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Sensors 2017, 17(3), 509; doi:10.3390/s17030509

Reconstruction of Undersampled Big Dynamic MRI Data Using Non-Convex Low-Rank and Sparsity Constraints

1
Department of Imaging and Interventional Radiology, The Chinese University of Hong Kong, Shatin 999077, N.T., Hong Kong, China
2
Department of Medicine and Therapeutics, The Chinese University of Hong Kong, Shatin 999077, N.T., Hong Kong, China
3
Chow Yuk Ho Technology Center for Innovative Medicine, The Chinese University of Hong Kong, Shatin 999077, N.T., Hong Kong, China
4
Department of Mathematics and Computer Science, Northeastern State University, Tahlequah, OK 74464, USA
5
Research Center for Medical Image Computing, The Chinese University of Hong Kong, Shatin 999077, N.T., Hong Kong, China
6
Shenzhen Research Institute, The Chinese University of Hong Kong, Shenzhen 518057, China
*
Authors to whom correspondence should be addressed.
Academic Editors: M. Shamim Hossain and Athanasios V. Vasilakos
Received: 10 November 2016 / Revised: 16 February 2017 / Accepted: 20 February 2017 / Published: 3 March 2017
(This article belongs to the Special Issue Multisensory Big Data Analytics for Enhanced Living Environments)
View Full-Text   |   Download PDF [10171 KB, uploaded 8 March 2017]   |  

Abstract

Dynamic magnetic resonance imaging (MRI) has been extensively utilized for enhancing medical living environment visualization, however, in clinical practice it often suffers from long data acquisition times. Dynamic imaging essentially reconstructs the visual image from raw (k,t)-space measurements, commonly referred to as big data. The purpose of this work is to accelerate big medical data acquisition in dynamic MRI by developing a non-convex minimization framework. In particular, to overcome the inherent speed limitation, both non-convex low-rank and sparsity constraints were combined to accelerate the dynamic imaging. However, the non-convex constraints make the dynamic reconstruction problem difficult to directly solve through the commonly-used numerical methods. To guarantee solution efficiency and stability, a numerical algorithm based on Alternating Direction Method of Multipliers (ADMM) is proposed to solve the resulting non-convex optimization problem. ADMM decomposes the original complex optimization problem into several simple sub-problems. Each sub-problem has a closed-form solution or could be efficiently solved using existing numerical methods. It has been proven that the quality of images reconstructed from fewer measurements can be significantly improved using non-convex minimization. Numerous experiments have been conducted on two in vivo cardiac datasets to compare the proposed method with several state-of-the-art imaging methods. Experimental results illustrated that the proposed method could guarantee the superior imaging performance in terms of quantitative and visual image quality assessments. View Full-Text
Keywords: compressed sensing; dynamic magnetic resonance imaging; low-rank; non-convex optimization; robust principal component analysis compressed sensing; dynamic magnetic resonance imaging; low-rank; non-convex optimization; robust principal component analysis
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Liu, R.W.; Shi, L.; Yu, S.C.H.; Xiong, N.; Wang, D. Reconstruction of Undersampled Big Dynamic MRI Data Using Non-Convex Low-Rank and Sparsity Constraints. Sensors 2017, 17, 509.

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