Gradient-Based Low Rank Method for Highly Undersampled Magnetic Resonance Imaging Reconstruction

doi:10.1007/s12204-018-1927-8

sa ›› 2018, Vol. 23 ›› Issue (3): 384-.doi: 10.1007/s12204-018-1927-8

Gradient-Based Low Rank Method for Highly Undersampled Magnetic Resonance Imaging Reconstruction

XU Xiaoling (徐晓玲), LIU Yiling (刘沂玲), LIU Qiegen (刘且根),LU Hongyang (卢红阳), ZHANG Minghui (张明辉)

(Department of Electronic Information Engineering, Nanchang University, Nanchang 330031, China)

出版日期:2018-05-31 发布日期:2018-06-17
通讯作者: ZHANG Minghui (张明辉) E-mail: zhangminghui@ncu.edu.cn

Gradient-Based Low Rank Method for Highly Undersampled Magnetic Resonance Imaging Reconstruction

XU Xiaoling (徐晓玲), LIU Yiling (刘沂玲), LIU Qiegen (刘且根),LU Hongyang (卢红阳), ZHANG Minghui (张明辉)

(Department of Electronic Information Engineering, Nanchang University, Nanchang 330031, China)

Online:2018-05-31 Published:2018-06-17
Contact: ZHANG Minghui (张明辉) E-mail: zhangminghui@ncu.edu.cn

摘要/Abstract

摘要： Recently, exploiting low rank property of the data accomplished by the non-convex optimization has shown great potential to decrease measurements for compressed sensing. In this paper, the low rank regularization is adopted to gradient similarity minimization, and applied for highly undersampled magnetic resonance imaging (MRI) reconstruction, termed gradient-based low rank MRI reconstruction (GLRMRI). In the proposed method, by incorporating the spatially adaptive iterative singular-value thresholding (SAIST) to optimize our gradient scheme, the deterministic annealing iterates the procedure e±ciently and superior reconstruction performance is achieved. Extensive experimental results have consistently demonstrated that GLRMRI recovers both real- valued MR images and complex-valued MR data accurately, especially in the edge preserving perspective, and outperforms the current state-of-the-art approaches in terms of higher peak signal to noise ratio (PSNR) and lower high-frequency error norm (HFEN) values.

关键词: magnetic resonance imaging (MRI), low rank, image gradients, sparse representation, deterministic annealing

Abstract: Recently, exploiting low rank property of the data accomplished by the non-convex optimization has shown great potential to decrease measurements for compressed sensing. In this paper, the low rank regularization is adopted to gradient similarity minimization, and applied for highly undersampled magnetic resonance imaging (MRI) reconstruction, termed gradient-based low rank MRI reconstruction (GLRMRI). In the proposed method, by incorporating the spatially adaptive iterative singular-value thresholding (SAIST) to optimize our gradient scheme, the deterministic annealing iterates the procedure e±ciently and superior reconstruction performance is achieved. Extensive experimental results have consistently demonstrated that GLRMRI recovers both real- valued MR images and complex-valued MR data accurately, especially in the edge preserving perspective, and outperforms the current state-of-the-art approaches in terms of higher peak signal to noise ratio (PSNR) and lower high-frequency error norm (HFEN) values.

Key words: magnetic resonance imaging (MRI), low rank, image gradients, sparse representation, deterministic annealing

中图分类号:

TN 911.73

XU Xiaoling (徐晓玲), LIU Yiling (刘沂玲), LIU Qiegen (刘且根),LU Hongyang (卢红阳), ZHANG M. Gradient-Based Low Rank Method for Highly Undersampled Magnetic Resonance Imaging Reconstruction[J]. sa, 2018, 23(3): 384-.

XU Xiaoling (徐晓玲), LIU Yiling (刘沂玲), LIU Qiegen (刘且根),LU Hongyang (卢红阳), ZHANG Minghui (张明辉). Gradient-Based Low Rank Method for Highly Undersampled Magnetic Resonance Imaging Reconstruction[J]. Journal of Shanghai Jiao Tong University (Science), 2018, 23(3): 384-.

参考文献 21

[1]	LUSTIG M, DONOHO D, PAULY J M. Sparse MRI:The application of compressed sensing for rapid MRimaging [J]. Magnetic Resonance in Medicine, 2007,58: 1182-1195.
[2]	HALDAR J P, HERNANDO D, LIANG Z P.Compressed-sensing MRI with random encoding [J].IEEE Transactions on Medical Imaging, 2011, 30(4):893-903.
[3]	SMITH D S, WELCH E B. Non-sparse phan-tom for compressed sensing MRI reconstruction[C]//International Society for Magnetic Resonance inMedicine 19th Scientiˉc Meeting. [s.l.]: ISMEM, 2011:2845.
[4]	BILGIN A, KIM Y, LIU F, et al. Dictionary design forcompressed sensing MRI [C]//Proceedings of the 18thScientiˉc Meeting of ISMRM. Stockholm: ISMRM,2010: 4887.
[5]	RAVISHANKAR S, BRESLER Y. MR image recon-struction from highly undersampled k-space data bydictionary learning [J]. IEEE Transactions on MedicalImaging, 2011, 30: 1028-1041.
[6]	LIU Q, WANG S, YANG K, et al. Highly under-sampled magnetic resonance image reconstruction us-ing two-level Bregman method with dictionary updat-ing [J]. IEEE Transactions on Medical Imaging, 2013,32(7): 1290-1301.
[7]	MAIRAL J, BACH F, PONCE J, et al. Non-localsparse models for image restoration [C]//2009 IEEE12th International Conference on Computer Vision.[s.l.]: IEEE, 2009: 2272-2279.
[8]	BADRI H, YAHIA H. A non-local lowrank approach toenforce integrability [J]. IEEE Transactions on ImageProcessing, 2016, 25(8): 3562-3571.
[9]	REN W, CAO X, PAN J, et al. Image deblurring viaenhanced low-rank prior [J]. IEEE Transactions onImage Processing, 2016, 25(7): 3426-3437.
[10]	DONG W, SHI G, LI X. Nonlocal image restorationwith bilateral variance estimation: A low-rank ap-proach [J]. IEEE Transactions on Image Processing,2013, 22(2): 700-711.
[11]	PATEL V M, MALEH R, GILBERT A, et al.Gradient-based image recovery methods from incom-plete fourier measurements [J]. IEEE Transactions onImage Processing, 2012, 21(1): 94-105.
[12]	YANG J, ZHANG Y, YIN W. A fast alternating direc-tion method for TVL1-L2 signal reconstruction frompartial Fourier data [J]. IEEE Journal of Selected Top-ics in Signal Processing, 2010, 4(2): 288{297.
[13]	LIU Q, WANG S, YING L, et al. Adaptive dictionarylearning in sparse gradient domain for image recov-ery [J]. IEEE Transactions on Image Processing, 2013,22(12): 4652-4663.
[14]	HU Z, LIU Q, PENG X, et al. Image reconstructionfrom few-view CT data by gradient-domain dictionarylearning [J]. Journal of X-Ray Science and Technology,2016, 24(4): 627-638.
[15]	LUO X, SUO Z, LIU Q, et al. E±cient InSAR phasenoise ˉltering based on adaptive dictionary learning ingradient vector domain [J]. Journal of Xidian Univer-sity, 2016, 43(1): 18-23 (in Chinese).
[16]	CAI J F, CANDES E J, SHEN Z. A singular valuethresholding algorithm for matrix completion [J].SIAM Journal on Optimization, 2010, 20(4): 1956-1982.
[17]	ARIAS P, CASEL V, SAPIRO G. A variational frame-work for non-local image inpainting [C]//InternationalWorkshop on Energy Minimization Methods inComputer Vision and Pattern Recognition. Berlin:Springer, 2009: 345-358.
[18]	ARIAS P, FACCIOLO G, CASELLES V, et al.A variational framework for exemplar-based imageinpainting [J]. International Journal of ComputerVision, 2011, 93(3): 319-347.
[19]	P'EREZ P, GANGNET M, BLAKE A. Poisson imageediting [J]. InACM Transactions on Graphics (TOG),2003, 22(3): 313-318.
[20]	HORE A, ZIOU D. Image quality metrics: PSNRvs. SSIM [C]//International Conference on PatternRecognition. [s.l.]: IEEE, 2010: 2366-2369.
[21]	SHAH M A. Distributed continuous media streaming-Using redundant hierarchy (RED-Hi) servers [D]. Fam-agusta: Eastern Mediterranean University (EMU),2014.

Gradient-Based Low Rank Method for Highly Undersampled Magnetic Resonance Imaging Reconstruction

Gradient-Based Low Rank Method for Highly Undersampled Magnetic Resonance Imaging Reconstruction

可视化

摘要/Abstract

引用本文

使用本文

参考文献 21

相关文章 3

编辑推荐

Metrics

本文评价

[1]	HUANG Ningning (黄宁宁), MA Yixin (马艺馨), ZHANG Mingzhu (张明珠), GE Hao (葛浩), WU Huawei (吴华伟). Finite Element Modeling of Human Thorax Based on MRI Images for EIT Image Reconstruction[J]. J Shanghai Jiaotong Univ Sci, 2021, 26(1): 33-39.
[2]	L ¨U Wentao1* (吕文涛), WANG Junfeng2 (王军锋), YU Wenxian2 (郁文贤), BAO Xiaomin1 (包晓敏). Range Profile Target Recognition Using Sparse Representation Based on Feature Space[J]. 上海交通大学学报（英文版）, 2017, 22(5): 615-623.
[3]	ZHU Meng-yuan (朱梦媛), SHEN Guo-feng* (沈国峰), SU Zhi-qiang (苏志强),CHEN Sheng (陈晟), W. Real-Time MRI-Controlled Ultrasound Hyperthermia System for Superficial Tumor Treatment[J]. 上海交通大学学报（英文版）, 2014, 19(6): 715-717.