基于离散剪切波正则化的低剂量CT图像统计重建算法
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摘要
提出一种低剂量医学CT图像重建方法,能够在少视角投影或低X-射线管电流投影的情况下保证重建图像的质量。减少扫描视角的数量或者降低X-射线管电流强度均可以降低辐射剂量,从而减少X射线对人体伤害,但是前者会造成扫描数据欠完备,后者会使投影数据信噪比指数下降,传统算法不能保证重建图像满足诊断要求。提出一种离散剪切波变换正则化的低剂量CT图像统计迭代重建算法,在数据保真项加入符合数据统计特性的系数加权,以降低噪声对重建结果的影响,并将待建图像在剪切波域可以稀疏表示作为先验信息,利用增广拉格朗日方法将此先验信息作为正则化项加入目标函数,缩小了解空间,使不完备投影数据获得稳定而准确的重建。实验数据表明,重建图像在投影数据远远不满足完备性条件,或投影数据信噪比急剧下降的情况下,本算法能够重建出高质量图像。在辐射剂量降低到滤波反投影FBP算法的10%甚至更低时仍然能够得到清晰保留结构细节的重建图像。
Though reducing the number of projection angles or lowering the current intensity of Xray tube can reduce radiation dose and therefore alleviate damage to human bodies,the former measure can result in incomplete projection data while the later causes a declined signal to noise ratio of projection data.We propose a low-dose CT image statistical iterative reconstruction algorithm based on sparsity constraint in shearlet domain.The statistical weighting coefficient of data fidelity terms is introduced to reduce the influence of noise on the reconstruction results,and the sparse representation of intermediate images in shearlet domain is added into the objective function as a regularization item by means of the augmented Lagrangian method so as to narrow down the solution space and obtain stable and accurate reconstruction from incomplete projection data.According to experimental data,this algorithm can get high-quality images when projection data is far from completeness or the signal to noise ratio of projection data declines sharply.The proposed algorithm can be used for attaining reconstructed images that clearly keep structural details when the radiation dose is decreased to 10% of the filtered back projection(FBP)or even lower degrees.
Though reducing the number of projection angles or lowering the current intensity of Xray tube can reduce radiation dose and therefore alleviate damage to human bodies,the former measure can result in incomplete projection data while the later causes a declined signal to noise ratio of projection data.We propose a low-dose CT image statistical iterative reconstruction algorithm based on sparsity constraint in shearlet domain.The statistical weighting coefficient of data fidelity terms is introduced to reduce the influence of noise on the reconstruction results,and the sparse representation of intermediate images in shearlet domain is added into the objective function as a regularization item by means of the augmented Lagrangian method so as to narrow down the solution space and obtain stable and accurate reconstruction from incomplete projection data.According to experimental data,this algorithm can get high-quality images when projection data is far from completeness or the signal to noise ratio of projection data declines sharply.The proposed algorithm can be used for attaining reconstructed images that clearly keep structural details when the radiation dose is decreased to 10% of the filtered back projection(FBP)or even lower degrees.
引文
[1]Luo Li-min,Hu Yi-ning,Chen Yang.Research status and prospect for low-dose CT imaging[J].Journal of Data Acquisition&Processing,2015,30(1):24-34.(in Chinese)
[2]Sodickson A,Baeyens P F,Andriole K P,et al.Recurrent CT,cumulative radiation exposure,and associated radiationinduced cancer risks from CT of adults[J].Radiology,2009,251(1):175.
[3]Hsieh J.Adaptive streak artifact reduction in computed tomography resulting from excessive x-ray photon noise[J].Medical Physics,1998,25(11):2139-2147.
[4]Hara A K,Paden R G,Silva A C,et al.Iterative reconstruction technique for reducing body radiation dose at CT:Feasibility study[J].American Journal of Roentgenology,2009,193(3):764-771.
[5]Zhang Yuan-ke,Zhang Jun-ying,Lu Hong-bing.Parameter estimation and statistical noise reduction for low-dose CT sinogram[J].Journal of Xidian University(Natural Science Edition),2011,38(3):99-106.(in Chinese)
[6]Wang J,Lu H,Wen J,et al.Multiscale penalized weighted least-squares sinogram restoration for low-dose X-ray computed tomography[J].IEEE Transactions on Biomedical Engineering,2008,55(3):1022-1031.
[7]Zhang H,Zhang L,Sun Y,et al.Projection domain denoising method based on dictionary learning for low-dose CT image reconstruction[J].Journal of X-ray Science and Technology,2015,23(5):567-578.
[8]Zhang Quan,Luo Li-min,Gui Zhi-guo.Improved nonlocal prior-based Bayesian sinogram smoothing algorithm for lowdose CT[J].Journal of Southeast University(Natural Science Edition),2014,44(3):499-503.(in Chinese)
[9]Wang Li-yan,Wei Zhi-hui.Linearized Bregman iterations for low-dose CT reconstruction[J].Journal of Electronics&Information Technology,2013,35(10):2418-2424.(in Chinese)
[10]Xu Q,Yu H,Mou X,et al.Low-dose X-ray CT reconstruction via dictionary learning[J].IEEE Transactions on Medical Imaging,2012,31(9):1682-1697.
[11]Candes E J,Romberg J,Tao T.Robust uncertainty principles:Exact signal reconstruction from highly incomplete frequency information[J].IEEE Transactions on Information Theory,2006,52(2):489-509.
[12]Qian Shan-shan,Huang Jing,Ma Jian-hua,et al.Nonmonotone total variation minimization based projection restoration for low-dose CT reconstruction[J].Acta Electronica Sinica,2011,39(7):1702-1707.(in Chinese)
[13]Mao Bao-lin,Chen Xiao-zhao,Xiao Da-yu,et al.Ordered subset image reconstruction studied by means of total variation minimization and fast first-order method in low dose computed tomograhpy[J].Acta Physica Sinica,2014,63(13):138701.(in Chinese)
[14]Yu H,Wang G.A soft-threshold filtering approach for reconstruction from a limited number of projections[J].Physics in Medicine and Biology,2010,55(13):3905-3916.
[15]Wang Lin-yuan,Liu Hong-kui,Li Lei,et al.Review of sparse optimization-based computed tomography image reconstruction from few-view projections[J].Acta Physica Sinica,2014,63(20):208702.(in Chinese)
[16]Rantala M,VnskS,JrvenpS,et al.Wavelet-based reconstruction for limited-angle X-ray tomography[J].IEEE Transactions on Medical Imaging,2006,25(2):210-217.
[17]Guo De-quan,Yang Hong-yu,Liu Dong-quan,et al.Overview on sparse image denoising[J].Application Research of Computers,2012,29(2):406-413.(in Chinese)
[18]Guo K,Labate D.Optimally sparse multidimensional representation using shearlets[J].SIAM Journal on Mathematical Analysis,2007,39(1):298-318.
[19]Easley G,Labate D,Lim W Q.Sparse directional image representations using the discrete shearlet transform[J].Applied and Computational Harmonic Analysis,2008,25(1):25-46.
[20]Lim W Q.The discrete shearlet transform:A new directional transform and compactly supported shearlet frames[J].IEEE Transactions on Image Processing,2010,19(5):1166-1180.
[21]Wang Lei,Li Bin,Tian Lian-fang.Medical image fusion based on shift-invariant shearlet transformation[J].Journal of South China University of Technology(Natural Science Edition),2011,39(12):145-152.(in Chinese)
[22]Zhao J,LüL,Sun H.Multi-threshold image denoising based on shearlet transform[J].Applied Mechanics and Materials,2010,29-32:2251-2255.
[23]Guo K,Labate D.Characterization and analysis of edges using the continuous shearlet transform[J].SIAM Journal on Imaging Sciences,2009,2(3):959-986.
[24]Deng Cheng-zhi,Liu Juan-juan,Wang Sheng-qian,et al.Feature retained image inpainting based on sparsity regularization[J].Optics and Precision Engineering,2013,21(7):1906-1913.(in Chinese)
[25]Kalender W A.Computed tomography:Fundamentals,system technology,image quality,applications[M].Hoboken,NJ:John Wiley&Sons Inc.,2011.
[26]Chen S S,Donoho D L,Saunders M A.Atomic decomposition by basis pursuit[J].SIAM Review,2001,43(1):129-159.
[27]Wang Z,Bovik A C,Sheikh H R,et al.Image quality assessment:From error visibility to structural similarity[J].IEEE Transactions on Image Processing,2004,13(4):600-612.
[1]罗立民,胡轶宁,陈阳.低剂量CT成像的研究现状与展望[J].数据采集与处理,2015,30(1):24-34.
[5]张元科,张军英,卢虹冰.低剂量CT图像模型参数估计及统计去噪研究[J].西安电子科技大学学报(自然科学版),2011,38(3):99-106.
[8]张权,罗立民,桂志国.基于改进非局部先验的Bayesian低剂量CT投影平滑算法[J].东南大学学报(自然科学版),2014,44(3):499-503.
[9]王丽艳,韦志辉.低剂量CT的线性Bregman迭代重建算法[J].电子与信息学报,2013,35(10):2418-2424.
[12]钱姗姗,黄静,马建华,等.基于投影数据非单调性全变分恢复的低剂量CT重建[J].电子学报,2011,39(7):1702-1707.
[13]毛宝林,陈晓朝,孝大宇,等.基于全变分最小化和快速一阶方法的低剂量CT有序子集图像重建[J].物理学报,2014,63(13):138701.
[15]王林元,刘宏奎,李磊,等.基于稀疏优化的计算机断层成像图像不完全角度重建综述[J].物理学报,2014,63(20):208702.
[17]郭德全,杨红雨,刘东权,等.基于稀疏性的图像去噪综述[J].计算机应用研究,2012,29(2):406-413.
[21]王雷,李彬,田联房.基于平移不变剪切波变换的医学图像融合[J].华南理工大学学报(自然科学版),2011,39(12):145-152.
[24]邓承志,刘娟娟,汪胜前,等.保留结构特征的稀疏性正则化图像修复[J].光学精密工程,2013,21(7):1906-1913.
[2]Sodickson A,Baeyens P F,Andriole K P,et al.Recurrent CT,cumulative radiation exposure,and associated radiationinduced cancer risks from CT of adults[J].Radiology,2009,251(1):175.
[3]Hsieh J.Adaptive streak artifact reduction in computed tomography resulting from excessive x-ray photon noise[J].Medical Physics,1998,25(11):2139-2147.
[4]Hara A K,Paden R G,Silva A C,et al.Iterative reconstruction technique for reducing body radiation dose at CT:Feasibility study[J].American Journal of Roentgenology,2009,193(3):764-771.
[5]Zhang Yuan-ke,Zhang Jun-ying,Lu Hong-bing.Parameter estimation and statistical noise reduction for low-dose CT sinogram[J].Journal of Xidian University(Natural Science Edition),2011,38(3):99-106.(in Chinese)
[6]Wang J,Lu H,Wen J,et al.Multiscale penalized weighted least-squares sinogram restoration for low-dose X-ray computed tomography[J].IEEE Transactions on Biomedical Engineering,2008,55(3):1022-1031.
[7]Zhang H,Zhang L,Sun Y,et al.Projection domain denoising method based on dictionary learning for low-dose CT image reconstruction[J].Journal of X-ray Science and Technology,2015,23(5):567-578.
[8]Zhang Quan,Luo Li-min,Gui Zhi-guo.Improved nonlocal prior-based Bayesian sinogram smoothing algorithm for lowdose CT[J].Journal of Southeast University(Natural Science Edition),2014,44(3):499-503.(in Chinese)
[9]Wang Li-yan,Wei Zhi-hui.Linearized Bregman iterations for low-dose CT reconstruction[J].Journal of Electronics&Information Technology,2013,35(10):2418-2424.(in Chinese)
[10]Xu Q,Yu H,Mou X,et al.Low-dose X-ray CT reconstruction via dictionary learning[J].IEEE Transactions on Medical Imaging,2012,31(9):1682-1697.
[11]Candes E J,Romberg J,Tao T.Robust uncertainty principles:Exact signal reconstruction from highly incomplete frequency information[J].IEEE Transactions on Information Theory,2006,52(2):489-509.
[12]Qian Shan-shan,Huang Jing,Ma Jian-hua,et al.Nonmonotone total variation minimization based projection restoration for low-dose CT reconstruction[J].Acta Electronica Sinica,2011,39(7):1702-1707.(in Chinese)
[13]Mao Bao-lin,Chen Xiao-zhao,Xiao Da-yu,et al.Ordered subset image reconstruction studied by means of total variation minimization and fast first-order method in low dose computed tomograhpy[J].Acta Physica Sinica,2014,63(13):138701.(in Chinese)
[14]Yu H,Wang G.A soft-threshold filtering approach for reconstruction from a limited number of projections[J].Physics in Medicine and Biology,2010,55(13):3905-3916.
[15]Wang Lin-yuan,Liu Hong-kui,Li Lei,et al.Review of sparse optimization-based computed tomography image reconstruction from few-view projections[J].Acta Physica Sinica,2014,63(20):208702.(in Chinese)
[16]Rantala M,VnskS,JrvenpS,et al.Wavelet-based reconstruction for limited-angle X-ray tomography[J].IEEE Transactions on Medical Imaging,2006,25(2):210-217.
[17]Guo De-quan,Yang Hong-yu,Liu Dong-quan,et al.Overview on sparse image denoising[J].Application Research of Computers,2012,29(2):406-413.(in Chinese)
[18]Guo K,Labate D.Optimally sparse multidimensional representation using shearlets[J].SIAM Journal on Mathematical Analysis,2007,39(1):298-318.
[19]Easley G,Labate D,Lim W Q.Sparse directional image representations using the discrete shearlet transform[J].Applied and Computational Harmonic Analysis,2008,25(1):25-46.
[20]Lim W Q.The discrete shearlet transform:A new directional transform and compactly supported shearlet frames[J].IEEE Transactions on Image Processing,2010,19(5):1166-1180.
[21]Wang Lei,Li Bin,Tian Lian-fang.Medical image fusion based on shift-invariant shearlet transformation[J].Journal of South China University of Technology(Natural Science Edition),2011,39(12):145-152.(in Chinese)
[22]Zhao J,LüL,Sun H.Multi-threshold image denoising based on shearlet transform[J].Applied Mechanics and Materials,2010,29-32:2251-2255.
[23]Guo K,Labate D.Characterization and analysis of edges using the continuous shearlet transform[J].SIAM Journal on Imaging Sciences,2009,2(3):959-986.
[24]Deng Cheng-zhi,Liu Juan-juan,Wang Sheng-qian,et al.Feature retained image inpainting based on sparsity regularization[J].Optics and Precision Engineering,2013,21(7):1906-1913.(in Chinese)
[25]Kalender W A.Computed tomography:Fundamentals,system technology,image quality,applications[M].Hoboken,NJ:John Wiley&Sons Inc.,2011.
[26]Chen S S,Donoho D L,Saunders M A.Atomic decomposition by basis pursuit[J].SIAM Review,2001,43(1):129-159.
[27]Wang Z,Bovik A C,Sheikh H R,et al.Image quality assessment:From error visibility to structural similarity[J].IEEE Transactions on Image Processing,2004,13(4):600-612.
[1]罗立民,胡轶宁,陈阳.低剂量CT成像的研究现状与展望[J].数据采集与处理,2015,30(1):24-34.
[5]张元科,张军英,卢虹冰.低剂量CT图像模型参数估计及统计去噪研究[J].西安电子科技大学学报(自然科学版),2011,38(3):99-106.
[8]张权,罗立民,桂志国.基于改进非局部先验的Bayesian低剂量CT投影平滑算法[J].东南大学学报(自然科学版),2014,44(3):499-503.
[9]王丽艳,韦志辉.低剂量CT的线性Bregman迭代重建算法[J].电子与信息学报,2013,35(10):2418-2424.
[12]钱姗姗,黄静,马建华,等.基于投影数据非单调性全变分恢复的低剂量CT重建[J].电子学报,2011,39(7):1702-1707.
[13]毛宝林,陈晓朝,孝大宇,等.基于全变分最小化和快速一阶方法的低剂量CT有序子集图像重建[J].物理学报,2014,63(13):138701.
[15]王林元,刘宏奎,李磊,等.基于稀疏优化的计算机断层成像图像不完全角度重建综述[J].物理学报,2014,63(20):208702.
[17]郭德全,杨红雨,刘东权,等.基于稀疏性的图像去噪综述[J].计算机应用研究,2012,29(2):406-413.
[21]王雷,李彬,田联房.基于平移不变剪切波变换的医学图像融合[J].华南理工大学学报(自然科学版),2011,39(12):145-152.
[24]邓承志,刘娟娟,汪胜前,等.保留结构特征的稀疏性正则化图像修复[J].光学精密工程,2013,21(7):1906-1913.