Joint multi-channel total generalized variational algorithm for spectral CT reconstruction

Lian Xiangyuan; Kong Huihua; Pan Jinxiao; Gao Wenbo; Wang Pan

doi:10.12086/oee.2021.210211

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Lian X Y, Kong H H, Pan J X, et al. Joint multi-channel total generalized variational algorithm for spectral CT reconstruction[J]. Opto-Electron Eng, 2021, 48(9): 210211. doi: 10.12086/oee.2021.210211

Citation:

Lian X Y, Kong H H, Pan J X, et al. Joint multi-channel total generalized variational algorithm for spectral CT reconstruction[J]. Opto-Electron Eng, 2021, 48(9): 210211. doi: 10.12086/oee.2021.210211

Joint multi-channel total generalized variational algorithm for spectral CT reconstruction

1.
School of Science, North University of China, Taiyuan, Shanxi 030051, China
2.
Shanxi Key Laboratory of Signal Capturing & Processing, North University of China, Taiyuan, Shanxi 030051, China
3.
Hunan Vsngusrd Group. Co. Ltd, Chenxi, Hunan 419503, China

Fund Project: National Natural Science Foundation of China (61801437, 61871351, 61971381)

More Information

^*Corresponding author: Pan Jinxiao, E-mail: panjx@nuc.edu.cn

Received Date 23 June 2021

Revised Date 26 August 2021

Published Date 15 September 2021

Abstract

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.
- CT reconstruction /
- spectral CT /
- total generalized variation /
- nuclear norm /
- joint multi-channel

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References

[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 CrossRef Google Scholar
[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 CrossRef Google Scholar
[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 CrossRef Google Scholar
[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 CrossRef Google Scholar
[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 CrossRef Google Scholar
[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 CrossRef Google Scholar
[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 CrossRef Google Scholar
[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 CrossRef Google Scholar
[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 CrossRef Google Scholar
[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 CrossRef Google Scholar
[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 CrossRef Google Scholar
[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. Google Scholar 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. Google Scholar
[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 CrossRef Google Scholar
[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 CrossRef Google Scholar
[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 CrossRef Google Scholar
[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 CrossRef Google Scholar
[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 CrossRef Google Scholar

Overview

Overview

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.