Magnetic resonance image reconstruction based on nonlocal augmented Lagrangian multiplier method

LI Chao; DU Hongwei; QIU Bensheng

doi:10.3969/j.issn.0253-2778.2017.08.006

JUSTC > 2017 > 47(8): 674-678. > DOI: 10.3969/j.issn.0253-2778.2017.08.006

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Magnetic resonance image reconstruction based on nonlocal augmented Lagrangian multiplier method

Department of Electronic Science and Technology, University of Science and Technology of China, Hefei 230027, China

Cite this: JUSTC, 2017, 47(8): 674-678

https://doi.org/10.3969/j.issn.0253-2778.2017.08.006

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Received Date: April 11, 2016
Revised Date: May 23, 2016
Published Date: August 30, 2017

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Abstract

Abstract

Total variation (TV) is unable to recover the fine details and textures of magnetic resonance(MR) images since it often suffers from staircase artifact. To reduce these drawbacks, an improved TV MR image recovery algorithm is introduced by using nonlocal regularization into the CS optimization problem. The nonlocal regularization is built on nonlocal means (NLM) filtering and takes advantage of self-similarity in images, which helps to suppress the staircase effect and restore the fine details. On account of the complexity in implementing NLM filter, a modified MR imaging method called nonlocal Lagrange multiplier (MRNLM) is proposed to overcome the above shortcomings while boosting MR image quality. Experimental results demonstrate that the proposed algorithm shows significant improvements on the state-of-the-art TV based algorithms in both SNR and visual perception, as well as a fair balance between time and quality.

Abstract

Total variation (TV) is unable to recover the fine details and textures of magnetic resonance(MR) images since it often suffers from staircase artifact. To reduce these drawbacks, an improved TV MR image recovery algorithm is introduced by using nonlocal regularization into the CS optimization problem. The nonlocal regularization is built on nonlocal means (NLM) filtering and takes advantage of self-similarity in images, which helps to suppress the staircase effect and restore the fine details. On account of the complexity in implementing NLM filter, a modified MR imaging method called nonlocal Lagrange multiplier (MRNLM) is proposed to overcome the above shortcomings while boosting MR image quality. Experimental results demonstrate that the proposed algorithm shows significant improvements on the state-of-the-art TV based algorithms in both SNR and visual perception, as well as a fair balance between time and quality.

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References

[1]	FENG L, SRICHAI M B, LIM R P, et al. Highly accelerated real-time cardiac cine MRI using k-t SPARSE-SENSE[J]. Magnetic Resonance in Medicine, 2013, 70(1): 64-74.
[2]	UECKER M, LAI P, MURPHY M J, et al. ESPIRiT—an eigenvalue approach to autocalibrating parallel MRI: Where SENSE meets GRAPPA[J]. Magnetic Resonance in Medicine, 2014, 71(3): 990-1001.
[3]	DONOHO D. Compressed sensing[J]. IEEE Transactions on Information Theory, 2006, 52(4): 1289-1306.
[4]	CANDS E. J, ROMBERG J, TAO T. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information[J]. IEEE Transactions on Information Theory, 2006, 52(2): 489-509.
[5]	LUSTIG M, DONOHO D, PAULY J M. Sparse MRI: The application of compressed sensing for rapid MR imaging[J]. Magnetic Resonance in Medicine, 2007, 58(6): 1182-1195.
[6]	GUO W H, YIN W T. Edge guided reconstruction for compressive imaging[J]. SIAM Journal on Imaging Sciences, 2012, 5(3): 809-834.
[7]	ZHU Y G, SHI Y Y. A fast method for reconstruction of total-variation MR images with a periodic boundary condition[J]. IEEE Signal Processing Letters, 2013, 20(4): 291-294.
[8]	LI C B, YIN W T, JIANG H, et al. An efficient augmented Lagrangian method with applications to total variation minimization[J]. Computational Optimization and Applications, 2013, 56(3): 507-530.
[9]	NEEDELL D, WARD R. Stable image reconstruction using total variation minimization[J]. SIAM Journal on Imaging Sciences, 2013, 6(2): 1035-1058.
[10]	BUADES A, COLL B, MOREL J M. Image enhancement by non-local reverse heat equation[R].CMLA, 2006.
[11]	MANJN J V, COUP P, BUADES A, et al. New methods for MRI denoising based on sparseness and self-similarity[J]. Medical Image Analysis, 2012, 16(1): 18-27.
[12]	JAFARI-KHOUZANI K. MRI upsampling using feature-based nonlocal means approach[J]. IEEE Transactions on Medical Imaging, 2014, 33(10): 1969-1985.
[13]	ZHANG J, LIU S H, XIONG R Q, et al. Improved total variation based image compressive sensing recovery by nonlocal regularization[C]// IEEE International Symposium on Circuits and Systems. Beijing: IEEE Press, 2013: 2836-2839.
[14]	VAN TRINH C, DINH K Q, NGUYEN V A, et al. Total variation reconstruction for compressive sensing using nonlocal Lagrangian multiplier[C]// Proceedings of the 22nd European Signal Processing Conference. Lisbon, Portugal: IEEE Press, 2014: 231-235.

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References

[1]	FENG L, SRICHAI M B, LIM R P, et al. Highly accelerated real-time cardiac cine MRI using k-t SPARSE-SENSE[J]. Magnetic Resonance in Medicine, 2013, 70(1): 64-74.
[2]	UECKER M, LAI P, MURPHY M J, et al. ESPIRiT—an eigenvalue approach to autocalibrating parallel MRI: Where SENSE meets GRAPPA[J]. Magnetic Resonance in Medicine, 2014, 71(3): 990-1001.
[3]	DONOHO D. Compressed sensing[J]. IEEE Transactions on Information Theory, 2006, 52(4): 1289-1306.
[4]	CANDS E. J, ROMBERG J, TAO T. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information[J]. IEEE Transactions on Information Theory, 2006, 52(2): 489-509.
[5]	LUSTIG M, DONOHO D, PAULY J M. Sparse MRI: The application of compressed sensing for rapid MR imaging[J]. Magnetic Resonance in Medicine, 2007, 58(6): 1182-1195.
[6]	GUO W H, YIN W T. Edge guided reconstruction for compressive imaging[J]. SIAM Journal on Imaging Sciences, 2012, 5(3): 809-834.
[7]	ZHU Y G, SHI Y Y. A fast method for reconstruction of total-variation MR images with a periodic boundary condition[J]. IEEE Signal Processing Letters, 2013, 20(4): 291-294.
[8]	LI C B, YIN W T, JIANG H, et al. An efficient augmented Lagrangian method with applications to total variation minimization[J]. Computational Optimization and Applications, 2013, 56(3): 507-530.
[9]	NEEDELL D, WARD R. Stable image reconstruction using total variation minimization[J]. SIAM Journal on Imaging Sciences, 2013, 6(2): 1035-1058.
[10]	BUADES A, COLL B, MOREL J M. Image enhancement by non-local reverse heat equation[R].CMLA, 2006.
[11]	MANJN J V, COUP P, BUADES A, et al. New methods for MRI denoising based on sparseness and self-similarity[J]. Medical Image Analysis, 2012, 16(1): 18-27.
[12]	JAFARI-KHOUZANI K. MRI upsampling using feature-based nonlocal means approach[J]. IEEE Transactions on Medical Imaging, 2014, 33(10): 1969-1985.
[13]	ZHANG J, LIU S H, XIONG R Q, et al. Improved total variation based image compressive sensing recovery by nonlocal regularization[C]// IEEE International Symposium on Circuits and Systems. Beijing: IEEE Press, 2013: 2836-2839.
[14]	VAN TRINH C, DINH K Q, NGUYEN V A, et al. Total variation reconstruction for compressive sensing using nonlocal Lagrangian multiplier[C]// Proceedings of the 22nd European Signal Processing Conference. Lisbon, Portugal: IEEE Press, 2014: 231-235.

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