基于字典学习和TV的能谱CT重建算法
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摘要
能谱CT可以将较宽的能谱数据划分为几个单独的窄谱数据,从而同时获得多个能量通道下的投影.但由于窄谱通道内接收到的光子数较少,投影通常包含较大的噪声.针对这一问题,基于压缩感知理论提出了一种基于字典学习和全变分TV(total-variation)的迭代重建算法用于能谱CT重建,应用交替最小化方法优化相关目标函数,并采用Split-Bregman算法求解.同时,采用有序子集方法加速迭代收敛过程,提高运算速率.为了验证和评估所提出的方法,使用简单模型和实际临床小鼠模型进行了仿真实验,实验结果表明,所提出的算法有较好的去噪及细节保存能力.
Spectral CT can divide the broad energy data into several separate narrowenergy data. Therefore, it is possible to obtain projections under multiple energy channels simultaneously. But the narrow energy channel of spectral CT only contains a small part of photons, the projection usually contains very strong noise. In order to solve this problem, this paper proposes an iterative reconstruction algorithm based on dictionary learning and TV regularization item for spectral CT reconstruction, which relies on the theory of compressed sensing. Apply the alternating minimization method to optimize the related objective function and solve it by Split-Bregman algorithm. At the same time, the ordered subset method is used to accelerate the iterative convergence process and improve the operation rate. In order to validate and evaluate the proposed method, a simulation experiment was performed using a simple model and an actual clinical mouse model. The experimental results show that the proposed algorithm has a better denoising and detail preservation ability.
Spectral CT can divide the broad energy data into several separate narrowenergy data. Therefore, it is possible to obtain projections under multiple energy channels simultaneously. But the narrow energy channel of spectral CT only contains a small part of photons, the projection usually contains very strong noise. In order to solve this problem, this paper proposes an iterative reconstruction algorithm based on dictionary learning and TV regularization item for spectral CT reconstruction, which relies on the theory of compressed sensing. Apply the alternating minimization method to optimize the related objective function and solve it by Split-Bregman algorithm. At the same time, the ordered subset method is used to accelerate the iterative convergence process and improve the operation rate. In order to validate and evaluate the proposed method, a simulation experiment was performed using a simple model and an actual clinical mouse model. The experimental results show that the proposed algorithm has a better denoising and detail preservation ability.
引文
[1] Kong H H, Liu R, Pan J X, et al. Evaluation of an analytic reconstruction method as a platform for spectral cone-beam CT[J]. IEEE Access, 2018, 6:21323.
[2] Ding Y, Hu T. Efficient scheme of low-dose CT reconstruction using TV minimization with an adaptive stopping strategy and sparse dictionary learning for post-processing[J].信息与电子工程前沿,2017, 18(12):2001-2008.
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[4] Zhang C, Zhang T, Li M, et al. Low-dose CT reconstruction via L1 dictionary learning regularization using iteratively reweighted least-squares[J]. Biomedical Engineering Online, 2016, 15(1):1-21.
[5] Niu S Z, Yu G H, Ma J H, et al. Nonlocal low-rank and sparse matrix decomposition for spectral CT reconstruction[J]. Inverse Problems, 2017, 34(2):024003.
[6] Xu Q, Yu H, Bennett J, et al. Image reconstruction for hybrid true-color micro CT[J]. IEEE Transactions on Bio-medical Engineering, 2012, 59(6):1711-1719.
[7] Zeng D, Gao Y Y, Huang J, et al. Penalized weighted least-squares approach for multi energy computed tomography image reconstruction via structure tensor total variation regularization[J].Computerized Medical Imaging and Graphics, 2016,53:19-29.
[8] Xu Q, Yu H, Wang G, et al. Dictionary learning based low-dose X-Ray CT reconstruction[J]. IEEE Trans Med Imaging, 2012, 31(9):1682-1697.
[9] Li L, Chen Z Q, Jiao P F. Dual-energy CT reconstruction based on dictionary learning and total variation constraint[C]//Nuclear Science Symposium and Medical Imaging Conference, 2012:6551536.
[10] Zhao B, Ding H J, Lu Y, et al. Dual-dictionary learning-based iterative image reconstruction for spectral computed tomography application[J]. Physics in Medicine and Biology, 2012, 57(24):8217-8229.
[11] Zhang Y B, Mou X Q, Wang G, et al. Tensor-Based dictionary learning for spectral CT reconstruc-tion[J]. IEEE Transactions on Medical Imaging, 2016, 36(1):142-154.
[12] Elbakri I A, Fessler J A. Statistical image reconstruction for poly energetic X-ray computed tomography[J]. IEEE Transactions on Medical Imaging, 2002, 21(2):89-99.
[13]张海娇,孔慧华,孙永刚.基于结构先验的加权NLTV能谱CT重建算法[J].光学学报,2018, 38(08):081103.
[2] Ding Y, Hu T. Efficient scheme of low-dose CT reconstruction using TV minimization with an adaptive stopping strategy and sparse dictionary learning for post-processing[J].信息与电子工程前沿,2017, 18(12):2001-2008.
[3] Xi Y, Chen Y, Tang R B, et al. United iterative reconstruction for spectral computed tomography[J].IEEE Transactions on Medical Imaging, 2015, 34(3):769-777.
[4] Zhang C, Zhang T, Li M, et al. Low-dose CT reconstruction via L1 dictionary learning regularization using iteratively reweighted least-squares[J]. Biomedical Engineering Online, 2016, 15(1):1-21.
[5] Niu S Z, Yu G H, Ma J H, et al. Nonlocal low-rank and sparse matrix decomposition for spectral CT reconstruction[J]. Inverse Problems, 2017, 34(2):024003.
[6] Xu Q, Yu H, Bennett J, et al. Image reconstruction for hybrid true-color micro CT[J]. IEEE Transactions on Bio-medical Engineering, 2012, 59(6):1711-1719.
[7] Zeng D, Gao Y Y, Huang J, et al. Penalized weighted least-squares approach for multi energy computed tomography image reconstruction via structure tensor total variation regularization[J].Computerized Medical Imaging and Graphics, 2016,53:19-29.
[8] Xu Q, Yu H, Wang G, et al. Dictionary learning based low-dose X-Ray CT reconstruction[J]. IEEE Trans Med Imaging, 2012, 31(9):1682-1697.
[9] Li L, Chen Z Q, Jiao P F. Dual-energy CT reconstruction based on dictionary learning and total variation constraint[C]//Nuclear Science Symposium and Medical Imaging Conference, 2012:6551536.
[10] Zhao B, Ding H J, Lu Y, et al. Dual-dictionary learning-based iterative image reconstruction for spectral computed tomography application[J]. Physics in Medicine and Biology, 2012, 57(24):8217-8229.
[11] Zhang Y B, Mou X Q, Wang G, et al. Tensor-Based dictionary learning for spectral CT reconstruc-tion[J]. IEEE Transactions on Medical Imaging, 2016, 36(1):142-154.
[12] Elbakri I A, Fessler J A. Statistical image reconstruction for poly energetic X-ray computed tomography[J]. IEEE Transactions on Medical Imaging, 2002, 21(2):89-99.
[13]张海娇,孔慧华,孙永刚.基于结构先验的加权NLTV能谱CT重建算法[J].光学学报,2018, 38(08):081103.