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Joint multi-channel total generalized variational algorithm for spectral CT reconstruction
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摘要:
基于光子计数探测器的能谱CT在材料分解、组织表征、病变检测等应用中具有巨大的潜力。在重建过程中，通道数的增加会造成单通道中光子数减少，从而导致重建图像质量下降，难以满足实际需求。本文从能谱CT重建的角度出发，将广义总变分向矢量延伸，利用奇异值的稀疏性，促进图像梯度的线性依赖，提出一种基于核范数的多通道联合广义总变分的能谱CT重建算法。在图像重建过程中，多层共享结构信息，同时保留独特的差异。实验结果表明，本文提出的算法在抑制噪声的同时，能够更有效地恢复图像细节及边缘信息。
Abstract:Spectral computed tomography (CT) based on photon-counting detectors, has great potential in material decomposition, tissue characterization, lesion detection, and other applications. During the reconstruction, the increase of the number of channels will reduce the photon number in a single channel, resulting in the decline of the quality of the reconstructed image, which is difficult to meet the actual needs. To improve the quality of image reconstruction, joint multi-channel total generalized variational based on the unclear norm for spectral CT reconstruction was proposed in this paper. The algorithm will extend total generalized variation to the vector, and the sparsity of singular values is used to promote the linear dependence of the image gradient. The structural information of the multi-channel image is shared during the image reconstruction process while unique differences are preserved. Experimental results show that the proposed algorithm can effectively recover image details and marginal information while suppressing noise.
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Key words:
- CT reconstruction /
- spectral CT /
- total generalized variation /
- nuclear norm /
- joint multi-channel
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Overview: Spectral computed tomography (CT) based on photon-counting detectors, has great potential in material decomposition, tissue characterization, lesion detection, and other applications. During the reconstruction, the increase of the number of channels will reduce the photon number in a single channel, resulting in the decline of the quality of the reconstructed image, which is difficult to meet the actual needs. To improve the quality of image reconstruction, this paper proposes a joint multi-channel total generalized variational based on the unclear norm for spectral CT reconstruction. Firstly, in the reconstruction for spectral CT, the image structure of each channel is highly similar, and the reconstruction of a single channel will ignore the structural information of each channel. Second, gradient information contains a lot of structured information and features of the image. When two images have the same curve, the two images have the same direction gradient and the converse is also true. In order to better utilize the image's structural information between channels, the new regularization function is applied to spectral CT reconstruction. The research shows that if the edges of the two images are aligned, the two images have the same gradient. The image gradients between channels are parallel, which will minimize the nuclear norm. The algorithm will extend total generalized variation to the vector, with the aim of overcoming defects of existing derivative-based regularization. The paper proposed a joint multi-channel total generalized variational for spectral CT reconstruction, employing a vectorial second-order total generalized variation function as joint regularization. The method adopts pixel-by-pixel updating in the image reconstruction, and the multi-channel image coupling is realized by kernel norm and F-norm constraints at the level of first and second derivatives. The nuclear norm and frobenius norm coupling promote joint sparsity of the edge sets and dependence of the gradients. Joint multi-channel total generalized variational is used to promote the linear dependence of the multi-channel image's gradient so that the image edges of each channel are aligned. The structural information of the multi-channel image is shared during the image reconstruction process while unique differences are preserved. The experiment was done on a numerical mouse thorax phantom and clinical mouse data. The quantitative results of peak signal to noise ratio (PSNR), normalized root mean square error (NRMSE) and structure similarity index (SSIM) show that the proposed algorithm greatly improves the image quality. Experimental results show that the proposed algorithm can effectively recover image details and marginal information while suppressing noise.
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图 1 小鼠模型的重建结果。从左到右的方法依次为FBP、SART、TV、TDL、TGV与Mutli-NTGV，从上到下依次为1到4通道
Figure 1. The reconstruction results of the mouse model. From left to right, the rows are FBP, SART, TV, TDL, TGV and Mutli-NTGV. From top to bottom, the columns are 1st, 2th, 3th and 4th energy channels
图 2 小鼠模型重建效果的数量性评价指标。
Figure 2. Quantitative evaluation index of reconstruction effect of the mouse model. From left to right, the rows are NRMSE, PSNR, SSIM. From (a) to (d), the columns are 1st, 2th, 3th and 4th energy channels
图 3 临床小鼠模型的重建结果。从左到右的方法依次为FBP、SART、TV、TDL、TGV与Mutli-NTGV, 从上到下依次为1, 3, 5, 7通道
Figure 3. Reconstruction results of the clinical mouse model. From left to right, the methods are FBP, SART, TV, TDL, TGV, and Mutli-NTGV. From top to bottom, the columns are the 1st, 3th, 5th and 7th energy channels
初始化： p0=0，q0=0，${w^0} = {\bar w^0} = 0$，${u^0} = {v^0} = 0$， ${\bar v^0} = 0$，$k = 0$，maxloop=30; 主循环：当k < maxloop时，执行循环； 利用式(9)更新${{\boldsymbol{u}}^{(k + 1)}} $； 利用式(13)、式(14)更新辅助变量${{\boldsymbol{p}}^{(k + 1)}}$，${{\boldsymbol{q}}^{(k + 1)}}$； 利用式(15)、式(16)更新图像变量${{\boldsymbol{v}}^{(k + 1)}}$与结构化变量${{\boldsymbol{w}}^{(k + 1)}}$； 利用式(17)、式(18)更新${{\boldsymbol{v}}^{(k + 1)}}$, ${{\boldsymbol{w}}^{(k + 1)}}$的对偶变量${{\boldsymbol{\bar v}}^{(k + 1)}}$，${{\boldsymbol{\bar w}}^{(k + 1)}}$； 直到k=maxloop，循环结束，输出${{\boldsymbol{u}}^{(maxloop)}}$。 
下载: 导出CSV
表 1 FBP重建的数量性评价指标
Table 1. Quantitative evaluation index of FBP reconstruction
Channel 1 Channel 2 Channel 3 Channel 4 NRMSE 0.2128 0.2795 0.3132 0.4059 PSNR 30.7993 27.8948 25.6016 22.4276 SSIM 0.9942 0.9625 0.9704 0.9702
下载: 导出CSV
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[1] Niu S Z, Bian Z Y, Zeng D, et al. Total image constrained diffusion tensor for spectral computed tomography reconstruction[J]. Appl Math Model, 2019, 68: 487-508. doi: 10.1016/j.apm.2018.11.020
[2] Taguchi K, Iwanczyk J S. Vision 20/20: Single photon counting X-ray detectors in medical imaging[J]. Med Phys, 2013, 40(10): 100901. doi: 10.1118/1.4820371
[3] Dong X, Niu T Y, Zhu L. Combined iterative reconstruction and image-domain decomposition for dual energy CT using total-variation regularization[J]. Med Phys, 2014, 41(5): 051909. doi: 10.1118/1.4870375
[4] Yu Z C, Leng S, Li Z B, et al. Spectral prior image constrained compressed sensing (spectral PICCS) for photon-counting computed tomography[J]. Phys Med Biol, 2016, 61(18): 6707-6732. doi: 10.1088/0031-9155/61/18/6707
[5] Zhang W K, Zhang H M, Wang L Y, et al. Limited angle CT reconstruction by simultaneous spatial and Radon domain regularization based on TV and data-driven tight frame[J]. Nucl Instr Meth Phys Res A, 2018, 880: 107-117. doi: 10.1016/j.nima.2017.10.056
[6] Luo X Q, Yu W, Wang C X. An image reconstruction method based on total variation and wavelet tight frame for limited-angle CT[J]. IEEE Access, 2018, 6: 1461-1470. doi: 10.1109/ACCESS.2017.2779148
[7] Us D, Ruotsalainen U, Pursiainen S. Combining dual-tree complex wavelets and multiresolution in iterative CT reconstruction with application to metal artifact reduction[J]. BioMed Eng OnLine, 2019, 18: 116. doi: 10.1186/s12938-019-0727-1
[8] Miao J Y, Cao H L, Jin X B, et al. Joint sparse regularization for dictionary learning[J]. Cogn Comput, 2019, 11(5): 697-710. doi: 10.1007/s12559-019-09650-2
[9] Zhang Y, Xi Y, Yang Q S, et al. Spectral CT reconstruction with image sparsity and spectral mean[J]. IEEE Trans Comput Imaging, 2016, 2(4): 510-523. doi: 10.1109/TCI.2016.2609414
[10] Li B, Shen C Y, Chi Y J, et al. Multienergy cone-beam computed tomography reconstruction with a spatial spectral nonlocal means algorithm[J]. SIAM J Imaging Sci, 2018, 11(2): 1205-1229. doi: 10.1137/17M1123237
[11] Hu D L, Wu W W, Xu M R, et al. SISTER: spectral-image similarity-based tensor with enhanced-sparsity reconstruction for sparse-view multi-energy CT[J]. IEEE Trans Comput Imaging, 2020, 6: 477-490. doi: 10.1109/TCI.2019.2956886
[12] 陈佩君, 冯鹏, 伍伟文, 等. 基于图像总变分和张量字典的多能谱CT材料识别研究[J]. 光学学报, 2018, 38(11): 1111002.
Chen P J, Feng P, Wu W W, et al. Material discrimination by multi-spectral CT based on image total variation and tensor dictionary[J]. Acta Opt Sin, 2018, 38(11): 1111002.
[13] Rigie D S, Patrick J L R. Joint reconstruction of multi-channel, spectral CT data via constrained total nuclear variation minimization[J]. Phys Med Biol, 2015, 60(5): 1741-1762. doi: 10.1088/0031-9155/60/5/1741
[14] Niu S Z, Huang J, Bian Z Y, et al. Iterative reconstruction for sparse-view X-ray CT using alpha-divergence constrained total generalized variation minimization[J]. J X-Ray Sci Technol, 2017, 25(4): 673-688. doi: 10.3233/XST-16239
[15] Kristian B, Karl K, Thomas P. Total Generalized Variation[J]. SIAM Journal on Imaging Sciences, 2010, 3(3): 492-526. doi: 10.1137/090769521
[16] Ehrhardt M J, Arridge S R. Vector-valued image processing by parallel level sets[J]. IEEE Trans Image Process, 2014, 23(1): 9-18. doi: 10.1109/TIP.2013.2277775
[17] Sidky E Y, Jørgensen J H, Pan X C. Convex optimization problem prototyping for image reconstruction in computed tomography with the Chambolle-Pock algorithm[J]. Phys Med Biol, 2012, 57(10): 3065-3091. doi: 10.1088/0031-9155/57/10/3065
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