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In this survey, we provide a detailed review of recent advances in the recovery of continuous domain multidimensional signals from their few non-uniform (multichannel) measurements using structured low-rank matrix completion formulation.
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1989
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1995
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I. Dologlou, D. van Ormondt, and G. Carayannis, “MRI scan time reduction through non-uniform sampling and SVD-based estimation,” Signal Processing , vol. 55, no. 2, pp. 207–219, 1996
1996
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B. Scholkopf and A. J. Smola, Learning with kernels: support vector machines, regularization, optimization, and beyond . MIT press, 2001
2001
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M. Vetterli, P. Marziliano, and T. Blu, “Sampling signals with finite rate of innovation,” IEEE Transactions on Signal Processing , vol. 50, no. 6, pp. 1417–1428, 2002
2002
Earlier work this paper cites.
M. A. Griswold, P. M. Jakob, R. M. Heidemann, M. Nittka, V. Jellus, J. Wang, B. Kiefer, and A. Haase, “Generalized autocalibrating partially parallel acquisitions (GRAPPA),” Magn. Reson. Med , vol. 47, no. 6, pp. 1202–1210, 2002
2002
Earlier work this paper cites.
N. Srebro, “Learning with matrix factorizations,” Ph.D. dissertation, Dept. of Elect. Eng., Comput. Sci., Massachusetts Inst. of Technol., Cambridge, MA, USA , 2004
2004
Earlier work this paper cites.
E. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. on Information Theory , vol. 52, no. 2, pp. 489–509, Feb. 2006
2006
Earlier work this paper cites.
R. Morrisson, M. Jacob, and M. Do, “Multichannel estimation of coil sensitivities in parallel MRI,” IEEE International Symposium on Biomedical Imaging , 2007
2007
Earlier work this paper cites.
H. Nguyen, B. Sutton, R. Morrison, and M. Do, “Joint estimation and correction of geometric distortions for EPI functional MRI using harmonic retrieval,” IEEE Trans Med Imaging. , vol. 28, pp. 423–34, 2009
2009
Earlier work this paper cites.
J. Zhang, C. Liu, and M. E. Moseley, “Parallel reconstruction using null operations (pruno),” Magnetic Resonance in Medicine , vol. 66, no. 5, 2011
2011
Earlier work this paper cites.
K. Mohan and M. Fazel, “Iterative reweighted algorithms for matrix rank minimization,” Journal of Machine Learning Research , vol. 13, no. Nov, pp. 3441–3473, 2012
2012
Earlier work this paper cites.
P. J. Shin, P. E. Larson, M. A. Ohliger, M. Elad, J. M. Pauly, D. B. Vigneron, and M. Lustig, “Calibrationless parallel imaging reconstruction based on structured low-rank matrix completion,” Magnetic Resonance in Medicine , vol. 72, no. 4, pp. 959–970, 2014
2014
Cited alongside, same era.
M. Uecker, P. Lai, M. J. Murphy, P. Virtue, M. Elad, J. M. Pauly, S. Vasanawala, and M. Lustig, “ESPIRIT - an eigenvalue approach to autocalibrating parallel MRI: where sense meets grappa,” Magn. Reson. Med , vol. 71, no. 3, pp. 990–1001, 2014
2014
Cited alongside, same era.
J. P. Haldar, “Low-Rank Modeling of Local-Space Neighborhoods (LORAKS) for Constrained MRI,” IEEE Trans. on Medical Imaging , vol. 33, no. 3, pp. 668–681, 2014
2014
Cited alongside, same era.
E. Candes and C. Granda, “Towards a mathematical theory of super‐resolution,” Pure and Applied Mathematics , vol. 67, no. 6, pp. 906–956, 2014
2014
Cited alongside, same era.
K. H. Jin, J.-Y. Um, D. Lee, J. Lee, S.-H. Park, and J. C. Ye, “MRI artifact correction using sparse+ low-rank decomposition of annihilating filter-based Hankel matrix,” Magnetic Resonance in Medicine , vol. 78, no. 1, pp. 327–340, 2017
2017
Later among the works it cites.
M. Mani, M. Jacob, D. Kelley, and V. Magnotta, “Multi-shot sensitivity-encoded diffusion data recovery using structured low-rank matrix completion (MUSSELS),” Magnetic Resonance in Medicine , vol. 78, no. 2, pp. 494–507, 2017
2017
Later among the works it cites.
D. Guo, H. Lu, and X. Qu, “A fast low rank hankel matrix factorization reconstruction method for non-uniformly sampled magnetic resonance spectroscopy,” IEEE Access , vol. 5, pp. 16 033 – 16 039, 2017
2017
Later among the works it cites.
M. Bydder, S. Rapacchi, O. G. O, M. Guye, and J. P. Ranjeva, “Trimmed autocalibrating k-space estimation based on structured matrix completion.” Magnetic Resonance Imaging , vol. 43, no. 88, pp. 88–94, 2017
2017
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H. Pan, T. Blu, and P. L. Dragotti, “Sampling curves with finite rate of innovation,” IEEE Transactions on Signal Processing , vol. 62, no. 2, pp. 458–471, 2014
2014
Cited alongside, same era.
X. Qu, M. Mayzel, J.-F. Cai, Z. Chen, and V. Orekhov, “Accelerated NMR spectroscopy with low-rank reconstruction,” Angewandte Chemie International Edition , vol. 54, no. 3, pp. 852–854, 2015
2015
Cited alongside, same era.
K. H. Jin, D. Lee, and J. C. Ye, “A general framework for compressed sensing and parallel MRI using annihilating filter based low-rank Hankel matrix,” IEEE Transactions on Computational Imaging , vol. 2, no. 4, pp. 480–495, 2016
2016
Cited alongside, same era.
G. Ongie and M. Jacob, “Off-the-grid recovery of piecewise constant images from few Fourier samples,” SIAM Journal on Imaging Sciences , vol. 9, no. 3, pp. 1004–1041, 2016
2016
Cited alongside, same era.
P. Cao, P. J. Shin, I. Park, C. Najac, I. Marco-Rius, D. B. Vigneron, S. J. Nelson, . Sabrina M. Ronen, and P. E. Z. Larson, “Accelerated high bandwidth MR spectroscopic imaging using compressed sensing,” Magnetic Resonance in Medicine , vol. 76, no. 2, pp. 369–379, 2016
2016
Cited alongside, same era.
X. Peng, L. Ying, Y. Liu, J. Yuan, X. Liu, and D. Liang, “Accelerated exponential parameterization of T2 relaxation with model-driven low rank and sparsity priors,” Magnetic Resonance in Medicine , vol. 76, no. 6, pp. 1865–78, 2016
2016
Cited alongside, same era.
J. P. Haldar and J. Zhuo, “P-LORAKS: Low-rank modeling of local k-space neighborhoods with parallel imaging data,” Magnetic resonance in medicine , vol. 75, no. 4, pp. 1499–1514, 2016
2016
Cited alongside, same era.
J. C. Ye, J. M. Kim, K. H. Jin, and K. Lee, “Compressive sampling using annihilating filter-based low-rank interpolation,” IEEE Transactions on Information Theory , vol. 63, no. 2, pp. 777–801, Feb. 2017
2017
Cited alongside, same era.
Later among the works it cites.
G. Ongie, S. Biswas, and M. Jacob, “Convex recovery of continuous domain piecewise constant images from nonuniform Fourier samples,” IEEE Transactions on Signal Processing , vol. 66, no. 1, pp. 236–250, 2018
2018
Later among the works it cites.
B. Bilgic, T. H. Kim, C. Liao, M. K. Manhard, L. L. Wald, J. P. Haldar, and K. Setsompop, “Improving parallel imaging by jointly reconstructing multi-contrast data,” Magnetic Resonance in Medicine , vol. 80, pp. 619–632, 2018
2018
Later among the works it cites.
Y. Hu, X. Liu, and M. Jacob, “A generalized structured low-rank matrix completion algorithm for MR image recovery,” IEEE Transactions On Medical Imaging , 2018
2018
Later among the works it cites.
S. Poddar, Y. Mohsin, D. Ansah, B. Thattaliyath, R. Ashwath, and M. Jacob, “Free-breathing cardiac MRI using bandlimited manifold modelling,” IEEE Trans. on Computational Imaging , vol. 35, no. 4, pp. 1106–1115, 2018
2018
Later among the works it cites.
J. Ye, Y. Han, and E. Cha, “Deep convolutional framelets: A general deep learning framework for inverse problems,” SIAM Journal on Imaging Sciences , vol. 11, no. 2, pp. 991–1048, 2018
2018
Later among the works it cites.
J. C. Ye and W. K. Sung, “Understanding geometry of encoder-decoder CNNs,” in Proceedings of the 36th International Conference on Machine Learning , ser. Proceedings of Machine Learning Research, K. Chaudhuri and R. Salakhutdinov, Eds., vol. 97. Long Beach, California, USA: PMLR, 09–15 Jun 2019, pp. 7064–7073
2019
Closest in time.
W. Jiang, P. E. Z. Larson, and M. Lustig, “Simultaneous auto-calibration and gradient delays estimation (SAGE) in non-Cartesian parallel MRI using low-rank constraints,” Magnetic Resonance in Medicine , vol. 80, pp. 2006–2016, 2019
2019
Closest in time.
M. Doneva, “An overview of mathematical models for computational MRI,” IEEE Signal Processing Magazine , 2020
2020
Closest in time.
J. P. Haldar and K. Setsompop, “Linear predictability in MRI reconstruction: Leveraging shift-invariant Fourier structure for faster and better imaging,” IEEE Signal Processing Magazine, Special Issue on Computational MRI (this issue) , 2020
2020
Closest in time.