A second-order TV-based coupling model and an ADMM algorithm for MR image reconstruction

• Autorzy: Zhou Bo , Yang Yu-Fei , Hu Bo-Xia

Identyfikatory

DOI

10.34768/amcs-2020-0009

• Języki publikacji: EN

Abstrakty

EN

Motivated by ideas from two-step models and combining second-order TV regularization in the LLT model, we propose a coupling model for MR image reconstruction. By applying the variables splitting technique, the split Bregman iterative scheme, and the alternating minimization method twice, we can divide the proposed model into several subproblems only related to second-order PDEs so as to avoid solving a fourth-order PDE. The solution of every subproblem is based on generalized shrinkage formulas, the shrink operator or the diagonalization technique of the Fourier transform, and hence can be obtained very easily. By means of the Barzilai–Borwein step size selection scheme, an ADMM type algorithm is proposed to solve the equations underlying the proposed model. The results of numerical implementation demonstrate the feasibility and effectiveness of the proposed model and algorithm.

Słowa kluczowe

EN

MRI reconstruction; LLT model; LOT model; coupling model; ADMM algorithm; split Bregman; wavelet transform

PL

rezonans magnetyczny; metoda Bregmana; transformata falkowa

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2020
• Tom: Vol. 30, no. 1
• Strony: 113--122
• Opis fizyczny: Bibliogr. 19 poz., rys., tab.

Twórcy

autor

Zhou Bo

• College of Mathematics and Econometrics, Hunan University, Changsha 410082, Hunan, China; College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, Hunan, China

autor

Yang Yu-Fei

• School of Computer Engineering and Applied Mathematics, Changsha University, Changsha 410003, Hunan, China; College of Mathematics and Econometrics, Hunan University, Changsha 410082, Hunan, China

autor

Hu Bo-Xia

• College of Mathematics and Econometrics, Hunan University, Changsha 410082, Hunan, China; College of Mathematics and Statistics, Hengyang Normal University, Hengyang 421000, Hunan, China

Bibliografia

• [1] Chan, R.H., Yang, J. and Yuan, X. (2011). Alternating direction method for image inpainting in wavelet domains, SIAM Journal on Imaging Sciences 4(4): 807–826.
• [2] Chen, Y., Hager, W., Huang, F., Phan, D. and Ye, X. (2012). A fast algorithm for image reconstruction with application to partially parallel MR imaging, SIAM Journal on Imaging Sciences 5(1): 90–118.
• [3] Dong, F., Liu, Z., Kong, D. and Liu, K. (2009). An improved lot model for image restoration, Journal of Mathematical Imaging and Vision 34(1): 89–97.
• [4] Hao, Y., Feng, X.C. and Xu, J.L. (2012). Split Bregman algorithm for a novel denoising model, Journal of Electronics and Information Technology 34(3): 557–563.
• [5] Lustig,M., Donoho, D. and Pauly, J.M. (2007). SparseMRI: The application of compressed sensing for rapid MR imaging, Magnetic Resonance in Medicine 58(6): 1182–1195.
• [6] Lysaker, M., Lundervold, A. and Tai, X.C. (2003). Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time, IEEE Transactions on Image Processing 12(12): 1579–1590.
• [7] Lysaker, M., Osher, S. and Tai, X.C. (2004). Noise removal using smoothed normals and surface fitting, IEEE Transactions on Image Processing 13(10): 1345–1357.
• [8] Miao, J., Wong, W.C.K., Narayan, S., Huo, D. and Wilson, D.L. (2011). Modeling non-stationarity of kernel weights for k-space reconstruction in partially parallel imaging, Medical Physics 38(8): 4760–4773.
• [9] Och, J., Clarke, G. and Sobol, W.T. (1992). Acceptance testing of magnetic resonance imaging systems: Report of AAPM nuclear magnetic resonance task group no. 6, Medical Physics 19(1): 217–229.
• [10] Price, R.R., Axel, L., Morgan, T., Newman, R., Perman, W., Schneiders, N., Selikson, M., Wood, M. and Thomas, S.R. (1990). Quality assurance methods and phantoms for magnetic resonance imaging: Report of the AAPM nuclear magnetic resonance task group no. 1, Medical Physics 17(2): 287–295.
• [11] Rudin, L.I., Osher, S. and Fatemi, E. (1992). Nonlinear total variation based noise removal algorithms, Physica D: Nonlinear Phenomena 60(1–4): 259–268.
• [12] Steidl, G. (2006). A note on the dual treatment of higher order regularization functionals, Computing 76(1–2): 135–148.
• [13] Wang, Y., Yin, W. and Zhang, Y. (2007). A fast algorithm for image deblurring with total variation regularization, CAAM technical report, Rice University, Houston, TX, pp. TR07–10.
• [14] Wright, S.J., Nowak, R.D. and Figueiredo, M.A.T. (2009). Sparse reconstruction by separable approximation, IEEE Transactions on Signal Processing 57(7): 2479–2493.
• [15] Xie, W.S., Yang, Y.F. and Zhou, B. (2014). An ADMM algorithm for second-order TV-based MR image reconstruction, Numerical Algorithms 67(4): 827–843.
• [16] Yang, J., Zhang, Y. and Yin, W. (2010). A fast alternating direction method for TVL1-L2 signal reconstruction from partial Fourier data, IEEE Journal of Selected Topics in Signal Processing 4(2): 288–297.
• [17] Yang, Y.F., Pang, Z.F., Shi, B.L. and Wang, Z.G. (2011). Split Bregman method for the modified lot model in image denoising, Applied Mathematics and Computation 217(12): 5392–5403.
• [18] Ye, X., Chen, Y. and Huang, F. (2011). Computational acceleration for MR image reconstruction in partially parallel imaging, IEEE Transactions on Medical Imaging 30(5): 1055–1063.
• [19] You, Y.L. and Kaveh,M. (2000). Fourth-order partial differential equations for noise removal, IEEE Transactions on Image Processing 9(10): 1723–1730.

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).