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Learning circulant sensing kernels
Weighted-average alternating minimization method for magnetic resonance image reconstruction based on compressive sensing
1. | School of Science, Communication University of China, Beijing, 100024, China, China, China |
2. | Department of Mathematics and Physics, North China Electric Power University, Beijing, 102206, China |
References:
[1] |
A. Beck and M. Teboulle, Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems,, IEEE Transaction on Image Processing, 5 (2009), 2419.
doi: 10.1109/TIP.2009.2028250. |
[2] |
A. Beck and M. Teboulle, A fast iterative shrinkage-thresholding algorithm for linear inverse problems,, SIAM Journal on Imaging Sciences, 2 (2009), 183.
doi: 10.1137/080716542. |
[3] |
E. J. Candès, J. Romberg and T. Tao, Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,, IEEE Transactions on Information Theory, 52 (2006), 489.
doi: 10.1109/TIT.2005.862083. |
[4] |
E. J. Candès and J. Romberg, Sparsity and incoherence in compressive sampling,, Inverse Problems, 23 (2007), 969.
doi: 10.1088/0266-5611/23/3/008. |
[5] |
Y. Chen, X. Ye and F. Huang, A novel method and fast algorithm for MR image reconstruction with significantly under-sampled data,, Inverse Problems and Imaging, 4 (2010), 223.
doi: 10.3934/ipi.2010.4.223. |
[6] |
P. L. Combettes and V. R. Wajs, Signal recovery by proximal forward-backward splitting,, Multiscale Modeling and Simulation, 4 (2005), 1168.
doi: 10.1137/050626090. |
[7] |
P. L. Combettes, Iterative construction of the resolvent of a sum of maximal monotone operators,, Journal of Convex Analysis, 16 (2009), 727.
|
[8] |
P. L. Combettes and J.-C. Pesquet, A proximal decomposition method for solving convex variational in verse problems,, Inverse Problems, 24 (2008).
doi: 10.1088/0266-5611/24/6/065014. |
[9] |
D. L. Donoho, Compressed sensing,, IEEE Transactions on Information Theory, 52 (2006), 1289.
doi: 10.1109/TIT.2006.871582. |
[10] |
D. L. Donoho and X. Huo, Uncertainty principles and ideal atomic decompositions,, IEEE Transactions on Information Theory, 47 (2001), 2845.
doi: 10.1109/18.959265. |
[11] |
J. Eckstein and B. F. Svaiter, General projective splitting methods for sums of maximal monotone operators,, SIAM Journal on Control Optimization, 48 (2009), 787.
doi: 10.1137/070698816. |
[12] |
M. Figueiredo, R. Nowak and S. Wright, Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,, IEEE Journal of Selected Topics in Signal Processing, 1 (2007), 586.
doi: 10.1109/JSTSP.2007.910281. |
[13] |
J.-J. Fuchs, On sparse representations in arbitrary redundant bases,, IEEE Transactions on Information Theory, 50 (2004), 1341.
doi: 10.1109/TIT.2004.828141. |
[14] |
D. Gabay, Chapter IX applications of the method of multipliers to variational inequalities,, Studies in Mathematics and its Applications, 15 (1983), 299.
doi: 10.1016/S0168-2024(08)70034-1. |
[15] |
D. Gabay and B. Mercier, A dual algorithm for the solution of nonlinear variational problems via finite element approximations,, Computers and Mathematics with Applications, 2 (1976), 17.
doi: 10.1016/0898-1221(76)90003-1. |
[16] |
R. Glowinski and P. Le Tallec, Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics,, SIAM Studies in Applied Mathematics, (1989).
doi: 10.1137/1.9781611970838. |
[17] |
D. Goldfarb and S. Ma, Fast multiple-splitting algorithms for convex optimization,, SIAM Journal on Optimization, 22 (2012), 533.
doi: 10.1137/090780705. |
[18] |
T. Goldstein and O. Osher, The split Bregman method for L1-regularized problems,, SIAM Journal on Imaging Sciences, 2 (2009), 323.
doi: 10.1137/080725891. |
[19] |
J. Huang, S. Zhang and D. Metaxas, Efficient MR image reconstruction for compressed MR imaging,, in Medical Image Computing and Computer-Assisted Intervention-MICCAI 2010, (2010), 135.
doi: 10.1007/978-3-642-15705-9_17. |
[20] |
M. Lustig, D. L. Donoho and J. Pauly, Sparse MRI: The application of compressed sensing for rapid MR imaging,, Magnetic Resonance in Medicine, 58 (2007), 1182.
doi: 10.1002/mrm.21391. |
[21] |
J.-J. Moreau, Proximité et dualité dans un espace hilbertien,, Bull. Soc. Math. France, 93 (1965), 273.
|
[22] |
B. K. Natarajan, Sparse approximate solutions to linear systems,, SIAM Journal on Computing, 24 (1995), 227.
doi: 10.1137/S0097539792240406. |
[23] |
Z. Opal, Weak convergence of the sequence of successive approximations for nonexpansive mappings,, Bull. Amer. Math. Soc., 73 (1967), 591.
doi: 10.1090/S0002-9904-1967-11761-0. |
[24] |
L. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms,, Physica D, 60 (1992), 259.
doi: 10.1016/0167-2789(92)90242-F. |
[25] |
J. E. Spingarn, Partial inverse of monotone operator,, Applied Mathematics and Optimization, (1983), 247.
doi: 10.1007/BF01448388. |
[26] |
X. C. Tai and C. Wu, Augmented Lagrangian method, dual methods and split Bregman iteration for ROF model,, in Scale Space and Variational Methods in Computer Vision, (5567), 502. Google Scholar |
[27] |
P. Tseng, A modified forward-backward splitting method for maximal monotone mappings,, SIAM Journal on Control and Optimization, 38 (2000), 431.
doi: 10.1137/S0363012998338806. |
[28] |
P. Tseng and S. Yun, A coordinate gradient descent method for nonsmooth separable minimization,, Math. Prog. B., 117 (2009), 387.
doi: 10.1007/s10107-007-0170-0. |
[29] |
Y. Wang, J. Yang, W. Yin and Y. Zhang, A new alternating minimization algorithm for total variation image reconstruction,, SIAM Journal on Imaging Sciences, 1 (2008), 248.
doi: 10.1137/080724265. |
[30] |
J. Yang, Y. Zhang and W. Yin, A fast alternating direction method for TV-L1-L2 Signal reconstruction from partial Fourier data,, IEEE Journal of Selected Topics in Signal Processing, 4 (2010), 288. Google Scholar |
[31] |
W. Yin, S. Osher, D. Goldfarb and J. Darbon, Bregman Iterative algorithms for $l_1$-minimization with applications to compressed sensing,, SIAM Journal on Imaging Sciences, 1 (2008), 143.
doi: 10.1137/070703983. |
[32] |
Y. Zhu and I. Chern, Fast alternating minimization method for compressive sensing MRI under wavelet sparsity and TV sparsity,, in 2011 Sixth International Conference on Image and Graphics, (2011), 356.
doi: 10.1109/ICIG.2011.23. |
[33] |
Y. Zhu and I. Chern, Convergence of the alternating minimization method for sparse MR image reconstruction,, Journal of Information and Computational Science, 8 (2011), 2067. Google Scholar |
[34] |
Y. Zhu and Y. Shi, A fast method for reconstruction of total-variation MR images with a periodic boundary condition,, IEEE Signal Processing Letters, 20 (2013), 291.
doi: 10.1109/LSP.2013.2245502. |
show all references
References:
[1] |
A. Beck and M. Teboulle, Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems,, IEEE Transaction on Image Processing, 5 (2009), 2419.
doi: 10.1109/TIP.2009.2028250. |
[2] |
A. Beck and M. Teboulle, A fast iterative shrinkage-thresholding algorithm for linear inverse problems,, SIAM Journal on Imaging Sciences, 2 (2009), 183.
doi: 10.1137/080716542. |
[3] |
E. J. Candès, J. Romberg and T. Tao, Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,, IEEE Transactions on Information Theory, 52 (2006), 489.
doi: 10.1109/TIT.2005.862083. |
[4] |
E. J. Candès and J. Romberg, Sparsity and incoherence in compressive sampling,, Inverse Problems, 23 (2007), 969.
doi: 10.1088/0266-5611/23/3/008. |
[5] |
Y. Chen, X. Ye and F. Huang, A novel method and fast algorithm for MR image reconstruction with significantly under-sampled data,, Inverse Problems and Imaging, 4 (2010), 223.
doi: 10.3934/ipi.2010.4.223. |
[6] |
P. L. Combettes and V. R. Wajs, Signal recovery by proximal forward-backward splitting,, Multiscale Modeling and Simulation, 4 (2005), 1168.
doi: 10.1137/050626090. |
[7] |
P. L. Combettes, Iterative construction of the resolvent of a sum of maximal monotone operators,, Journal of Convex Analysis, 16 (2009), 727.
|
[8] |
P. L. Combettes and J.-C. Pesquet, A proximal decomposition method for solving convex variational in verse problems,, Inverse Problems, 24 (2008).
doi: 10.1088/0266-5611/24/6/065014. |
[9] |
D. L. Donoho, Compressed sensing,, IEEE Transactions on Information Theory, 52 (2006), 1289.
doi: 10.1109/TIT.2006.871582. |
[10] |
D. L. Donoho and X. Huo, Uncertainty principles and ideal atomic decompositions,, IEEE Transactions on Information Theory, 47 (2001), 2845.
doi: 10.1109/18.959265. |
[11] |
J. Eckstein and B. F. Svaiter, General projective splitting methods for sums of maximal monotone operators,, SIAM Journal on Control Optimization, 48 (2009), 787.
doi: 10.1137/070698816. |
[12] |
M. Figueiredo, R. Nowak and S. Wright, Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,, IEEE Journal of Selected Topics in Signal Processing, 1 (2007), 586.
doi: 10.1109/JSTSP.2007.910281. |
[13] |
J.-J. Fuchs, On sparse representations in arbitrary redundant bases,, IEEE Transactions on Information Theory, 50 (2004), 1341.
doi: 10.1109/TIT.2004.828141. |
[14] |
D. Gabay, Chapter IX applications of the method of multipliers to variational inequalities,, Studies in Mathematics and its Applications, 15 (1983), 299.
doi: 10.1016/S0168-2024(08)70034-1. |
[15] |
D. Gabay and B. Mercier, A dual algorithm for the solution of nonlinear variational problems via finite element approximations,, Computers and Mathematics with Applications, 2 (1976), 17.
doi: 10.1016/0898-1221(76)90003-1. |
[16] |
R. Glowinski and P. Le Tallec, Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics,, SIAM Studies in Applied Mathematics, (1989).
doi: 10.1137/1.9781611970838. |
[17] |
D. Goldfarb and S. Ma, Fast multiple-splitting algorithms for convex optimization,, SIAM Journal on Optimization, 22 (2012), 533.
doi: 10.1137/090780705. |
[18] |
T. Goldstein and O. Osher, The split Bregman method for L1-regularized problems,, SIAM Journal on Imaging Sciences, 2 (2009), 323.
doi: 10.1137/080725891. |
[19] |
J. Huang, S. Zhang and D. Metaxas, Efficient MR image reconstruction for compressed MR imaging,, in Medical Image Computing and Computer-Assisted Intervention-MICCAI 2010, (2010), 135.
doi: 10.1007/978-3-642-15705-9_17. |
[20] |
M. Lustig, D. L. Donoho and J. Pauly, Sparse MRI: The application of compressed sensing for rapid MR imaging,, Magnetic Resonance in Medicine, 58 (2007), 1182.
doi: 10.1002/mrm.21391. |
[21] |
J.-J. Moreau, Proximité et dualité dans un espace hilbertien,, Bull. Soc. Math. France, 93 (1965), 273.
|
[22] |
B. K. Natarajan, Sparse approximate solutions to linear systems,, SIAM Journal on Computing, 24 (1995), 227.
doi: 10.1137/S0097539792240406. |
[23] |
Z. Opal, Weak convergence of the sequence of successive approximations for nonexpansive mappings,, Bull. Amer. Math. Soc., 73 (1967), 591.
doi: 10.1090/S0002-9904-1967-11761-0. |
[24] |
L. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms,, Physica D, 60 (1992), 259.
doi: 10.1016/0167-2789(92)90242-F. |
[25] |
J. E. Spingarn, Partial inverse of monotone operator,, Applied Mathematics and Optimization, (1983), 247.
doi: 10.1007/BF01448388. |
[26] |
X. C. Tai and C. Wu, Augmented Lagrangian method, dual methods and split Bregman iteration for ROF model,, in Scale Space and Variational Methods in Computer Vision, (5567), 502. Google Scholar |
[27] |
P. Tseng, A modified forward-backward splitting method for maximal monotone mappings,, SIAM Journal on Control and Optimization, 38 (2000), 431.
doi: 10.1137/S0363012998338806. |
[28] |
P. Tseng and S. Yun, A coordinate gradient descent method for nonsmooth separable minimization,, Math. Prog. B., 117 (2009), 387.
doi: 10.1007/s10107-007-0170-0. |
[29] |
Y. Wang, J. Yang, W. Yin and Y. Zhang, A new alternating minimization algorithm for total variation image reconstruction,, SIAM Journal on Imaging Sciences, 1 (2008), 248.
doi: 10.1137/080724265. |
[30] |
J. Yang, Y. Zhang and W. Yin, A fast alternating direction method for TV-L1-L2 Signal reconstruction from partial Fourier data,, IEEE Journal of Selected Topics in Signal Processing, 4 (2010), 288. Google Scholar |
[31] |
W. Yin, S. Osher, D. Goldfarb and J. Darbon, Bregman Iterative algorithms for $l_1$-minimization with applications to compressed sensing,, SIAM Journal on Imaging Sciences, 1 (2008), 143.
doi: 10.1137/070703983. |
[32] |
Y. Zhu and I. Chern, Fast alternating minimization method for compressive sensing MRI under wavelet sparsity and TV sparsity,, in 2011 Sixth International Conference on Image and Graphics, (2011), 356.
doi: 10.1109/ICIG.2011.23. |
[33] |
Y. Zhu and I. Chern, Convergence of the alternating minimization method for sparse MR image reconstruction,, Journal of Information and Computational Science, 8 (2011), 2067. Google Scholar |
[34] |
Y. Zhu and Y. Shi, A fast method for reconstruction of total-variation MR images with a periodic boundary condition,, IEEE Signal Processing Letters, 20 (2013), 291.
doi: 10.1109/LSP.2013.2245502. |
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