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Rank-one and sparse matrix decomposition for dynamic MRI

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  • We introduce a rank-one and sparse matrix decomposition model for dynamic magnetic resonance imaging (MRI). Since $l_p$-norm $(0 < p < 1)$ is generally nonconvex, nonsmooth, non-Lipschitz, we propose reweighted $l_1$-norm to surrogate $l_p$-norm. Based on this, we put forward a modified alternative direction method. Numerical experiments are also given to illustrate the efficiency of our algorithm.
    Mathematics Subject Classification: Primary: 90C90, 90C26; Secondary: 65K10.


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  • [1]

    K. Amin, W. Xu, A. Avestimehr and B. Hassibi, Weighted $l_1$ minimization for sparse recovery with prior information, IEEE International Symposium on Information Theory, 2 (2009), 483-487.


    O. Banerjee, L. Ghaouiand and A. D'Aspremont, Model selection through sparse maximum likelihood estimation for multivariate Gaussian or Binary data, The Journal of Machine Learning Research, 9 (2008), 485-516.


    S. Boyd, N. Parikh, E. Chu, B. Peleato and J. Eckstein, Distributed optimization and statistical learning via alternating direction method of multipliers, Foundations and Trends in Machine Learning, 3 (2011), 1-122.


    E. Candès, M. Wakin and S. Boyd, Enhancing sparsity by reweighted $l_1$ minimization, Journal of Fourier Analysis and Applications, 14 (2008), 877-905.doi: 10.1007/s00041-008-9045-x.


    V. Chandrasekaran, S. Sanghavi, P. Parrilo and A. Willsky, Rank-sparsity incoherence for matrix decomposition, SIAM Journal on Optimization, 21 (2011), 572-596.doi: 10.1137/090761793.


    X. Chen, D. Ge, Z. Wang and Y. Ye, Complexity of unconstrained $L_2-L_p$ minimization, Mathematical Programming, 143 (2014), 371-383.doi: 10.1007/s10107-012-0613-0.


    I. Daubechies, R. DeVore, M. Fornasier and C. Güntürk, Iteratively reweighted least squares minimization for sparse recovery, Communications on Pure and Applied Mathematics, 63 (2010), 1-38.doi: 10.1002/cpa.20303.


    S. Foucart and M. Lai, Sparsest solutions of underdetermined linear systems via $l_p$-minimization for 0 < q < 1, Applied and Computational Harmonic Analysis, 26 (2009), 395-407.doi: 10.1016/j.acha.2008.09.001.


    D. Ge, X. Jiang and Y. Ye, A note on the complexity of $l_p$ minimization, Mathematical Programming, 129 (2011), 285-299.doi: 10.1007/s10107-011-0470-2.


    X. Li, M. Ng and X. Yuan, Nuclear-norm-free variational models for background extraction from surveillance video, submitted to IEEE Transactions on Image Processing, 2013.


    Z. Lin, M. Chen and Y. Ma, The augmented Lagrange multiplier method for exact recovery of a corrupted low-rank matrices, Preprint, 2010.


    R. Otazo, E. Candès and D. Sodickson, Low-rank plus sparse matrix decomposition for accelerated dynamic MRI with separation of background and dynamic components, Magnetic Resonance in Medicine, 73 (2015), 1125-1136.


    J. Wright, A. Ganesh, S. Rao, Y. Peng and Y. Ma, Robust principal component analysis: exact recovery of corrupted low-rank matrices via convex optimization, Advances in Neural Information Processing Systems, (2009), 2080-2088.


    S. Wright, R. Nowak and M. Figueiredo, Sparse reconstruction by separable approximation, IEEE Transactions on Signal Processing, 57 (2009), 2479-2493.doi: 10.1109/TSP.2009.2016892.


    X. Xiu, L. Kong and S. Zhou, Modified iterative reweighted $l_1$ algorithm for surveillance video, Preprint, 2014.


    X. Yuan and J. Yang, Sparse and low-rank matrix decomposition via alternating direction methods, Pacific Journal of Optimization, 9 (2013), 167-180.


    Y. Zhao and D. Li, Reweighted $l_1$-minimization for sparse solutions to underdetermined linear systems, SIAM Journal on Optimization, 22 (2012), 1065-1088.doi: 10.1137/110847445.


    S. Zhou, N. Xiu, Y. Wang and L. Kong, Exact recovery for sparse signal via weighted $l_1$ minimization, Preprint, 2014.

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