Rank-one and sparse matrix  decomposition for dynamic MRI

Xianchao  Xiu; Lingchen  Kong

doi:10.3934/naco.2015.5.127

Article Contents

2015, Volume 5, Issue 2: 127-134. Doi: 10.3934/naco.2015.5.127

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Rank-one and sparse matrix decomposition for dynamic MRI

Xianchao Xiu^1, and
Lingchen Kong^1,

1.
Department of Applied Mathematics, Beijing Jiaotong University, Beijing 100044

Received: November 2014

Revised: April 2015

Published: May 2015

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Abstract

We introduce a rank-one and sparse matrix decomposition model for dynamic magnetic resonance imaging (MRI). Since $l_p$-norm $(0 < p < 1)$ is generally nonconvex, nonsmooth, non-Lipschitz, we propose reweighted $l_1$-norm to surrogate $l_p$-norm. Based on this, we put forward a modified alternative direction method. Numerical experiments are also given to illustrate the efficiency of our algorithm.

Keywords:

Dynamic MRI,
rank-one and sparse matrix decomposition,
modified alternative direction method.

Mathematics Subject Classification: Primary: 90C90, 90C26; Secondary: 65K10.

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