基于梯度域的卷积稀疏编码磁共振成像重建

Xiong Jiaojiao; Lu Hongyang; Zhang Minghui; Liu Qiegen

doi:10.16383/j.aas.2017.e160135

基于梯度域的卷积稀疏编码磁共振成像重建

doi: 10.16383/j.aas.2017.e160135

1.
南昌大学信息工程学院南昌 330031
2.
卡尔加里大学电子与计算机工程学院卡尔加里

基金项目:

Jiangxi Province Innovation Projects for Postgraduate Funds YC2016-S006

the National Natural Science Foundation of China 61661031

the National Natural Science Foundation of China 61362001

the International Postdoctoral Exchange Fellowship Program, and Jiangxi Advanced Project for Post-Doctoral Research Fund 2014KY02

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出版历程
- 收稿日期: 2016-02-13
- 录用日期: 2016-12-07
- 刊出日期: 2017-10-20

Convolutional Sparse Coding in Gradient Domain for MRI Reconstruction

1.
School of Information Engineering, Nanchang University, Nanchang 330031, China
2.
School of Electrical and Computer Engineering, University of Calgary, Calgary AB T2N 1N4, Canada

Funds:

Jiangxi Province Innovation Projects for Postgraduate Funds YC2016-S006

the National Natural Science Foundation of China 61661031

the National Natural Science Foundation of China 61362001

the International Postdoctoral Exchange Fellowship Program, and Jiangxi Advanced Project for Post-Doctoral Research Fund 2014KY02

More Information

Author Bio:
Jiaojiao Xiong is pursuing the M.Sc.degree at the School of Information Engineering, Nanchang University, Nanchang, China.Her research interests include image reconstruction and pattern recognition.E-mail:xiongjiaojiao0126@163.com

Hongyang Lu is a master student.Her research interests include sparse representation theory and its applications in image processing, computer vision and MRI reconstruction.E-mail:luhongyang6890@163.com

Minghui Zhang received the M.S.degree from Chongqing University, Chongqing, in 1990, majored in biomedical engineering.His research interests include MRI reconstruction, image compression and restoration, and pattern recognition.E-mail:zhangmh3529@163.com

Corresponding author: Qiegen Liu received the M.Sc.degree in computation mathematics and Ph.D.degree in biomedical engineering from Shanghai Jiaotong University.Since 2012, he has been with the School of Information Engineering, Nanchang University, Nanchang, China, where he is currently an Associate Professor.He is also a postdoc at Beckman Institute, University of Illinois at Urbana Champaign, USA.His research interests include compressed sensing, image reconstruction, and pattern recognition.Corresponding author of this paper.E-mail:liuqiegen@ncu.edu.cn

摘要

摘要: 从欠采样数据中进行磁共振成像（简称MRI）重建一直是一项具有挑战性和吸引力的任务，因为这是一个病态问题，且伴随着压缩感知理论会具有重要的意义.基于压缩感知的多数先进稀疏表示方法是将图像分割成重叠的图像块，然后每个图像块分开处理.然而，这些方法丢失了信号的重要空间结构，且忽略了对MR图像有强大约束的像素一致性.在文章中我们提出了一种新型的重建方法，这种方法是将最近提出的卷积稀疏编码与梯度域结合起来用于解决上述所提到的问题.不同于基于图像块状的方法，本文提出的算法是直接在整个梯度域图像中获取相邻局部的相关性，利用梯度域图像的全局相关性产生更好的梯度域图像边缘，锐利特征.提出的算法也能够高效的获取暗含在梯度域图像中的局部特征.与对比算法相比，大量的实验结果表明本文算法具有更好的质量重建，且在不同采样方案，不同K-空间加速因子情况下具有更快速的收敛.
- 交替方向法算法 /
- 卷积稀疏编码 /
- 滤波器学习 /
- 梯度图像 /
- 磁共振成像重建
Abstract: Magnetic resonance imaging (MRI) reconstruction from undersampled data has always been a challenging and fascinating task due to its implicit ill-posed nature and its significance accompanied with the emerging compressed sensing (CS) theory. Most state-of-the-art sparse representation based CS approaches partition the image into overlapped patches, and process each patch separately. These methods, however, lose important spatial structures of the signal of interest, and ignore the consistency of pixels, which is a strong constraint for MR image. In this paper, we propose a new reconstruction method, which builds on recently introduced ideas of convolutional sparse coding in gradient domain (GradCSC) to address above mentioned issue. As opposed to patch-based methods, GradCSC directly operates on the whole gradient image to capture the correlation between local neighborhoods and exploits the gradient image global correlation to produce better edges and sharp features of gradient image. It enables local features implicitly existed in the gradient images to be captured effectively. Extensive experimental results demonstrate that the proposed algorithm achieves higher quality reconstructions than alternative methods and converges quickly at various sampling schemes and k-space acceleration factors.
- Alternating direction method of multipliers /
- convolutional sparse coding(CSC) /
- filter learning /
- gradient image /
- magnetic resonance imaging(MRI)reconstruction
Recommended by Associate Editor Cong Wang
注释:

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Fig. 1 One illustration of filters learned. (a) Learned dictionary by DLMRI, (b) Learned dictionary by GradDL, and (c) Learned filter by GradCSC, respectively.

下载: 全尺寸图片幻灯片

Fig. 2 The reconstruction results of the Lumbar spine image under different undersampling factors with 2D random sampling.

下载: 全尺寸图片幻灯片

Fig. 3 The reconstruction results of the axial T2-weighted brain image under different undersampling schemes.

下载: 全尺寸图片幻灯片

Fig. 4 The reconstruction results of the COW image under different noise levels.

下载: 全尺寸图片幻灯片

Algorithm 1. The GradCSC algorithm

1: Initialization: ${{z}_{k}}^{0}=0$, ${{d}_{k}}^{0}=0$, ${{({{b}^{(i)}})}^{0}}=0$, $i=1, 2$; ${{u}^{0}}=F_{p}^{T}f$
2: For $j=1, 2, \ldots $ repeat until a stop-criterion is satisfied
3:     ${{({{w}^{(i)}})}^{j+1}}=\ \frac{{{\nu }_{2}}[{{({{b}^{(i)}})}^{j}}+{{({{\nabla }^{(i)}}u)}^{j}}]+\sum\limits_{k=1}^{K}{d_{_{k}}^{j}*z_{_{k}}^{j}}}{2{{\nu }_{2}}+1}, \ \ i=1, 2$
4:     Updating $\{{{d}_{k}}^{j+1}, {{z}_{k}}^{j+1}\}$ from difference images ${{({{w}^{(i)}})}^{j+1}}$ by (13), $i=1, 2$
5:     Updating $\{ r_{1}^{^{\ell +1}}, r_{2}^{^{\ell +1}}, r_{3}^{^{\ell +1}} \}$ from the coefficients, and the filters by (14)
6:     ${{u}^{j+1}}={{F}^{\rm{-}1}}( \frac{F[{{\nu }_{1}}F_{p}^{T}f+{{\nu }_{2}}{{\nabla }^{T}}({{({{w}^{(i)}})}^{j}}^{+1}-{{({{b}^{(i)}})}^{j}})]}{{{\nu }_{1}}FF_{p}^{T}{{F}_{p}}{{F}^{T}}+{{\nu }_{2}}F{{\nabla }^{T}}{{F}^{T}}F\nabla {{F}^{T}}} )$
7:     ${{({{b}^{(i)}})}^{j+1}}={{({{b}^{(i)}})}^{j}}+{{({{\nabla }^{(i)}}u)}^{j+1}}-{{({{w}^{(i)}})}^{j+1}}$, $i=1, 2$
8: End
9: Output ${{u}^{j+1}}$

下载: 导出CSV

Table Ⅰ Reconstruction PSNR Values at Different Undersampling Factors With the Same 2D Random Sampling Trajectories

Undersampling factors	2.5-fold	4-fold	6-fold	8-fold	10-fold	20-fold
DLMRI	35.92	35.19	31.26	30.76	30.13	26.39
GradDL	38.26	38.20	34.35	32.89	31.81	27.90
GradCSC	37.39	37.53	35.23	35.45	34.62	30.54

下载: 导出CSV

参考文献(33)

[1]	M. Lustig, D. Donoho, and J. M. Pauly, "Sparse MRI:The application of compressed sensing for rapid MR imaging, " Magn. Reson. Med., vol. 58, no. 6, pp. 1182-1195, Dec. 2007. doi: 10.1002/(ISSN)1522-2594
[2]	D. L. Donoho, "Compressed sensing, " IEEE Trans. Inform. Theory, vol. 52, no. 4, pp. 1289-1306, Apr. 2006. doi: 10.1109/TIT.2006.871582
[3]	D. Liang, B. Liu, J. Wang, and L. Ying, "Accelerating SENSE using compressed sensing, " Magn. Reson. Med., vol. 62, no. 6, pp. 1574-1584, Dec. 2009. doi: 10.1002/mrm.v62:6
[4]	M. Lustig, J. M. Santos, D. L. Donoho, and J. M. Pauly, "k-t SPARSE: high frame rate dynamic MRI exploiting spatiotemporal sparsity, " in Proc. 13th Ann. Meeting of ISMRM, Seattle, USA, 2006.
[5]	S. Q. Ma, W. T. Yin, Y. Zhang, and A. Chakraborty, "An efficient algorithm for compressed MR imaging using total variation and wavelets, " in Proc. IEEE Conf. Computer Vision and Pattern Recognition, Anchorage, AK, USA, 2008, pp. 1-8.
[6]	J. Trzasko and A. Manduca, "Highly undersampled magnetic resonance image reconstruction via homotopic e₀-minimization, " IEEE Trans. Med. Imaging, vol. 28, no. 1, pp. 106-121, Jan. 2009. doi: 10.1109/TMI.2008.927346
[7]	S. M. Gho, Y. Nam, S. Y. Zho, E. Y. Kim, and D. H. Kim, "Three dimension double inversion recovery gray matter imaging using compressed sensing, " Magn. Reson. Imaging, vol. 28, no. 10, pp. 1395-1402, Dec. 2010. doi: 10.1016/j.mri.2010.06.029
[8]	M. Guerquin-Kern, M. Haberlin, K. P. Pruessmann, and M. Unser, "A fast wavelet-based reconstruction method for magnetic resonance imaging, " IEEE Trans. Med. Imaging, vol. 30, no. 9, pp. 1649-1660, Sep. 2011. doi: 10.1109/TMI.2011.2140121
[9]	L. Y. Chen, M. C. Schabel, and E. V. R. DiBella, "Reconstruction of dynamic contrast enhanced magnetic resonance imaging of the breast with temporal constraints, " Magn. Reson. Imaging, vol. 28, no. 5, pp. 637-645, Jun. 2010. doi: 10.1016/j.mri.2010.03.001
[10]	Q. G. Liu, S. S. Wang, K. Yang, J. H. Luo, Y. M. Zhu, and D. Liang, "Highly undersampled magnetic resonance image reconstruction using two-level Bregman method with dictionary updating, " IEEE Trans. Med. Imaging, vol. 32, no. 7, pp. 1290-1301, Jul. 2013. doi: 10.1109/TMI.2013.2256464
[11]	X. B. Qu, D. Guo, B. D. Ning, Y. K. Hou, Y. L. Lin, S. H. Cai, and Z. Chen, "Undersampled MRI reconstruction with patch-based directional wavelets, " Magn. Reson. Imaging, vol. 30, no. 7, pp. 964-977, Sep. 2012. doi: 10.1016/j.mri.2012.02.019
[12]	S. Ravishankar and Y. Bresler, "MR image reconstruction from highly undersampled k-space data by dictionary learning, " IEEE Trans. Med. Imaging, vol. 30, no. 5, pp. 1028-1041, May 2011. doi: 10.1109/TMI.2010.2090538
[13]	Q. G. Liu, S. S. Wang, L. Ying, X. Peng, Y. J. Zhu, and D. Liang, "Adaptive dictionary learning in sparse gradient domain for image recovery, " IEEE Trans. Image Process., vol. 22, no. 12, pp. 4652-4663, Dec. 2013. doi: 10.1109/TIP.2013.2277798
[14]	Z. L. Hu, Q. G. Liu, N. Zhang, Y. W. Zhang, X. Peng, P. Z. Wu, H. R. Zheng, and D. Liang, "Image reconstruction from few-view CT data by gradient-domain dictionary learning, " J. X-Ray Sci. Technol., vol. 24, no. 4, pp. 627-638, Jul. 2016. doi: 10.3233/XST-160579
[15]	X. M. Luo, Z. Y. Suo, and Q. G. Liu, "Efficient InSAR phase noise filtering based on adaptive dictionary learning in gradient vector domain, " Chin. J. Eng. Math., vol. 32, no. 6, pp. 801-811, Dec. 2015. doi: 10.1162/neco.1995.7.6.1129
[16]	M. D. Zeiler, D. Krishnan, G. W. Taylor, and R. Fergus, "Deconvolutional networks, " in Proc. 2010 IEEE Conf. Computer Vision and Pattern Recognition (CVPR), San Francisco, CA, USA, 2010, pp. 2528-2535.
[17]	B. A. Olshausen and D. J. Field, "Sparse coding with an overcomplete basis set:a strategy employed by V1?, " Vision Res., vol. 37, no. 23, pp. 3311-3325, Dec. 1997. doi: 10.1016/S0042-6989(97)00169-7
[18]	A. Szlam, K. Kavukcuoglu, and Y. LeCun, "Convolutional matching pursuit and dictionary training, " arXiv: 1010. 0422, Oct. 2010.
[19]	B. Chen, G. Polatkan, G. Sapiro, D. Blei, D. Dunson, and L. Carin, "Deep learning with hierarchical convolutional factor analysis, " IEEE Trans. Pattern Anal. Mach. Intell., vol. 35, no. 8, pp. 1887-1901, Aug. 2013. doi: 10.1109/TPAMI.2013.19
[20]	K. Kavukcuoglu, P. Sermanet, Y. L. Boureau, K. Gregor, M. Mathieu, and Y. LeCun, "Learning convolutional feature hierarchies for visual recognition, " in Proc. 23rd Int. Conf. Neural Information Processing Systems, Vancouver, British Columbia, Canada, 2010, pp. 1090-1098.
[21]	M. D. Zeiler, G. W. Taylor, and R. Fergus, "Adaptive deconvolutional networks for mid and high level feature learning, " in Proc. 2011 IEEE Int. Conf. Computer Vision (ICCV), Barcelona, USA, 2011, pp. 2018-2025.
[22]	F. Heide, L. Xiao, A. Kolb, M. B. Hullin, and W. Heidrich, "Imaging in scattering media using correlation image sensors and sparse convolutional coding, " Opt. Express, vol. 22, no. 21, pp. 26338-26350, Oct. 2014. doi: 10.1364/OE.22.026338
[23]	X. M. Hu, Y. Deng, X. Lin, J. L. Suo, Q. H. Dai, C. Barsi, and R. Raskar, "Robust and accurate transient light transport decomposition via convolutional sparse coding, " Opt. Lett., vol. 39, no. 11, pp. 3177-3180, Jun. 2014. doi: 10.1364/OL.39.003177
[24]	J. Y. Xie, L. L. Xu, and E. H. Chen, "Image denoising and inpainting with deep neural networks, " in Proc. 25th Int. Conf. Neural Information Processing Systems, Lake Tahoe, Nevada, USA, 2012, pp. 341-349.
[25]	S. H. Gu, W. M. Zuo, Q. Xie, D. Y. Meng, X. C. Feng, and L. Zhang, "Convolutional sparse coding for image superresolution, " in Proc. 2015 IEEE Int. Conf. Computer Vision (ICCV), Santiago, Chile, 2015, pp. 1823-1831.
[26]	A. Krizhevsky, I. Sutskever, and G. E. Hinton, "Imagenet classification with deep convolutional neural networks, " in Proc. 25th Int. Conf. Neural Information Processing Systems, Lake Tahoe, Nevada, USA, 2012, pp. 1097-1105.
[27]	Y. Y. Zhu, M. Cox, and S. Lucey, "3D motion reconstruction for real-world camera motion, " in Proc. 2011 IEEE Conf. Computer Vision and Pattern Recognition (CVPR), Providence, RI, USA, 2011, pp. 1-8.
[28]	Y. Y. Zhu and S. Lucey, "Convolutional sparse coding for trajectory reconstruction, " IEEE Trans. Pattern Anal. Mach. Intell., vol. 37, no. 3, pp. 529-540, Mar. 2015. doi: 10.1109/TPAMI.2013.2295311
[29]	Y. Y. Zhu, D. Huang, F. De La Torre, and S. Lucey, "Complex non-rigid motion 3D reconstruction by union of subspaces, " in Proc. 2014 IEEE Conf. Computer Vision and Pattern Recognition (CVPR), Columbus, OH, USA, 2014, pp. 1542-1549.
[30]	A. Serrano, F. Heide, D. Gutierrez, G. Wetzstein, and B. Masia, "Convolutional sparse coding for high dynamic range imaging, " Computer Graphics, vol. 35, no. 2, pp. 153-163, May 2016. http://dl.acm.org/citation.cfm?id=3028600
[31]	J. F. Yang, Y. Zhang, and W. T. Yin, "A fast alternating direction method for TVL1-L2 signal reconstruction from partial Fourier data, " IEEE J. Sel. Topics Signal Process., vol. 4, no. 2, pp. 288-297, Apr. 2010. doi: 10.1109/JSTSP.2010.2042333
[32]	H. Bristow, A. Eriksson, and S. Lucey, "Fast convolutional sparse coding, " in Proc. 2013 IEEE Conf. Computer Vision and Pattern Recognition (CVPR), Portland, OR, USA, 2013, pp. 391-398.
[33]	B. Wohlberg, "Efficient convolutional sparse coding, " in Proc. 2014 IEEE Int. Conf. Acoustics, Speech and Signal Processing (ICASSP), Florence, Italy, 2014, pp. 7173-7177.