Research ArticleOpen AccessGoogle Scholar indexed
TV Sparsifying MR Image Reconstruction in Compressive Sensing
School of Science, Communication University of China
School of Science, Communication University of China
- 1 School of Science, Communication University of China
- 2 School of Science, Communication University of China
Journal of Signal and Information Processing·Volume 02 (2011)·Pages 44–51·Published 22 February 2011·DOI10.4236/jsip.2011.21007
Copy link · social · email
Abstract
In this paper, we apply alternating minimization method to sparse image reconstruction in compressed sensing. This approach can exactly reconstruct the MR image from under-sampled k-space data, i.e., the partial Fourier data. The convergence analysis of the fast method is also given. Some MR images are employed to test in the numerical experi-ments, and the results demonstrate that our method is very efficient in MRI reconstruction.
KeywordsCompressed SensingMagnetic Resonance ImageTotal VariationImage Reconstruction
- E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory, Vol. 52, 2006, pp. 489-509.
- D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory, Vol. 52, 2006, pp. 1289-1306.
- E. Candes and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Problems, Vol. 23, 2007, pp. 969-985.
- B. K. Natarajan, “Sparse approximate solutions to linear systems,” SIAM J. Comput., Vol. 24, 1995, pp.227-234.
- D. Donoho and X. Huo, “Uncertainty principles and ideal atomic decompositions,” IEEE Trans. Inf.Theory, Vol. 47, 2001, pp. 2845-2862.
- J. J. Fuchs, “On sparse representations in arbitrary redundant bases,” IEEE Trans. Inf. Theory, Vol. 50, 2004, pp. 1341-1344.
- L. Rudin, S. Osher and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D, Vol. 60, 1992, pp. 259-268.
- L. He, T. C. Chang, S. Osher, T. Fang and P. Speier, “MR image reconstruction by using the iterative refinement method and nonlinear inverse scale space methods,” UCLA CAM Report, 2006,06-35.
- M. Lustig, D. Donoho and J. Pauly, “Sparse MRI: The application of compressed sensing for rapid MR imaging,” Magnetic Resonance in Medicine, Vol. 58,2007,pp. 1182-1195.
- Y. Wang, J. Yang, W. Yin and Y. Zhang, “A alternating minimization algorithm for total variation image reconstruction,” SIAM J. Imag. Sci., Vol. 1, 2008,pp. 248-272.
- R. Courant, “Variational methods for the solution of problems with equilibrium and vibration,” Bull.Amer. Math. Soc., Vol. 49, 1943, pp. 1-23.
- M. K. Ng, R. H. Chan and W. C. Tang, “A fast algorithm for deblurring models with Neumann boundary conditions,” SIAM J. Sci. Comput., Vol. 21, pp. 851-866, 1999.
- Z. Opal, “Weak convergence of the sequence of successive approximations for nonexpansive mappings,” Bull. Amer. Math. Soc., Vol. 73, 1967, pp. 591-597.
- J. Yang, W. Yin and Y.Wang, “A Fast Algorithm for Edge-Preserving Variational Multichannel Image Restoration,” SIAM J. Sci. Comput., Vol. 2, 2009, pp. 569-592.
- J. Yang, Y. Zhang and W. Yin, “A Fast Alternating Direction Method for TVL1-L2 Signal Reconstruction From Partial Fourier Data,” IEEE Journal of Selected Topics in Signal Processing, Vol. 4, 2010, pp.288-297.