# Low-rank and Sparse Matrix Decomposition with a-priori Knowledge for Dynamic 3D MRI Reconstruction

### Dornoosh Zonoobi, Shahrooz Faghigh roohi, Ashraf. A. Kassim

#### Abstract

It has been recently shown that incorporating priori knowledge significantly improves the performance of basic compressive sensing based approaches. We have managed to successfully exploit this idea for recovering a matrix as a summation of a Low-rank and a Sparse component from compressive measurements. When applied to the problem of construction of 4D Cardiac MR image sequences in real-time from highly under-sampled k-space data, our proposed method achieves superior reconstruction quality compared to the other state-of-the-art methods.

#### References

- Beck, A. and Teboulle, M. (2009). A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM Journal on Imaging Sciences, 2(1):183-202.
- Cai, J.-F., Candès, E. J., and Shen, Z. (2010). A singular value thresholding algorithm for matrix completion. SIAM Journal on Optimization, 20(4):1956-1982.
- Candes, E., Li, X., Ma, Y., and Wright., J. (2009). Robust principal component analysis? Journals of the ACM, 58(3):1-37.
- Ensafi, S., Lu, S., Kassim, A. A., and Tan, C. L. (2014). 3d reconstruction of neurons in electron microscopy images. In Engineering in Medicine and Biology Society (EMBC), 2014 36th Annual International Conference of the IEEE, pages 6732-6735.
- Feng, L., Srichai, M. B., Lim, R. P., Harrison, A., King, W., Adluru, G., Dibella, E. V., Sodickson, D. K., Otazo, R., and Kim, D. (2012). Highly accelerated real-time cardiac cine MRI using k-t SPARSE-SENSE. Magnetic Resonance in Medicine.
- Gamper, U., Boesiger, P., and Kozerkey, S. (2008). Compressed sensing in dynamic MRI. Magnetic Resonance in Medicine, 59(2):365-373.
- Gao, H., Rapacchi, S., Wang, D., Moriarty, J., Meehan, C., Sayre, J., Laub, G., Finn, P., and Hu, P. (2012). Compressed sensing using prior rank, intensity and sparsity model (prism): applications in cardiac cine MRI. In Proceedings of the 20th Annual Meeting of ISMRM, Melbourne, Australia.
- Goud, S., Hu, Y., and Jacob, M. (2010). Real-time cardiac MRI using low-rank and sparsity penalties. In Biomedical Imaging: From Nano to Macro, 2010 IEEE International Symposium on, pages 988-991. IEEE.
- Haldar, J. P. and Liang, Z.-P. (2011). Low-rank approximations for dynamic imaging. In Biomedical Imaging: From Nano to Macro, 2011 IEEE International Symposium on, pages 1052-1055.
- Hu, Y., Lingala, S. G., and Jacob, M. (2012). A fast majorize-minimize algorithm for the recovery of sparse and low-rank matrices. Image Processing, IEEE Transactions on, 21(2):742-753.
- Jung, H., Sung, K., Nayak, K. S., Kim, E. Y., and Ye, J. C. (2009). k-t FOCUSS: A general compressed sensing framework for high resolution dynamic MRI. Magnetic Resonance in Medicine, 61(1):103-116.
- Kassim, A. A., Yan, N., and Zonoobi, D. (2008). Wavelet packet transform basis selection method for set partitioning in hierarchical trees. Journal of Electronic Imaging, 17(3):033007.
- Lingala, S. G., Hu, Y., DiBella, E., and Jacob, M. (2011). Accelerated dynamic MRI exploiting sparsity and low-rank structure: kt slr. Medical Imaging, IEEE Transactions on, 30(5):1042-1054.
- Lustig, M., Donoho, D. L., Santos, J. M., and Pauly, J. M. (2008). Compressed sensing MRI: A look at how CS can improve on current imaging techniques. IEEE Signal Processing Magazine, 25(2):72-82.
- Majumdar, A. and Ward, R. K. (2012a). Causal dynamic MRI reconstruction via nuclear norm minimization. Magnetic Resonance Imaging, 30:1483-1494.
- Majumdar, A. and Ward, R. K. (2012b). Exploiting rank deficiency and transform domain sparsity for MR image reconstruction. Magnetic resonance imaging, 30(1):9-18.
- Needell, D. and Tropp, J. (2009). Cosamp: Iterative signal recovery from incomplete and inaccurate samples. Applied and Computational Harmonic Analysis, 26(3):301 - 321.
- Otazo, R., Sodickson, D. K., and Candès, E. J. (2013). Low-rank+ sparse (l+ s) reconstruction for accelerated dynamic MRI with seperation of background and dynamic components. In SPIE Optical Engineering+ Applications, pages 88581Z-88581Z. International Society for Optics and Photonics.
- Vaswani, N. and Lu, W. (2010a). Modified-CS: Modifying compressive sensing for problems with partially known support. IEEE Transactions on Signal Processing, 58(9):4595 -4607.
- Vaswani, N. and Lu, W. (2010b). Modified-cs: Modifying compressive sensing for problems with partially known support. IEEE Transactions on Signal Processing, 58(9):4595 -4607.
- Venkatesh, Y. V., Kassim, A. A., and Zonoobi, D. (2010). Medical image reconstruction from sparse samples using simultaneous perturbation stochastic optimization. In Proc. of the ICIP Conference, Hong Kong, pages 3369-3372.
- Zhao, B., Haldar, J. P., Brinegar, C., and Liang, Z.-P. (2010). Low rank matrix recovery for real-time cardiac MRI. In Biomedical Imaging: From Nano to Macro, 2010 IEEE International Symposium on, pages 996-999.
- Zonoobi, D., Kassim, A., and Venkatesh, Y. (2011). Gini index as sparsity measure for signal reconstruction from compressive samples. IEEE Journal of Selected Topics in Signal Processing, 5(5):927 -932.
- Zonoobi, D. and Kassim, A. A. (2012). Weighted-CS for reconstruction of highly under-sampled dynamic MRI sequences. In Signal & Information Processing Association Annual Summit and Conference (APSIPA ASC), 2012 Asia-Pacific, pages 1-5.
- Zonoobi, D. and Kassim, A. A. (2013). On the reconstruction of sequences of sparse signals - The WeightedCS. Journal of Visual Communication and Image Representation, 24(2):196 - 202.
- Zonoobi, D. and Kassim, A. A. (2014a). A computationally efficient method for reconstructing sequences of MR images from undersampled k-space data. Medical image analysis, 18(6):857-865.
- Zonoobi, D. and Kassim, A. A. (2014b). On ecg reconstruction using weighted-compressive sensing. Healthcare Technology Letters, 1(2):68-73.
- Zonoobi, D., Roohi, S. F., and Kassim, A. A. (2014). Dependent nonparametric Bayesian group dictionary learning for online reconstruction of dynamic MR images. arXiv preprint arXiv:1408.5667.

#### Paper Citation

#### in Harvard Style

Zonoobi D., Faghigh roohi S. and Kassim A. (2015). **Low-rank and Sparse Matrix Decomposition with a-priori Knowledge for Dynamic 3D MRI Reconstruction** . In *Proceedings of the International Conference on Bioimaging - Volume 1: BIOIMAGING, (BIOSTEC 2015)* ISBN 978-989-758-072-7, pages 82-88. DOI: 10.5220/0005228800820088

#### in Bibtex Style

@conference{bioimaging15,

author={Dornoosh Zonoobi and Shahrooz Faghigh roohi and Ashraf. A. Kassim},

title={Low-rank and Sparse Matrix Decomposition with a-priori Knowledge for Dynamic 3D MRI Reconstruction},

booktitle={Proceedings of the International Conference on Bioimaging - Volume 1: BIOIMAGING, (BIOSTEC 2015)},

year={2015},

pages={82-88},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005228800820088},

isbn={978-989-758-072-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Bioimaging - Volume 1: BIOIMAGING, (BIOSTEC 2015)

TI - Low-rank and Sparse Matrix Decomposition with a-priori Knowledge for Dynamic 3D MRI Reconstruction

SN - 978-989-758-072-7

AU - Zonoobi D.

AU - Faghigh roohi S.

AU - Kassim A.

PY - 2015

SP - 82

EP - 88

DO - 10.5220/0005228800820088