Weighted-average alternating minimization method for magnetic resonance image reconstruction based on compressive sensing

Yonggui Zhu; Yuying Shi; Bin Zhang; Xinyan Yu

doi:10.3934/ipi.2014.8.925

Article Contents

2014, Volume 8, Issue 3: 925-937. Doi: 10.3934/ipi.2014.8.925

This issue Previous Article Learning circulant sensing kernels Next Article

Weighted-average alternating minimization method for magnetic resonance image reconstruction based on compressive sensing

1.
School of Science, Communication University of China, Beijing, 100024
2.
Department of Mathematics and Physics, North China Electric Power University, Beijing, 102206

Received: July 31, 2012

Revised: July 31, 2013

Published: July 2014

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Abstract

The problem of compressive-sensing (CS) L2-L1-TV reconstruction of magnetic resonance (MR) scans from undersampled $k$-space data has been addressed in numerous studies. However, the regularization parameters in models of CS L2-L1-TV reconstruction are rarely studied. Once the regularization parameters are given, the solution for an MR reconstruction model is fixed and is less effective in the case of strong noise. To overcome this shortcoming, we present a new alternating formulation to replace the standard L2-L1-TV reconstruction model. A weighted-average alternating minimization method is proposed based on this new formulation and a convergence analysis of the method is carried out. The advantages of and the motivation for the proposed alternating formulation are explained. Experimental results demonstrate that the proposed formulation yields better reconstruction results in the case of strong noise and can improve image reconstruction via flexible parameter selection.

Keywords:

Compressive sensing,
alternating minimization method,
weighted average,
magnetic resonance image reconstruction.

Mathematics Subject Classification: Primary: 65N20, 97M10, 97M60; Secondary: 65Q30.

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