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Magnetic resonance image restoration via least absolute deviations measure with isotropic total variation constraint

  • Received: 06 January 2023 Revised: 23 March 2023 Accepted: 30 March 2023 Published: 12 April 2023
  • This paper presents a magnetic resonance image deblurring and denoising model named the isotropic total variation regularized least absolute deviations measure (LADTV). More specifically, the least absolute deviations term is first adopted to measure the violation of the relation between the desired magnetic resonance image and the observed image, and to simultaneously suppress the noise that may corrupt the desired image. Then, in order to preserve the smoothness of the desired image, we introduce an isotropic total variation constraint, yielding the proposed restoration model LADTV. Finally, an alternating optimization algorithm is developed to solve the associated minimization problem. Comparative experiments on clinical data demonstrate the effectiveness of our approach to synchronously deblur and denoise magnetic resonance image.

    Citation: Xiaolei Gu, Wei Xue, Yanhong Sun, Xuan Qi, Xiao Luo, Yongsheng He. Magnetic resonance image restoration via least absolute deviations measure with isotropic total variation constraint[J]. Mathematical Biosciences and Engineering, 2023, 20(6): 10590-10609. doi: 10.3934/mbe.2023468

    Related Papers:

  • This paper presents a magnetic resonance image deblurring and denoising model named the isotropic total variation regularized least absolute deviations measure (LADTV). More specifically, the least absolute deviations term is first adopted to measure the violation of the relation between the desired magnetic resonance image and the observed image, and to simultaneously suppress the noise that may corrupt the desired image. Then, in order to preserve the smoothness of the desired image, we introduce an isotropic total variation constraint, yielding the proposed restoration model LADTV. Finally, an alternating optimization algorithm is developed to solve the associated minimization problem. Comparative experiments on clinical data demonstrate the effectiveness of our approach to synchronously deblur and denoise magnetic resonance image.



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    [1] S. J. Garnier, G. L. Bilbro, J. W. Gault, W. E. Snyder, Magnetic resonance image restoration, J. Math. Imaging Vis., 5 (1995), 7–19. https://doi.org/10.1007/BF01250250 doi: 10.1007/BF01250250
    [2] H. V. Bhujle, B. H. Vadavadagi, NLM based magnetic resonance image denoising-A review, Biomed. Signal Process. Control, 47 (2019), 252–261. https://doi.org/10.1016/j.bspc.2018.08.031 doi: 10.1016/j.bspc.2018.08.031
    [3] R. Kala, P. Deepa, Adaptive fuzzy hexagonal bilateral filter for brain MRI denoising, Multimed. Tools Appl., 79 (2020), 15513–15530. https://doi.org/10.1007/s11042-019-7459-x doi: 10.1007/s11042-019-7459-x
    [4] A. Hadri, A. Laghrib, H. Oummi, An optimal variable exponent model for Magnetic Resonance Images denoising, Pattern Recognit. Lett., 151 (2021), 302–309. https://doi.org/10.1016/j.patrec.2021.08.031 doi: 10.1016/j.patrec.2021.08.031
    [5] S. Kollem, K. R. Reddy, D. S. Rao, Improved partial differential equation-based total variation approach to non-subsampled contourlet transform formedical image denoising, Multimed. Tools Appl., 80 (2021), 2663–2689. https://doi.org/10.1007/s11042-020-09745-1 doi: 10.1007/s11042-020-09745-1
    [6] H. Aetesam, S. K. Maji, Attention-based noise prior network for magnetic resonance image denoising, in Proceedings of the IEEE 19th International Symposium on Biomedical Imaging, 2022. https://doi.org/10.1109/ISBI52829.2022.9761530
    [7] Y. Xu, K. Han, Y. Zhou, J. Wu, X. Xie, W. Xiang, Deep adaptive blending network for 3D magnetic resonance image denoising, IEEE J. Biomed. Health Inf., 25 (2021), 3321–3331. https://doi.org/10.1109/JBHI.2021.3087407 doi: 10.1109/JBHI.2021.3087407
    [8] R. W. Liu, L. Shi, S. C. Yu, D. Wang, A two-step optimization approach for nonlocal total variation-based rician noise reduction in MR images, Med. Phys., 42 (2015), 5167–5187. https://doi.org/10.1118/1.4927793 doi: 10.1118/1.4927793
    [9] F. Shi, J. Cheng, L. Wang, P. T. Yap, D. Shen, LRTV: MR image super-resolution with low-rank and total variation regularizations, IEEE Trans. Med. Imaging, 34 (2015), 2459–2466. https://doi.org/10.1109/TMI.2015.2437894 doi: 10.1109/TMI.2015.2437894
    [10] P. K. Mishro, S. Agrawal, R. Panda, A. Abraham, A survey on state-of-the-art denoising techniques for brain magnetic resonance images, IEEE Rev. Biomed. Eng., 15 (2022), 184–199. https://doi.org/10.1109/RBME.2021.3055556 doi: 10.1109/RBME.2021.3055556
    [11] L. Rudin, S. Osher, E. Fatemi, Nonlinear total variation based noise removal algorithms, Phys. D, 60 (1992), 259–268. https://doi.org/10.1016/0167-2789(92)90242-F doi: 10.1016/0167-2789(92)90242-F
    [12] L. Condat, Discrete total variation: New definition and minimization, SIAM J. Imaging Sci., 10 (2017), 1258–1290. https://doi.org/10.1137/16M1075247 doi: 10.1137/16M1075247
    [13] D. Goldfarb, W. Yin, Second-order cone programming methods for total variation-based image restoration, SIAM J. Sci. Comput., 27 (2005), 622–645. https://doi.org/10.1137/040608982 doi: 10.1137/040608982
    [14] A. Chambolle, An algorithm for total variation minimization and applications, J. Math. Imaging Vis., 20 (2004), 89–97. https://doi.org/10.1023/B:JMIV.0000011325.36760.1e doi: 10.1023/B:JMIV.0000011325.36760.1e
    [15] A. Chambolle, Total variation minimization and a class of binary MRF models, in Proceedings of the International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition, (2005), 136–152. https://doi.org/10.1007/11585978_10
    [16] G. Yu, L. Qi, Y. Dai, On nonmonotone Chambolle gradient projection algorithms for total variation image restoration, J. Math. Imaging Vis., 35 (2009), 143–154. https://doi.org/10.1007/s10851-009-0160-3 doi: 10.1007/s10851-009-0160-3
    [17] J. Dahl, P. C. Hansen, S. H. Jensen, T. L. Jensen, Algorithms and software for total variation image reconstruction via first-order methods, Numer. Algor., 53 (2010), 67–92. https://doi.org/10.1007/s11075-009-9310-3 doi: 10.1007/s11075-009-9310-3
    [18] M. Zhu, S. J. Wright, T. F. Chan, Duality-based algorithms for total-variation-regularized image restoration, Comput. Optim. Appl., 47 (2010), 377–400. https://doi.org/10.1007/s10589-008-9225-2 doi: 10.1007/s10589-008-9225-2
    [19] S. Bonettini, V. Ruggiero, On the convergence of primal–dual hybrid gradient algorithms for total variation image restoration, J. Math. Imaging Vis., 44 (2012), 236–253. https://doi.org/10.1007/s10851-011-0324-9 doi: 10.1007/s10851-011-0324-9
    [20] C. He, C. Hu, W. Zhang, B. Shi, A fast adaptive parameter estimation for total variation image restoration, IEEE Trans. Image Process., 23 (2014), 4954–4967. https://doi.org/10.1109/TIP.2014.2360133 doi: 10.1109/TIP.2014.2360133
    [21] G. Yu, W. Xue, Y. Zhou, A nonmonotone adaptive projected gradient method for primal-dual total variation image restoration, Signal Process., 103 (2014), 242–249. http://dx.doi.org/10.1016/j.sigpro.2014.02.025 doi: 10.1016/j.sigpro.2014.02.025
    [22] V. B. S. Prasath, D. Vorotnikov, R. Pelapur, S. Jose, G. Seetharaman, K. Palaniappan, Multiscale Tikhonov-total variation image restoration using spatially varying edge coherence exponent, IEEE Trans. Image Process., 24 (2015), 5220–5235. https://doi.org/10.1109/TIP.2015.2479471 doi: 10.1109/TIP.2015.2479471
    [23] D. O'Connor, L. Vandenberghe, On the equivalence of the primal-dual hybrid gradient method and Douglas–Rachford splitting, Math. Program., 179 (2020), 85–108. https://doi.org/10.1007/s10107-018-1321-1 doi: 10.1007/s10107-018-1321-1
    [24] E. K. Ryu, W. Yin, Proximal-proximal-gradient method, J. Comp. Math., 37 (2019), 778–812. https://doi.org/10.4208/jcm.1906-m2018-0282 doi: 10.4208/jcm.1906-m2018-0282
    [25] Y. Yang, M. Pesavento, Z. Q. Luo, B. Ottersten, Inexact block coordinate descent algorithms for nonsmooth nonconvex optimization, IEEE Trans. Signal Process., 68 (2019), 947–961. https://doi.org/10.1109/TSP.2019.2959240 doi: 10.1109/TSP.2019.2959240
    [26] A. Beck, M. Teboulle, A fast iterative shrinkage-thresholding algorithm for linear inverse problems, SIAM J. Imaging Sci., 2 (2009), 183–202. https://doi.org/10.1137/080716542 doi: 10.1137/080716542
    [27] A. Beck, M. Teboulle, Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems, IEEE Trans. Image Process., 18 (2009), 2419–2434. https://doi.org/10.1109/TIP.2009.2028250 doi: 10.1109/TIP.2009.2028250
    [28] I. Selesnick, Total variation denoising via the Moreau envelope, IEEE Signal Process. Lett., 24 (2017), 216–220. https://doi.org/10.1109/LSP.2017.2647948 doi: 10.1109/LSP.2017.2647948
    [29] M. Shen, J. Li, T. Zhang, J. Zou, Magnetic resonance imaging reconstruction via non‐convex total variation regularization, Int. J. Imaging Syst. Technol., 31 (2021), 412–424. https://doi.org/10.1002/ima.22463 doi: 10.1002/ima.22463
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