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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 192895, 11 pages
Research Article

Nonlocal Regularized Algebraic Reconstruction Techniques for MRI: An Experimental Study

Lane Department of Computer Science and Electrical Engineering, West Virginia University, Morgantown, WV 26506-6109, USA

Received 2 April 2013; Revised 20 May 2013; Accepted 26 May 2013

Academic Editor: Ming Li

Copyright © 2013 Xin Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We attempt to revitalize researchers' interest in algebraic reconstruction techniques (ART) by expanding their capabilities and demonstrating their potential in speeding up the process of MRI acquisition. Using a continuous-to-discrete model, we experimentally study the application of ART into MRI reconstruction which unifies previous nonuniform-fast-Fourier-transform- (NUFFT-) based and gridding-based approaches. Under the framework of ART, we advocate the use of nonlocal regularization techniques which are leveraged from our previous research on modeling photographic images. It is experimentally shown that nonlocal regularization ART (NR-ART) can often outperform their local counterparts in terms of both subjective and objective qualities of reconstructed images. On one real-world k-space data set, we find that nonlocal regularization can achieve satisfactory reconstruction from as few as one-third of samples. We also address an issue related to image reconstruction from real-world k-space data but overlooked in the open literature: the consistency of reconstructed images across different resolutions. A resolution-consistent extension of NR-ART is developed and shown to effectively suppress the artifacts arising from frequency extrapolation. Both source codes and experimental results of this work are made fully reproducible.