Low-rank and sparse matrix decomposition based on S1/2 and L1/2 regularizations in dynamic MRI

In recent years, compressed sensing (CS) has been proposed and successfully applied to speed up the acquisition in dynamic MRI. However, how to improve the quality of dynamic MRI is still a worthwhile question. Recently, a low-rank plus sparse (L+S) matrix decomposition model with S1 and L1 regularizations is proposed for reconstruction of under-sampled dynamic MRI with separation of background and dynamic components. It can effectively detect dynamic information in the process of imaging. In our work, we propose an improved L+S matrix decomposition model with S1/2 and L1/2 regularizations in order to improve the quality of original separation. To solve the model, we use an iterative half-thresholding decomposition algorithm. Finally, empirical results show that the new model can produce better performance and capture more completed dynamic information than the existing model.

[1]  Zhi-Pei Liang,et al.  SPATIOTEMPORAL IMAGINGWITH PARTIALLY SEPARABLE FUNCTIONS , 2007, 2007 4th IEEE International Symposium on Biomedical Imaging: From Nano to Macro.

[2]  David Mumford,et al.  Communications on Pure and Applied Mathematics , 1989 .

[3]  D. Donoho,et al.  Sparse MRI: The application of compressed sensing for rapid MR imaging , 2007, Magnetic resonance in medicine.

[4]  Yi Ma,et al.  Robust principal component analysis? , 2009, JACM.

[5]  Daniel K Sodickson,et al.  Low‐rank plus sparse matrix decomposition for accelerated dynamic MRI with separation of background and dynamic components , 2015, Magnetic resonance in medicine.

[6]  I. Daubechies,et al.  An iterative thresholding algorithm for linear inverse problems with a sparsity constraint , 2003, math/0307152.

[7]  S. Frick,et al.  Compressed Sensing , 2014, Computer Vision, A Reference Guide.

[8]  P. Babyn,et al.  Accelerating dynamic MRI by compressed sensing reconstruction from undersampled k-t space with spiral trajectories , 2014, 2nd Middle East Conference on Biomedical Engineering.

[9]  Emmanuel J. Candès,et al.  A Singular Value Thresholding Algorithm for Matrix Completion , 2008, SIAM J. Optim..

[10]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[11]  Hao Gao,et al.  Compressed Sensing using Prior Rank , Intensity and Sparsity Model ( PRISM ) : Applications in Cardiac Cine MRI , 2011 .

[12]  Hongkai Zhao,et al.  Robust principal component analysis-based four-dimensional computed tomography , 2011, Physics in medicine and biology.

[13]  Pablo A. Parrilo,et al.  Rank-Sparsity Incoherence for Matrix Decomposition , 2009, SIAM J. Optim..

[14]  Zongben Xu,et al.  L1/2 regularization , 2010, Science China Information Sciences.

[15]  Leon Axel,et al.  Combination of Compressed Sensing and Parallel Imaging for Highly-Accelerated 3 D First-Pass Cardiac Perfusion MRI , 2009 .

[16]  Stephen P. Boyd,et al.  Enhancing Sparsity by Reweighted ℓ1 Minimization , 2007, 0711.1612.

[17]  Wang Yao,et al.  L 1/2 regularization , 2010 .

[18]  Justin P. Haldar,et al.  Spatiotemporal imaging with partially separable functions: A matrix recovery approach , 2010, 2010 IEEE International Symposium on Biomedical Imaging: From Nano to Macro.

[19]  P. Boesiger,et al.  SENSE: Sensitivity encoding for fast MRI , 1999, Magnetic resonance in medicine.

[20]  Rick Chartrand,et al.  Exact Reconstruction of Sparse Signals via Nonconvex Minimization , 2007, IEEE Signal Processing Letters.