# zbMATH — the first resource for mathematics

Compressed sensing MR image reconstruction exploiting TGV and wavelet sparsity. (English) Zbl 1423.92192
Summary: Compressed sensing (CS) based methods make it possible to reconstruct magnetic resonance (MR) images from undersampled measurements, which is known as CS-MRI. The reference-driven CS-MRI reconstruction schemes can further decrease the sampling ratio by exploiting the sparsity of the difference image between the target and the reference MR images in pixel domain. Unfortunately existing methods do not work well given that contrast changes are incorrectly estimated or motion compensation is inaccurate. In this paper, we propose to reconstruct MR images by utilizing the sparsity of the difference image between the target and the motion-compensated reference images in wavelet transform and gradient domains. The idea is attractive because it requires neither the estimation of the contrast changes nor multiple times motion compensations. In addition, we apply total generalized variation (TGV) regularization to eliminate the staircasing artifacts caused by conventional total variation (TV). Fast composite splitting algorithm (FCSA) is used to solve the proposed reconstruction problem in order to improve computational efficiency. Experimental results demonstrate that the proposed method can not only reduce the computational cost but also decrease sampling ratio or improve the reconstruction quality alternatively.

##### MSC:
 92C55 Biomedical imaging and signal processing 42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
Full Text:
##### References:
 [1] Donoho, D. L., Compressed sensing, IEEE Transactions on Information Theory, 52, 4, 1289-1306, (2006) · Zbl 1288.94016 [2] Donoho, D. L.; Huo, X., Uncertainty principles and ideal atomic decomposition, IEEE Transactions on Information Theory, 47, 7, 2845-2862, (2001) · Zbl 1019.94503 [3] Donoho, D. L.; Elad, M.; Temlyakov, V. N., Stable recovery of sparse overcomplete representations in the presence of noise, IEEE Transactions on Information Theory, 52, 1, 6-18, (2006) · Zbl 1288.94017 [4] Candès, E. J.; Tao, T., Decoding by linear programming, IEEE Transactions on Information Theory, 51, 12, 4203-4215, (2005) · Zbl 1264.94121 [5] Candès, E. J.; Romberg, J.; Tao, T., Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information, IEEE Transactions on Information Theory, 52, 2, 489-509, (2006) · Zbl 1231.94017 [6] Candès, E. J., The restricted isometry property and its implications for compressed sensing, Comptes Rendus Mathematique, 346, 9-10, 589-592, (2008) · Zbl 1153.94002 [7] Lustig, M.; Donoho, D.; Pauly, J. M., Sparse MRI: the application of compressed sensing for rapid MR imaging, Magnetic Resonance in Medicine, 5, 1182-1195, (2007) [8] Gamper, U.; Boesiger, P.; Kozerke, S., Compressed sensing in dynamic MRI, Magnetic Resonance in Medicine, 59, 2, 365-373, (2008) [9] Trzasko, J.; Manduca, A., Highly undersampled magnetic resonance image reconstruction via homotopic $$l_0$$-minimization, IEEE Transactions on Medical Imaging, 28, 1, 106-121, (2009) [10] Haldar, J. P.; Hernando, D.; Liang, Z.-P., Compressed-sensing MRI with random encoding, IEEE Transactions on Medical Imaging, 30, 4, 893-903, (2011) [11] Ji, J.; Lang, T., Dynamic MRI with compressed sensing imaging using temporal correlations, Proceedings of the 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro (ISBI ’08) [12] Majumdar, A.; Ward, R. K.; Aboulnasr, T., Compressed sensing based real-time dynamic MRI reconstruction, IEEE Transactions on Medical Imaging, 31, 12, 2253-2266, (2012) [13] Peng, X.; Du, H.-Q.; Lam, F.; Babacan, S. D.; Liang, Z.-P., Reference-driven MR image reconstruction with sparsity and support constraints, Proceedings of the 8th IEEE International Symposium on Biomedical Imaging: From Nano to Macro (ISBI ’11) [14] Liang, Z. P.; Lauterbur, P. C., An efficient method for dynamic magnetic resonance imaging, IEEE Transactions on Medical Imaging, 13, 4, 677-686, (1994) [15] Jung, H.; Sung, K.; Nayak, K. S.; Kim, E. Y.; Ye, J. C., K-t FOCUSS: a general compressed sensing framework for high resolution dynamic MRI, Magnetic Resonance in Medicine, 61, 1, 103-116, (2009) [16] Jung, H.; Park, J.; Yoo, J.; Ye, J. C., Radial k-t FOCUSS for high-resolution cardiac cine MRI, Magnetic Resonance in Medicine, 63, 1, 68-78, (2010) [17] Jung, H.; Ye, J. C., Motion estimated and compensated compressed sensing dynamic magnetic resonance imaging: what we can learn from video compression techniques, International Journal of Imaging Systems and Technology, 20, 2, 81-98, (2010) [18] Du, H. Q.; Lam, F., Compressed sensing MR image reconstruction using a motion-compensated reference, Magnetic Resonance Imaging, 30, 7, 954-963, (2012) [19] Lam, F.; Haldar, J. P.; Liang, Z.-P., Motion compensation for reference-constrained image reconstruction from limited data, Proceedings of the 8th IEEE International Symposium on Biomedical Imaging: From Nano to Macro (ISBI ’11) [20] Bredies, K.; Kunisch, K.; Pock, T., Total generalized variation, SIAM Journal on Imaging Sciences, 3, 3, 492-526, (2010) · Zbl 1195.49025 [21] Knoll, F.; Bredies, K.; Pock, T.; Stollberger, R., Second order total generalized variation (TGV) for MRI, Magnetic Resonance in Medicine, 65, 2, 480-491, (2011) [22] Guo, W.; Qin, J.; Yin, W., A new detail-preserving regularity scheme, 13-01, (2013), Rice CAAM [23] Huang, J.; Yang, F., Compressed magnetic resonance imaging based on wavelet sparsity and nonlocal total variation, Proceedings of the 9th IEEE International Symposium on Biomedical Imaging: From Nano to Macro (ISBI ’12) [24] Huang, J.; Zhang, S.; Metaxas, D., Efficient MR image reconstruction for compressed MR imaging, Medical Image Analysis, 15, 5, 670-679, (2011) [25] Lam, F., Motion compensation from limited data for reference constrained image reconstruction [M.S. thesis], (2011), Urbana, Ill, USA: University of Illinois, Urbana, Ill, USA [26] Maintz, J. B. A.; Viergever, M. A., A survey of medical image registration, Medical Image Analysis, 2, 1, 1-36, (1998) [27] Hajnal, J. V.; Hill, D. L.; Hawkes, D. J., Medical Image Registration. Medical Image Registration, Biomedical Engineering Series, (2001), Boca Raton, Fla, USA: CRC Press, Boca Raton, Fla, USA [28] Chambolle, A.; Pock, T., A first-order primal-dua l algorithm for convex problems with applications to imaging, (2010), Graz, Austria: Institute for Computer Graphics and Vision, Graz University of Technology, Graz, Austria
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.