Noise Reduction by Projection Direction Dependent Diffusion for Low Dose Fan-beam X-ray Computed Tomography Shaojie Tang a,b , Xuanqin Mou a , Yanbo Zhang a , Hengyong Yu c,d a Institute of Image processing & Pattern recognition, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, China; b School of Automation, Xi'an University of Posts and Telecommunications, Xi'an, Shaanxi, 710121, China; c Department of Radiology, Division of Radiologic Sciences, Wake Forest University Health Sciences, Winston-Salem, NC, 27157, USA; d Biomedical Imaging Division, VT-WFU School of Biomedical Engineering and Sciences, Wake Forest University Health Sciences, Winston-Salem, NC, 27157, USA ABSTRACT We propose a novel method to reduce the noise in fan-beam computed tomography (CT) imaging. First, the inverse Radon transform is induced for a family of differential expression of projection function. Second, the diffusion partial differential equation (PDE) is generalized from image space to projection space in parallel-beam geometry. Third, the diffusion PDE is further induced from parallel-beam geometry to fan-beam geometry. Finally, the projection direction dependent diffusion is developed to reduce CT noise, which arises from the quantum variation in the low dose exposure of a medical x-ray CT (XCT) system. The proposed noise reduction processes projections iteratively and dependently on x-ray path position, followed by a general CT reconstruction. Numerical simulation studies have demonstrated its feasibility in the noise reduction of low dose fan-beam XCT imaging. Keywords: Noise Reduction, X-ray CT, Low Dose, Fan-beam 1. INTRODUCTION Worldwide there are growing concerns on radiation induced genetic, cancerous and other diseases. Facing the increasing radiation risk, the well-known ALARA (As Low As Reasonably Achievable) principle is widely accepted in the medical community. Therefore, a large number of researches have been carried out to decrease radiation dosage while keep the diagnostic image quality. One of important strategies is the so-called noise reduction technique. First, a patient is irradiated by an x-ray source with a low radiation dose during XCT imaging; Then, a noise reduction scheme is utilized to remove the noise in image or projection space. As for the noise reduction in image space, anisotropic diffusion is a superior processing tool [1,2]. Simultaneously, the research on the noise reduction in projection space has also become a hot topic at present [3-13]. Now, researchers have understood the statistical features of the sinogram data in a medical XCT [3,4], which becomes the solid basis for the developments of the sophisticated algorithms in projection space. Here, we have a simple review for those algorithms. Hsieh proposed an ‘ATM’ algorithm based on the local statistical results in projection space [5], which combined the effects of both mean and median filters together. Kachelrieβ et al. generalized a multi- dimensional adaptive filtering for the conventional, spiral single-slice, multi-slice, and cone-beam CT. CT image noise is dramatically reduced, while the degradation of resolution can be neglected [6]. La Riviere estimated the line integrals from the noisy projection by maximizing a penalized-likelihood objective function, which was constructed based on the assumption of a compound Poisson distribution of the polychromatic XCT imaging [7]. Based on the experimental study result on the noise properties of XCT sinogram data [4], Wang et al. developed a sequence of noise reduction algorithms mainly in projection space [8-12], which include Maximum a posteriori (MAP), Penalized weighted least-squares (PWLS), and Multi-scale Penalized Weighted Least-Squares (Multi-scale PWLS). Recently, Zhu et al. explored an improved PWLS algorithm in projection space. There is a substantial insight to the essential effect of scatter estimation and correction on the performance of noise reduction and resolution [13]. In this paper, we will generalize the isotropic diffusion PDE to the projection space in fan-beam geometry, and develop a noise reduction scheme by using a projection direction dependent diffusion in projection space. Begin the Medical Imaging 2011: Physics of Medical Imaging, edited by Norbert J. Pelc, Ehsan Samei, Robert M. Nishikawa, Proc. of SPIE Vol. 7961, 79613L · © 2011 SPIE · CCC code: 1605-7422/11/$18 · doi: 10.1117/12.877635 Proc. of SPIE Vol. 7961 79613L-1 Downloaded from SPIE Digital Library on 02 Jun 2011 to 117.32.153.146. Terms of Use: http://spiedl.org/terms