title: Magnetic resonance image reconstruction from undersampled measurements using a patch-based nonlocal operator.
abstract: Compressed sensing MRI (CS-MRI) has shown great potential in reducing data acquisition time in MRI. Sparsity or compressibility plays an important role to reduce the image reconstruction error. Conventional CS-MRI typically uses a pre-defined sparsifying transform such as wavelet or finite difference, which sometimes does not lead to a sufficient sparse representation for the image to be reconstructed. In this paper, we design a patch-based nonlocal operator (PANO) to sparsify magnetic resonance images by making use of the similarity of image patches. The definition of PANO results in sparse representation for similar patches and allows us to establish a general formulation to trade the sparsity of these patches with the data consistency. It also provides feasibility to incorporate prior information learnt from undersampled data or another contrast image, which leads to optimized sparse representation of images to be reconstructed. Simulation results on in vivo data demonstrate that the proposed method achieves lower reconstruction error and higher visual quality than conventional CS-MRI methods.
authors.affiliation: Department of Electronic Science, Fujian Provincial Key Laboratory of Plasma and Magnetic Resonance, State Key Laboratory of Physical Chemistry of Solid Surfaces, Xiamen University, Xiamen 361005, China. Electronic address: quxiaobo@xmu.edu.cn.
authors.forename: Xiaobo
authors.initials: X
authors.lastname: Qu
authors.affiliation: School of Information Science and Technology, Taishan University, Taian 271021, China.
authors.forename: Yingkun
authors.initials: Y
authors.lastname: Hou
authors.affiliation: Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA.
authors.forename: Fan
authors.initials: F
authors.lastname: Lam
authors.affiliation: School of Computer and Information Engineering, Xiamen University of Technology, Xiamen 361024, China.
authors.forename: Di
authors.initials: D
authors.lastname: Guo
authors.affiliation: Department of Imaging Sciences, University of Rochester, Box 648, Elmwood Avenue, Rochester, NY 14642-8648, USA.
authors.forename: Jianhui
authors.initials: J
authors.lastname: Zhong
authors.affiliation: Department of Electronic Science, Fujian Provincial Key Laboratory of Plasma and Magnetic Resonance, State Key Laboratory of Physical Chemistry of Solid Surfaces, Xiamen University, Xiamen 361005, China. Electronic address: chenz@xmu.edu.cn.
authors.forename: Zhong
authors.initials: Z
authors.lastname: Chen
mesh_terms: D000465:Algorithms; D001931:Brain Mapping / Q000379:methods*; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional; D008279:Magnetic Resonance Imaging / Q000379:methods*; D015233:Models, Statistical; D015203:Reproducibility of Results; D059629:Signal-To-Noise Ratio
keywords: Compressed sensing; Image reconstruction; Magnetic resonance imaging; Nonlocal operator; Sparsity