Compressively sampled magnetic resonance image reconstruction using separable surrogate functional method

• Published in: Concepts in magnetic resonance. Part A, Bridging education and research Vol. 43; no. 5; pp. 157 - 165
• Main Authors: Shah, Jawad Ali, Qureshi, Ijaz M., Omer, Hammad, Khaliq, Amir A., Deng, Yiming
• Format: Journal Article
• Language: English
• Published: Blackwell Publishing Ltd 01.09.2014
• Subjects: compressed sensing; Computational geometry; Convexity; Image reconstruction; iterated shrinkage; Magnetic resonance; Mathematical models; nonlinear reconstruction; Reconstruction; Recovery; sparse signal recovery
• ISSN: 1546-6086; 1552-5023
• DOI: 10.1002/cmr.a.21314

ABSTRACT According to the theory of compressed sensing, magnetic resonance (MR) images can be well reconstructed from randomly sub‐Nyquist sampling of the k‐space data using a nonlinear recovery technique if certain conditions are satisfied. The sparse coefficients of the partial Fourier data can be estimated by minimizing the reconstruction cost function. Separable surrogate functional (SSF) method is one of the effective numerical techniques for minimizing mixed l1−l2 convex optimization problems. This article presents a novel recovery technique for compressively sampled MR images that uses SSF method subject to the data consistency constraints. The experimental results show that the proposed recovery algorithm outperforms the projection onto convex sets and low resolution‐based reconstruction techniques in terms of artifact power, improved signal‐to‐noise ratio, and correlation for the same number of iterations. The results are validated using the phantom and original human head MR images taken from the magnetic resonance imaging scanner at St. Mary's Hospital, London. © 2015 Wiley Periodicals, Inc. Concepts Magn Reson Part A 43A: 157–165, 2015.