Journal of Mathematical Imaging and Vision

, Volume 57, Issue 3, pp 366–380 | Cite as

CUSTOM: A Calibration Region Recovery Approach for Highly Subsampled Dynamic Parallel Magnetic Resonance Imaging



We propose a recovery approach for highly subsampled dynamic parallel MRI image without auto-calibration signals (ACSs) or prior knowledge of coil sensitivity maps. By exploiting the between-frame redundancy of dynamic parallel MRI data, we first introduce a new low-rank matrix recovery-based model, termed as calibration using spatial–temporal matrix (CUSTOM), for ACSs recovery. The recovered ACSs from data are used for estimating coil sensitivity maps and further dynamic image reconstruction. The proposed non-convex and non-smooth minimization for the CUSTOM step is solved by a proximal alternating linearized minimization method, and we provide its convergence result for this specific minimization problem. Numerical experiments on several highly subsampled test data demonstrate that the proposed overall approach outperforms other state-of-the-art methods for calibrationless dynamic parallel MRI reconstruction.


Dynamic parallel magnetic resonance image Calibrationless Sensitivity maps Low-rank matrix completion Proximal alternating direction method 



Xue Zhang, Likun Hou and Xiaoqun Zhang are partially supported by NSFC (Nos. 91330102 and GZ1025) and 973 Program (No. 2015CB856004). Hao Gao is partially supported by the NSFC (No. 11405105), the 973 Program (No. 2015CB856004), and the Shanghai Pujiang Talent Program (No. 14PJ1404500). We would thank the authors of [23, 24, 26, 29] for making their codes, demos and experimental datasets free for academic use.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.School of Mathematical SciencesShanghai Jiao Tong UniversityShanghaiChina
  2. 2.Institute of Natural SciencesShanghai Jiao Tong UniversityShanghaiChina
  3. 3.Department of Radiation OncologyDuke University Medical centerDurhamUSA
  4. 4.School of Mathematical Sciences and Institute of Natural SciencesShanghai Jiao Tong UniversityShanghaiChina

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