City, Iowa 52242 Received 23 December 2005; revised 19 July 2006; accepted for publication 20 July 2006; published 13 September 2006 Over the past several years there has been an increasing interest in cone-beam computed tomogra- phy CT for breast imaging. In this article, we propose a new scheme for theoretically exact cone-beam mammo-CT and develop a corresponding Katsevich-type reconstruction algorithm. In our scheme, cone-beam scans are performed along two tilting arcs to collect a sufficient amount of information for exact reconstruction. In our algorithm, cone-beam data are filtered in a shift- invariant fashion and then weighted backprojected into the three-dimensional space for the final reconstruction. Our approach has several desirable features, including tolerance of axial data trun- cation, efficiency in sequential/parallel implementation, and accuracy for quantitative analysis. We also demonstrate the system performance and clinical utility of the proposed technique in numerical simulations. © 2006 American Association of Physicists in Medicine. DOI: 10.1118/1.2336510 Key words: cone-beam CT, mammography, exact reconstruction, Katsevich algorithm I. INTRODUCTION Breast cancer is ranked as the second leading cause of cancer death in women in the United States. It has been recognized that mass screening and early treatment are extremely impor- tant to reduce the mortality of breast cancer. Due to its speci- ficity and sensitivity, x-ray mammography has been the method of choice for screening and diagnosis. 1,2 However, x-ray mammography is far from being perfect because up to 17% of breast cancers are not identified with mammography, and normal breasts are associated with 70%–90% of mam- mograms suspicious of cancers. 3 A major limitation of x-ray mammography is its projective nature, while the real anatomy and pathology is really in three dimensions 3D. To address this problem, x-ray tomosynthesis and cone-beam computed tomography CT are two compelling solutions. Tomosynthesis is a three-dimensional 3D imaging tech- nique to reconstruct a series of images from a limited num- ber of projections. 4 Since its introduction in 1972, the area of tomosynthesis has been significantly advanced largely due to the development of the area detectors. 5 A primary application of tomosynthesis is for breast imaging. 6–8 The tomosynthetic algorithms are either analytic or iterative. The analytic algo- rithms are straightforward and efficient, such as self-masking, 9 selective plane removal, 10 and matrix inver- sion tomosynthesis. 11 While the iterative algorithms are ro- bust against noisy data and flexible to integrate prior knowl- edge, as it is done using algebraic reconstruction techniques, 12,13 expectation-maximization, 14 etc. none of these algorithms can avoid the inherent drawback of tomo- synthesis due to the data incompleteness. Technically speaking, a breast volume should be imaged very well by cone-beam CT. Since more information of the object is acquired, the image quality of CT is much better than tomosynthesis, in terms of contrast resolution, geometri- cal distortion, etc. The concept of breast CT was proposed two decades ago, 15 but little progress had been made initially because of compromised image quality and involved radia- tion exposure. Again, thanks to the advancement in the digi- tal detector technology, a number of groups investigated the feasibility and prototypes of cone-beam mammo-CT. 16,17 Nevertheless, the algorithms for breast CT are still based on the traditional Feldkamp-type algorithms, 18 and reconstruct images approximately with various artifacts. The fundamental classic results on exact cone-beam CT reconstruction were achieved by Grangeat, 19 Smith, 20 and Tuy. 21 The recent breakthroughs on exact cone-beam CT al- gorithms were reviewed by Zhao et al. 22 Up to now, there are a number of accurate and efficient cone-beam CT algorithms for various scanning trajectories, such as a helix, 23–25 an arc-plus-line, 26,27 a circle-plus-arc, 28,29 and a saddle curve. 30,31 Also, there are several algorithms which allow exact image reconstruction in the case of general trajectories. 32–36 To improve image quality with cone-beam mammo-CT, we are motivated to design a cone-beam scanning mode that allows theoretically exact image reconstruction. In this ar- ticle, we propose a novel scheme for cone-beam mammo-CT, which is theoretically exact, and develop a corresponding Katsevich-type reconstruction algorithm. In our scheme, cone-beam scans are performed along two tilting arcs to col- lect a sufficient amount of information for exact reconstruc- tion. We derive our corresponding algorithm in the frame- work established by Katsevich, 29,33 which may handle axial truncation of cone beam data. In what follows, we describe our system setup and derive the algorithm in Sec. II, describe numerical simulation results in Sec. III, and discuss relevant issues and conclude the article in Sec. IV. II. METHODS AND MATERIALS A. Cone-beam mammo-CT system In the proposed cone-beam mammo-CT system Fig. 1,a patient lays down on a table with one breast hanging through a hole. The x-ray tube and a flat-panel camera are fixed to a 3621 3621 Med. Phys. 33 „10…, October 2006 0094-2405/2006/33„10…/3621/13/$23.00 © 2006 Am. Assoc. Phys. Med.