MR Image Reconstruction via Sparse Representation: Modeling and Algorithm.

作者: Xiaojing Ye , Yunmei Chen , Feng Huang

DOI:

关键词: Model parametersCompressed sensingAcquisition timeRobustness (computer science)Mr imagesAlgorithmSparse approximationEstimatorComputer scienceFidelity

摘要: To reduce acquisition time in magnetic resonance (MR) imaging, compressive sensing and sparse representation techniques have been developed to reconstruct MR images with partially acquired data. Although this has a hot research topic the field, it not used clinically due three inherent problems of its current framework: potential loss fine structures, difficulty predefine model parameters, long reconstruction time. The aim work is tackle these problems. We propose minimize total variation underlying image, together `1 norm coefficients using trained dictionary, as well fidelity term. Using dictionary can take advantage prior knowledge hence improve accuracy reconstruction. Our data constraint derived from likelihood estimator recovering error partial k-space robustness parameter selection. Moreover, simple efficient numerical scheme provided solve faster. consequent experiments on both synthetic vivo indicate improvement proposed preserving structure, reducing computational cost, flexibility decision.

参考文章(21)
J.F. Murray, K. Kreutz-Delgado, An improved FOCUSS-based learning algorithm for solving sparse linear inverse problems asilomar conference on signals, systems and computers. ,vol. 1, pp. 347- 351 ,(2001) , 10.1109/ACSSC.2001.986949
Yilun Wang, Junfeng Yang, Wotao Yin, Yin Zhang, A New Alternating Minimization Algorithm for Total Variation Image Reconstruction Siam Journal on Imaging Sciences. ,vol. 1, pp. 248- 272 ,(2008) , 10.1137/080724265
Scott Shaobing Chen, David L. Donoho, Michael A. Saunders, Atomic Decomposition by Basis Pursuit SIAM Journal on Scientific Computing. ,vol. 20, pp. 33- 61 ,(1998) , 10.1137/S1064827596304010
Wotao Yin, Stanley Osher, Donald Goldfarb, Jerome Darbon, Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing Siam Journal on Imaging Sciences. ,vol. 1, pp. 143- 168 ,(2008) , 10.1137/070703983
Jian-Feng Cai, Stanley Osher, Zuowei Shen, Linearized Bregman iterations for compressed sensing Mathematics of Computation. ,vol. 78, pp. 1515- 1536 ,(2009) , 10.1090/S0025-5718-08-02189-3
David L. Donoho, For most large underdetermined systems of linear equations the minimal 1-norm solution is also the sparsest solution Communications on Pure and Applied Mathematics. ,vol. 59, pp. 797- 829 ,(2006) , 10.1002/CPA.20132
Bin Dong, Yu Mao, Stanley Osher, Wotao Yin, Fast linearized Bregman iteration for compressive sensing and sparse denoising Communications in Mathematical Sciences. ,vol. 8, pp. 93- 111 ,(2008) , 10.4310/CMS.2010.V8.N1.A6
Michael Lustig, David Donoho, John M Pauly, None, Sparse MRI: The application of compressed sensing for rapid MR imaging. Magnetic Resonance in Medicine. ,vol. 58, pp. 1182- 1195 ,(2007) , 10.1002/MRM.21391
Leonid I. Rudin, Stanley Osher, Emad Fatemi, Nonlinear total variation based noise removal algorithms Physica D: Nonlinear Phenomena. ,vol. 60, pp. 259- 268 ,(1992) , 10.1016/0167-2789(92)90242-F
Jong Chul Ye, Sungho Tak, Yeji Han, Hyun Wook Park, Projection reconstruction MR imaging using FOCUSS. Magnetic Resonance in Medicine. ,vol. 57, pp. 764- 775 ,(2007) , 10.1002/MRM.21202