Bayesian statistical reconstruction for low-dose X-ray computed tomography using an adaptive-weighting nonlocal prior☆
Introduction
Since the introduction of computed tomography (CT) in the 1970s, the X-ray exposure represents the largest source of radiation exposure because of the rapidly increasing use of X-ray CT. Minimizing the radiation exposure to patients has been one of the major concerns in the CT field and modern clinical radiology [1]. On the other hand, HELICAL/SPIRAL CT (HCT) makes it possible to scan adequately a vital organ volume in a single breath-hold, thus problems related to patient motion can be minimized. In recent years, HCT has replaced conventional stop-and-shoot CT in many clinical applications. The helical scanning is of significant benefit to CT angiography and multi-phase abdominal imaging. Although HCT has many advantages, the effective dose of HCT can be up to four times higher than that of a corresponding conventional stop-and-shoot CT [1], [2].
Low-dose CT imaging has been under development in the last decade and is currently clinically desired [2], [3]. A simple and cost-effective means among many strategies to achieve low-dose CT applications is to lower X-ray tube current (mA) as low as achievable (for both helical and stop-and-shoot modes). However, the image quality of low mA acquisition protocol will be severely degraded due to the excessive X-ray quantum noise. Statistical iterative reconstruction approaches have shown good results in application and usually outperform the FBP method as the noise increases [4], [5], [6], [7], [8], [9], [10], [11], [12], [13]. Statistical methods can also incorporate the object constraints and prior information into the reconstruction through Bayesian approaches. Based on Markov random fields (MRF) theory [13], the original ill-posed reconstruction can be greatly improved by Bayesian methods [8], [9], [10], [11], [12].
How to devise an effective prior for Bayesian reconstruction has been widely studied in the past 10 years [8], [9], [10], [11], [12], [13], [14]. Lowering the noise effect and preserving the edge are the two main aims in devising priors. Under Bayesian and MRF paradigm, the work in this paper is to devise an effective prior for low-dose X-ray statistical tomographic reconstruction.
The simple and widely used quadratic membrane (QM) prior tends to produce an unfavorable oversmoothing effect. And some edge-preserving nonquadratic priors are able to produce sharp edges by choosing a nonquadratic prior energy [8], [9], [10], [11], [12], [13]. And in 1998, edge-preserving median root prior (MRP) was proposed by Alenius and his colleagues for iterative reconstruction of PET transmission images [11]. However, in the case of low X-ray scan when the noise level is relatively significant, such edge-preserving nonquadratic priors tend to produce blocky piecewise regions or staircase artifacts. None of these priors addresses the information of global connectivity and continuity in objective image. Only local and indiscriminatively prior information is provided. We term these traditional priors local priors.
Yu and Fessler devised a boundary-based Bayesian method which incorporates global information of image by level-set methods [12]. But such boundary-based method relies heavily on the level-set operations whose effect in different images is unpredictable and parameter-dependent. Recently, Buades et al. put forward a novel algorithm for image denoising [14]. Illuminated by their nonlocal idea, a nonlocal MRF quadratic prior model for Bayesian image reconstruction is proposed [15]. In this article, we propose a novel AW nonlocal (adaptive-weighting nonlocal) prior for X-ray CT Bayesian reconstruction. Such AW nonlocal prior reconstruction approach can selectively and adaptively include the relevant neighbor pixels for the regularization,and eliminate the negative regularization effect from the irrelevant neighbor pixels. In Section 2, a review of the old prior model and the theory for the proposed AW nonlocal prior model are both illustrated. In Sections 3 Statistical reconstruction, 4 Experimentation, we give the iterative reconstruction algorithm and perform simulated statistical CT image reconstruction with two different dose levels. Relevant comparisons show the proposed AW nonlocal prior’s good properties in low-dose X-ray computed tomography. Conclusions and plans for future work are given in Section 5.
Section snippets
Theory of the proposed aw nonlocal prior model
Based on Bayesian and MRF theory, regularization from prior information can be imposed on image reconstruction to suppress noise effect. And we can build following posterior probability for image reconstruction.where is the likelihood distribution. is the prior distribution. The partition function Z is a normalizing constant. is the prior energy function, and is the notation for the value of the energy function U
Statistical model
In X-ray CT statistical reconstruction, we model scanned photon counts vectors as Poisson random variables. , the measured photon counts detected by projection i can be well modelled as Poisson random with expectation as a function of the underlying attenuation map for X-ray CT or transmission tomography [4], [5], [6], [7], [8]. So, the likelihood function is the probability of obtaining the measurement vector g if the objective attenuation map is f. Based on above, we can get
Experimentation
Computer simulations are performed using a modified 2D Shepp–Logan transverse attenuation map phantom (Fig. 2(a)) with four straight lines added for resolution analysis. The phantom is composed by square pixels with pixel intensities from 0 to 240. The size of every pixel is set to be . A single-slice detector band CT scanner is considered in experiments. The detector band is on an arc concentric to the X-ray source with a distance of 100 cm. The distance from the rotation center
Conclusions and future work plan
From above experiments and analysis, we can see our proposed AW nonlocal prior, which is devised to selectively and adaptively exploit the global connectivity information in objective image, is capable of effectively suppressing background noise and preserving details in the objective CT image for different X-ray dose levels.
Nevertheless, the building of the proposed prior needs computations over large neighborhoods and introduces several hand-adjusting parameters to the reconstruction
Acknowledgments
This research was supported by the Natural Science Research Program of Fujian Province under grant No. 2008J0321, and the Medical Research Program 115 of Nanjing Military Region under grant No. 06MA99. The authors would like to thank Professor J.A. Fessler of the university of Michigan for software support.
Yang Chen received his B.S., M.S. and Ph.D. degrees in biomedical engineering from the Department of Biomedical Engineering, First Military Medical University, China. He is currently a Lecturer at the Laboratory of Image Science and Technology, Southeast University, Nanjing, China. His research interests include medical imaging reconstruction (especially on PET/CT), and medical image analysis.
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Cited by (0)
Yang Chen received his B.S., M.S. and Ph.D. degrees in biomedical engineering from the Department of Biomedical Engineering, First Military Medical University, China. He is currently a Lecturer at the Laboratory of Image Science and Technology, Southeast University, Nanjing, China. His research interests include medical imaging reconstruction (especially on PET/CT), and medical image analysis.
Dazhi Gao received his B.S. degrees from the Department of Biomedical Engineering, First Military Medical University, China. He is currently a doctor in the Department of Radiology, Nanjing General Hospital, Nanjing Military Command of PLA, Nanjing, China.
Cong Nie received his B.S. degrees from the Department of Biomedical Engineering, First Military Medical University, China. He is currently a senior engineer in the Department of Radiology, Nanjing General Hospital, Nanjing Military Command of PLA, Nanjing, China.
Limin Luo is currently a professor at Laboratory of Image Science and Technology, Southeast University, Nanjing, China. He is also a senior member of IEEE. His research interests include medical imaging instrumentation and biomedical engineering.
Wufan Chen received the B.S. and M.S. degrees in applied mathematics, computational fluid dynamics from Peking University of Aeronautics and Astronautics (BUAA), China, in 1975 and 1981, respectively. Since September 2004, he has been with Southern Medical University, China, where he holds the rank of Professor in the School of Biomedical Engineering and the director of the Key Lab for Medical Image Processing of Guangdong province. His research focuses on the medical imaging and medical image analysis.
Xindao Yin received a medical degree from the University of SuZhou, China, in 1989 and Ph.D. from the University of FuDan, China, in 2002. Since 2003, he has been working in Nanjing First Hospital Affiliated to Nanjing Medical University, where he is an associate professor in radiology and a chief in CT/MRI Department. His main interests are CT or MRI clinical diagnosis and medical image post-processing.
Yazhong Lin received his B.S. degrees from the Department of Biomedical Engineering, First Military Medical University, China. He is currently a senior engineer in the Department of Medical Information, 175 Hospital (Southeast Hospital of XiaMen University), Nanjing Military Command of PLA, Zhangzhou, Fujian, China.
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This research was supported by National Basic Research Program of China under grant, No. 2010CB732503, and the Natural Science Research Program of Fujian Province under grant No. 2008J0321, and the Medical Research Program 115 of Nanjing Military Region under grant No. 06MA99.