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Volume 10 Issue 11
Nov.  2023

IEEE/CAA Journal of Automatica Sinica

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B. S. Shi and  K. X. Liu,  “Regularization by multiple dual frames for compressed sensing magnetic resonance imaging with convergence analysis,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 11, pp. 2136–2153, Nov. 2023. doi: 10.1109/JAS.2023.123543
Citation: B. S. Shi and  K. X. Liu,  “Regularization by multiple dual frames for compressed sensing magnetic resonance imaging with convergence analysis,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 11, pp. 2136–2153, Nov. 2023. doi: 10.1109/JAS.2023.123543

Regularization by Multiple Dual Frames for Compressed Sensing Magnetic Resonance Imaging With Convergence Analysis

doi: 10.1109/JAS.2023.123543
Funds:  This work was supported in part by the National Natural Science Foundation of China (62371414, 61901406), the Hebei Natural Science Foundation (F2020203025), the Young Talent Program of Universities and Colleges in Hebei Province (BJ2021044), the Hebei Key Laboratory Project (202250701010046), and the Central Government Guides Local Science and Technology Development Fund Projects (216Z1602G)
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  • Plug-and-play priors are popular for solving ill-posed imaging inverse problems. Recent efforts indicate that the convergence guarantee of the imaging algorithms using plug-and-play priors relies on the assumption of bounded denoisers. However, the bounded properties of existing plugged Gaussian denoisers have not been proven explicitly. To bridge this gap, we detail a novel provable bounded denoiser termed as BMDual, which combines a trainable denoiser using dual tight frames and the well-known block-matching and 3D filtering (BM3D) denoiser. We incorporate multiple dual frames utilized by BMDual into a novel regularization model induced by a solver. The proposed regularization model is utilized for compressed sensing magnetic resonance imaging (CSMRI). We theoretically show the bound of the BMDual denoiser, the bounded gradient of the CSMRI data-fidelity function, and further demonstrate that the proposed CSMRI algorithm converges. Experimental results also demonstrate that the proposed algorithm has a good convergence behavior, and show the effectiveness of the proposed algorithm.

     

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  • [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/mrm.21391
    [2]
    X. Zhang, D. Guo, Y. Huang, Y. Chen, L. Wang, F. Huang, Q. Xu, and X. Qu, “Image reconstruction with low-rankness and self-consistency of k-space data in parallel MRI,” Med. Image Anal., vol. 63, p. 101687, Jul. 2020. doi: 10.1016/j.media.2020.101687
    [3]
    Q. Liu, Q. Yang, H. Cheng, S. Wang, M. Zhang, and D. Liang, “Highly undersampled magnetic resonance imaging reconstruction using autoencoding priors,” Magn. Reson. Med., vol. 83, no. 1, pp. 322–336, Jan. 2020. doi: 10.1002/mrm.27921
    [4]
    Y. Hu, X. Zhang, D. Chen, Z. Yan, X. Shen, G. Yan, L. Ouyang, J. Lin, J. Dong, and X. Qu, “Spatiotemporal flexible sparse reconstruction for rapid dynamic contrast-enhanced MRI,” IEEE Trans. Biomed. Eng., vol. 69, no. 1, pp. 229–243, Jan. 2022. doi: 10.1109/TBME.2021.3091881
    [5]
    X. Zhang, H. Lu, D. Guo, L. Bao, F. Huang, Q. Xu, and X. Qu, “A guaranteed convergence analysis for the projected fast iterative soft-thresholding algorithm in parallel MRI,” Med. Image Anal., vol. 69, p. 101987, Apr. 2021. doi: 10.1016/j.media.2021.101987
    [6]
    Y. Liu, Z. Zhan, J. F. Cai, D. Guo, Z. Chen, and X. Qu, “Projected iterative soft-thresholding algorithm for tight frames in compressed sensing magnetic resonance imaging,” IEEE Trans. Med. Imaging, vol. 35, no. 9, pp. 2130–2140, Sept. 2016. doi: 10.1109/TMI.2016.2550080
    [7]
    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
    [8]
    X. Qu, Y. Hou, F. Lam, D. Guo, J. Zhong, and Z. Chen, “Magnetic resonance image reconstruction from undersampled measurements using a patch-based nonlocal operator,” Med. Image Anal., vol. 18, no. 6, pp. 843–856, Aug. 2014. doi: 10.1016/j.media.2013.09.007
    [9]
    W. Dong, G. Shi, X. Li, Y. Ma, and F. Huang, “Compressive sensing via nonlocal low-rank regularization,” IEEE Trans. Image Process., vol. 23, no. 8, pp. 3618–3632, Aug. 2014. doi: 10.1109/TIP.2014.2329449
    [10]
    M. Jacob, M. P. Mani, and J. C. Ye, “Structured low-rank algorithms: Theory, magnetic resonance applications, and links to machine learning,” IEEE Signal Process. Mag., vol. 37, no. 1, pp. 54–68, Jan. 2020. doi: 10.1109/MSP.2019.2950432
    [11]
    J. P. Haldar and K. Setsompop, “Linear predictability in magnetic resonance imaging reconstruction: Leveraging shift-invariant Fourier structure for faster and better imaging,” IEEE Signal Process. Mag., vol. 37, no. 1, pp. 69–82, Jan. 2020. doi: 10.1109/MSP.2019.2949570
    [12]
    J. F. Cai, J. K. Choi, and K. Wei, “Data driven tight frame for compressed sensing MRI reconstruction via off-the-grid regularization,” SIAM J. Imaging Sci., vol. 13, no. 3, pp. 1272–1301, Jan. 2020. doi: 10.1137/19M1298524
    [13]
    Y. Chen, C. B. Schonlieb, P. Liò, T. Leiner, P. L. Dragotti, G. Wang, D. Rueckert, D. Firmin, and G. Yang, “AI-based reconstruction for fast MRI — A systematic review and meta-analysis,” Proc. IEEE, vol. 110, no. 2, pp. 224–245, Feb. 2022. doi: 10.1109/JPROC.2022.3141367
    [14]
    M. Seitzer, G. Yang, J. Schlemper, O. Oktay, T. Würfl, V. Christlein, T. Wong, R. Mohiaddin, D. Firmin, J. Keegan, D. Rueckert, and A. Maier, “Adversarial and perceptual refinement for compressed sensing MRI reconstruction,” in Proc. 21st Int. Conf. Medical Image Computing and Computer Assisted Intervention, Granada, Spain, 2018, pp. 232–240.
    [15]
    S. Wang, Z. Su, L. Ying, X. Peng, S. Zhu, F. Liang, D. Feng, and D. Liang, “Accelerating magnetic resonance imaging via deep learning,” in Proc. IEEE 13th Int. Symp. Biomedical Imaging, Prague, Czech Republic, 2016, pp. 514–517.
    [16]
    F. Hashimoto, K. Ote, T. Oida, A. Teramoto, and Y. Ouchi, “Compressed-sensing magnetic resonance image reconstruction using an iterative convolutional neural network approach,” Appl. Sci., vol. 10, no. 6, p. 1902, Mar. 2020. doi: 10.3390/app10061902
    [17]
    P. Deora, B. Vasudeva, S. Bhattacharya, and P. M. Pradhan, “Structure preserving compressive sensing MRI reconstruction using generative adversarial networks,” in Proc. IEEE/CVF Conf. Computer Vision and Pattern Recognition Workshops, Seattle, WA, USA, 2020, pp. 2211–2219.
    [18]
    G. Yang, S. Yu, H. Dong, G. Slabaugh, P. L. Dragotti, X. Ye, F. Liu, S. Arridge, J. Keegan, Y. Guo, and D. Firmin, “DAGAN: Deep de-aliasing generative adversarial networks for fast compressed sensing MRI reconstruction,” IEEE Trans. Med. Imaging, vol. 37, no. 6, pp. 1310–1321, Jun. 2018. doi: 10.1109/TMI.2017.2785879
    [19]
    T. M. Quan, T. Nguyen-Duc, and W.-K. Jeong, “Compressed sensing MRI reconstruction using a generative adversarial network with a cyclic loss,” IEEE Trans. Med. Imaging, vol. 37, no. 6, pp. 1488–1497, Jun. 2018. doi: 10.1109/TMI.2018.2820120
    [20]
    G. Yang, Q. Ye, and J. Xia, “Unbox the black-box for the medical explainable AI via multi-modal and multi-centre data fusion: A mini-review, two showcases and beyond,” Inf. Fusion, vol. 77, pp. 29–52, Jan. 2022. doi: 10.1016/j.inffus.2021.07.016
    [21]
    H. K. Aggarwal, M. P. Mani, and M. Jacob, “MoDL: Model-based deep learning architecture for inverse problems,” IEEE Trans. Med. Imaging, vol. 38, no. 2, pp. 394–405, Feb. 2019. doi: 10.1109/TMI.2018.2865356
    [22]
    Y. Yang, J. Sun, H. Li, and Z. Xu, “Deep ADMM-Net for compressive sensing MRI,” in Proc. 30th Int. Conf. Neural Information Processing Systems, Barcelona, Spain, 2016, pp. 10–18.
    [23]
    Y. Yang, J. Sun, H. Li, and Z. Xu, “ADMM-CSNet: A deep learning approach for image compressive sensing,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 42, no. 3, pp. 521–538, Mar. 2020. doi: 10.1109/TPAMI.2018.2883941
    [24]
    Y. Yang, N. Wang, H. Yang, J. Sun, and Z. Xu, “Model-driven deep attention network for ultra-fast compressive sensing MRI guided by cross-contrast MR image,” in Proc. 23rd Int. Conf. Medical Image Computing and Computer Assisted Intervention, Lima, Peru, 2020, pp. 188–198.
    [25]
    J. Schlemper, J. Caballero, J. V. Hajnal, A. N. Price, and D. Rueckert, “A deep cascade of convolutional neural networks for dynamic MR image reconstruction,” IEEE Trans. Med. Imaging, vol. 37, no. 2, pp. 491–503, Feb. 2018. doi: 10.1109/TMI.2017.2760978
    [26]
    A. Q. Wang, A. V. Dalca, and M. R. Sabuncu, “Neural network-based reconstruction in compressed sensing MRI without fully-sampled training data,” in Proc. 3rd Int. Workshop Machine Learning for Medical Image Reconstruction, Lima, Peru, 2020, pp. 27–37.
    [27]
    R. Ahmad, C. A. Bouman, G. T. Buzzard, S. Chan, S. Z. Liu, E. T. Reehorst, and P. Schniter, “Plug-and-play methods for magnetic resonance imaging: Using denoisers for image recovery,” IEEE Signal Process. Mag., vol. 37, no. 1, pp. 105–116, Jan. 2020. doi: 10.1109/MSP.2019.2949470
    [28]
    S. V. Venkatakrishnan, C. A. Bouman, and B. Wohlberg, “Plug-and-play priors for model based reconstruction,” in Proc. IEEE Global Conf. Signal and Information Processing, Austin, TX, USA, 2013, pp. 945–948.
    [29]
    X. Yuan, Y. Liu, J. Suo, and Q. Dai, “Plug-and-play algorithms for large-scale snapshot compressive imaging,” in Proc. IEEE/CVF Conf. Computer Vision and Pattern Recognition, Seattle, WA, USA, 2020, pp. 1444–1454.
    [30]
    K. Zhang, Y. Li, W. Zuo, L. Zhang, L. Van Gool, and R. Timofte, “Plug-and-play image restoration with deep denoiser prior,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 44, no. 10, pp. 6360–6376, Oct. 2022. doi: 10.1109/TPAMI.2021.3088914
    [31]
    Y. Romano, M. Elad, and P. Milanfar, “The little engine that could: Regularization by denoising (RED),” SIAM J. Imaging Sci., vol. 10, no. 4, pp. 1804–1844, Jan. 2017. doi: 10.1137/16M1102884
    [32]
    B. Shi, Q. Lian, and H. Chang, “Deep prior-based sparse representation model for diffraction imaging: A plug-and-play method,” Signal Process., vol. 168, p. 107350, Mar. 2020. doi: 10.1016/j.sigpro.2019.107350
    [33]
    K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” IEEE Trans. Image Process., vol. 16, no. 8, pp. 2080–2095, Aug. 2007. doi: 10.1109/TIP.2007.901238
    [34]
    K. Zhang, W. Zuo, Y. Chen, D. Meng, and L. Zhang, “Beyond a Gaussian denoiser: Residual learning of deep CNN for image denoising,” IEEE Trans. Image Process., vol. 26, no. 7, pp. 3142–3155, Jul. 2017. doi: 10.1109/TIP.2017.2662206
    [35]
    H. Zheng, H. Yong, and L. Zhang, “Deep convolutional dictionary learning for image denoising,” in Proc. IEEE/CVF Conf. Computer Vision and Pattern Recognition, Nashville, TN, USA, 2021, pp. 630–641.
    [36]
    E. M. Eksioglu, “Decoupled algorithm for MRI reconstruction using nonlocal block matching model: BM3D-MRI,” J. Math. Imaging Vis., vol. 56, no. 3, pp. 430–440, Mar. 2016. doi: 10.1007/s10851-016-0647-7
    [37]
    E. M. Eksioglu and A. K. Tanc, “Denoising AMP for MRI reconstruction: BM3D-AMP-MRI,” SIAM J. Imaging Sci., vol. 11, no. 3, pp. 2090–2109, 2018. doi: 10.1137/18M1169655
    [38]
    E. K. Ryu, J. Liu, S. Wang, X. Chen, Z. Wang, and W. Yin, “Plug-and-play methods provably converge with properly trained denoisers,” in Proc. 36th Int. Conf. Machine Learning, Long Beach, CA, USA, 2019, pp. 5546–5557.
    [39]
    P. Bohra, D. Perdios, A. Goujon, S. Emery, and M. Unser, “Learning Lipschitz-controlled activation functions in neural networks for plug-and-play image reconstruction methods,” in Proc. Workshop Deep Learning and Inverse Problems, Montreal, Canada, 2021.
    [40]
    A. M. Teodoro, J. M. Bioucas-Dias, and M. A. T. Figueiredo, “Scene-adapted plug-and-play algorithm with convergence guarantees,” in Proc. IEEE 27th Int. Workshop Machine Learning for Signal Processing, Tokyo, Japan, 2017, pp. 1–6.
    [41]
    R. G. Gavaskar and K. N. Chaudhury, “Plug-and-play ISTA converges with kernel denoisers,” IEEE Signal Process. Lett., vol. 27, pp. 610–614, Apr. 2020. doi: 10.1109/LSP.2020.2986643
    [42]
    G. T. Buzzard, S. H. Chan, S. Sreehari, and C. A. Bouman, “Plug-and-play unplugged: Optimization-free reconstruction using consensus equilibrium,” SIAM J. Imaging Sci., vol. 11, no. 3, pp. 2001–2020, Jan. 2018. doi: 10.1137/17M1122451
    [43]
    S. H. Chan, X. Wang, and O. A. Elgendy, “Plug-and-play ADMM for image restoration: Fixed-point convergence and applications,” IEEE Trans. Comput. Imaging, vol. 3, no. 1, pp. 84–98, Mar. 2017. doi: 10.1109/TCI.2016.2629286
    [44]
    R. G. Gavaskar and K. N. Chaudhury, “On the proof of fixed-point convergence for plug-and-play ADMM,” IEEE Signal Process. Lett., vol. 26, no. 12, pp. 1817–1821, Dec. 2019. doi: 10.1109/LSP.2019.2950611
    [45]
    D. Geman and C. Yang, “Nonlinear image recovery with half quadratic regularization,” IEEE Trans. Image Process., vol. 4, no. 7, pp. 932–946, Jul. 1995. doi: 10.1109/83.392335
    [46]
    M. Terris, A. Repetti, J.-C. Pesquet, and Y. Wiaux, “Enhanced convergent PnP algorithms for image restoration,” in Proc. IEEE Int. Conf. Image Processing, Anchorage, AK, USA, 2021, pp. 1684–1688.
    [47]
    S. Mallat, A Wavelet Tour of Signal Processing: The Sparse Way. 3rd ed. Orlando, USA: Academic Press, 2008.
    [48]
    K. Isogawa, T. Ida, T. Shiodera, and T. Takeguchi, “Deep shrinkage convolutional neural network for adaptive noise reduction,” IEEE Signal Process. Lett., vol. 25, no. 2, pp. 224–228, Feb. 2018. doi: 10.1109/LSP.2017.2782270
    [49]
    Y. Zhang, Y. Tian, Y. Kong, B. Zhong, and Y. Fu, “Residual dense network for image restoration,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 43, no. 7, pp. 2480–2495, Jul. 2021. doi: 10.1109/TPAMI.2020.2968521
    [50]
    J. Hu, L. Shen, and G. Sun, “Squeeze-and-excitation networks,” in Proc. IEEE/CVF Conf. Computer Vision and Pattern Recognition, Salt Lake City, UT, USA, 2018, pp. 7132–7141.
    [51]
    A. Danielyan, V. Katkovnik, and K. Egiazarian, “BM3D frames and variational image deblurring,” IEEE Trans. Image Process., vol. 21, no. 4, pp. 1715–1728, Apr. 2012. doi: 10.1109/TIP.2011.2176954
    [52]
    B. Landman, “2013 Diencephalon standard challenge”.
    [53]
    N. Bien, P. Rajpurkar, R. L. Ball, J. Irvin, A. Park, E. Jones, M. Bereket, B. N. Patel, K. W. Yeom, K. Shpanskaya, S. Halabi, E. Zucker, G. Fanton, D. F. Amanatullah, C. F. Beaulieu, G. M. Riley, R. J. Stewart, F. G. Blankenberg, D. B. Larson, R. H. Jones, C. P. Langlotz, A. Y. Ng, and M. P. Lungren, “Deep-learning-assisted diagnosis for knee magnetic resonance imaging: Development and retrospective validation of MRNet,” PLoS Med., vol. 15, no. 11, p. e1002699, Nov. 2018. doi: 10.1371/journal.pmed.1002699
    [54]
    B. Shi, Q. Lian, S. Chen, and X. Fan, “SBM3D: Sparse regularization model induced by BM3D for weighted diffraction imaging,” IEEE Access, vol. 6, pp. 46266–46280, Aug. 2018. doi: 10.1109/ACCESS.2018.2865997
    [55]
    V. Y. Katkovnik and K. Egiazarian, “Sparse superresolution phase retrieval from phase-coded noisy intensity patterns,” Opt. Eng., vol. 56, no. 9, p. 094103, Sept. 2017.
    [56]
    Q. Zhang, J. Xiao, C. Tian, J. C.-W. Lin, and S. Zhang, “A robust deformed convolutional neural network (CNN) for image denoising,” CAAI Trans. Intell. Technol., vol. 8, no. 2, pp. 331–342, Jun. 2023. doi: 10.1049/cit2.12110
    [57]
    C. Tian, M. Zheng, W. Zuo, B. Zhang, Y. Zhang, and D. Zhang, “Multi-stage image denoising with the wavelet transform,” Pattern Recogn., vol. 134, p. 109050, Feb. 2023. doi: 10.1016/j.patcog.2022.109050
    [58]
    S. Herbreteau and C. Kervrann, “DCT2net: An interpretable shallow CNN for image denoising,” IEEE Trans. Image Process., vol. 31, pp. 4292–4305, Jun. 2022. doi: 10.1109/TIP.2022.3181488

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    Highlights

    • We propose a trainable bounded Gaussian denoiser
    • We propose a novel regularization model using multiple dual frames
    • We prove the convergence of the proposed CSMRI algorithm
    • Our algorithm achieves better reconstructions than existing CSMRI algorithms

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