\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Rank-one and sparse matrix decomposition for dynamic MRI

Abstract Related Papers Cited by
  • 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.

    Citation:

    \begin{equation} \\ \end{equation}
  • [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.

    [2]

    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.

    [3]

    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.

    [4]

    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.

    [5]

    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.

    [6]

    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.

    [7]

    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.

    [8]

    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.

    [9]

    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.

    [10]

    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.

    [11]

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

    [12]

    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.

    [13]

    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.

    [14]

    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.

    [15]

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

    [16]

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

    [17]

    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.

    [18]

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

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(233) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return