nips nips2012 nips2012-78 nips2012-78-reference knowledge-graph by maker-knowledge-mining
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Author: Chen Chen, Junzhou Huang
Abstract: In Compressive Sensing Magnetic Resonance Imaging (CS-MRI), one can reconstruct a MR image with good quality from only a small number of measurements. This can significantly reduce MR scanning time. According to structured sparsity theory, the measurements can be further reduced to O(K + log n) for tree-sparse data instead of O(K + K log n) for standard K-sparse data with length n. However, few of existing algorithms have utilized this for CS-MRI, while most of them model the problem with total variation and wavelet sparse regularization. On the other side, some algorithms have been proposed for tree sparse regularization, but few of them have validated the benefit of wavelet tree structure in CS-MRI. In this paper, we propose a fast convex optimization algorithm to improve CS-MRI. Wavelet sparsity, gradient sparsity and tree sparsity are all considered in our model for real MR images. The original complex problem is decomposed into three simpler subproblems then each of the subproblems can be efficiently solved with an iterative scheme. Numerous experiments have been conducted and show that the proposed algorithm outperforms the state-of-the-art CS-MRI algorithms, and gain better reconstructions results on real MR images than general tree based solvers or algorithms. 1
[1] Donoho, D. (2006) Compressed sensing. IEEE Trans. on Information Theory 52(4):1289-1306.
[2] Candes, E., Romberg, J. & Tao, T. (2006) Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Trans. on Information Theory 52(2):489-509.
[3] Lustig, M., Donoho, D. & Pauly, J. (2007) Sparse MRI: The application of compressed sensing for rapid MR imaging. Magnetic Resonance in Medicine 58(6):1182-1195.
[4] Huang, J., Zhang, T. & Metaxas, D. (2011) Learning With Structured Sparsity. Journal of Machine Learning Research 12:3371-3412.
[5] Baraniuk, R.G., Cevher, V., Duarte, M.F. & Hegde, C. (2010) Model-based compressive sensing. IEEE Trans. on Information Theory 56:1982-2001.
[6] Bach, F., Jenatton, R., Mairal, J. & Obozinski, G. (2012) Structured sparsity through convex optimization. Technical report, HAL 00621245-v2, to appear in Statistical Science.
[7] Rao, N., Nowak, R., Wright, S. & Kingsbury, N. (2011) Convex approaches to model wavelet sparsity patterns. In IEEE International Conference On Image Processing, ICIP’11
[8] He, L. & Carin, L. (2009) Exploiting Structure in Wavelet-Based Bayesian Compressive Sensing. IEEE Trans. on Signal Processing 57(9):3488-3497.
[9] He, L., Chen, H. & Carin, L. (2010) Tree-Structured Compressive Sensing with Variational Bayesian Analysis. IEEE Signal Processing Letters 17(3):233-236
[10] Som, S., Potter, L.C. & Schniter, P. (2010) Compressive Imaging using Approximate Message Passing and a Markov-Tree Prior. In Proceedings of Asilomar Conference on Signals, Systems, and Computers.
[11] Wright, S.J., Nowak, R.D. & Figueiredo, M.A.T. (2009) Sparse reconstruction by separable approximation. IEEE Trans. on Signal Processing 57:2479-2493.
[12] Ma, S., Yin, W., Zhang, Y. & Chakraborty, A.(2008) An efficient algorithm for compressed MR imaging using total variation and wavelets. In In Proc. of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR’08.
[13] Yang, J., Zhang, Y. & Yin, W. (2010) A fast alternating direction method for tvl1-l2 signal reconstruction from partial fourier data. IEEE Journal of Selected Topics in Signal Processing, Special Issue on Compressive Sensing 4(2):288-297.
[14] Huang, J., Zhang, S. & Metaxas, D. (2011) Efficient MR Image Reconstruction for Compressed MR Imaging. Medical Image Analysis 15(5):670-679.
[15] Huang, J., Zhang, S. & Metaxas, D. (2010) Efficient MR Image Reconstruction for Compressed MR Imaging. In Proc. of the 13th Annual International Conference on Medical Image Computing and Computer Assisted Intervention, MICCAI’10.
[16] Beck, A. & Teboulle, M. (2009) A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM Journal on Imaging Sciences 2(1):183-202.
[17] Beck, A. & Teboulle, M. (2009) Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems. IEEE Trans. on Image Processing 18(113):2419-2434
[18] Liu, J., Ji, S. & Ye, J. (2009) SLEP: Sparse Learning with Efficient Projections. Arizona State University. http://www.public.asu.edu/ jye02/Software/SLEP.
[19] Deng, W., Yin, W. & Zhang, Y. (2011) Group Sparse Optimization by Alternating Direction Method. Rice CAAM Report TR11-06.
[20] Manduca A., & Said A. (1996) Wavelet Compression of Medical Images with Set Partitioning in Hierarchical Trees. In Proceedings of International Conference IEEE Engineering in Medicine and Biology Society, EMBS.
[21] Huang, J., Chen, C. & Axel, L. (2012) Fast Multi-contrast MRI Reconstruction. In Proc. of the 15th Annual International Conference on Medical Image Computing and Computer Assisted Intervention, MICCAI’12.
[22] Huang, J., & Yang, F. (2012) Compressed Magnetic Resonace Imaging Based on Wavelet Sparsity and Nonlocal Total Variation. IEEE International Symposium on Biomedical Imaging, ISBI’12. 9