Advances in Communication and Computing pp 115-125 | Cite as
A Practical Under-Sampling Pattern for Compressed Sensing MRI
Abstract
Typically, magnetic resonance (MR) images are stored in k-space where the higher energy samples, i.e., the samples with maximum information are concentrated near the center only; whereas, relatively lower energy samples are present near the outer periphery. Recently, variable density (VD) random under-sampling patterns have been increasingly popular and a topic of active research in compressed sensing (CS)-based MR image reconstruction. In this paper, we demonstrate a simple approach to design an efficient k-space under-sampling pattern, namely, the VD Poisson Disk (VD-PD) for sampling MR images in k-space and then implementing the same for CS-MRI reconstruction. Results are also compared with those obtained from some of the most prominent and commonly used sampling patterns, including the VD random with estimated PDF (VD-PDF), the VD Gaussian density (VD-Gaus), the VD uniform random (VD-Rnd), and the Radial Type in the CS-MRI literature.
Keywords
Magnetic resonance imaging k-space Compressed sensing Variable density under-sampling patternNotes
Acknowledgments
The authors want to thank UGC for the financial support of the above project No. 41-603/2012 (SR) dated 16th July, 2012 and the Department of ECE, Tezpur University for giving us the opportunity and necessary infrastructure to carry out the project work.
References
- 1.Lustig, M., Donoho, D., Pauly, J.M.: Sparse MRI: the application of compressed sensing for rapid MR imaging. Magn. Reson. Med. 58, 1182–1195 (2007)CrossRefGoogle Scholar
- 2.Nayak, K.S., Nishimura, D.G.: Randomized trajectories for reduced aliasing artifact. In: Proceedings of the Scientific Meeting and Exhibition of ISMRM. Sydney (1998)Google Scholar
- 3.Sersa, I., Macura, S.: Excitation of arbitrary shapes by gradient optimized random walk in discrete k-space. Magn. Reson. Med. 37, 920–931 (1997)CrossRefGoogle Scholar
- 4.Usman, M., Batchelor, P.G.: Optimized sampling patterns for practical compressed MRI. In: International Conference on Sampling Theory and Applications (SAMPTA’09), Marseille (2009)Google Scholar
- 5.Cusack, R.: \(\text{ Generate }\_\text{ Poisson }\_2\)d.m. https://www.github.com/gpeyre/2014-JMIV-SlicedTransport/blob/master/sliced/generate_poisson_2d.m (2013)
- 6.Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press (2004)Google Scholar
- 7.Koh, K., Kim, S.J., Boyd, S., Lin, Yi.: An interior-point method for large-scale l1-regularized logistic regression. J. Mach. Learn. Res. 8(22), 1519–1555 (2007)Google Scholar
- 8.Daubechies, I., Defrise, M., De Mol, C.: An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun. Pure Appl. Math. 57(11), 1413–1457 (2004)MATHCrossRefGoogle Scholar
- 9.Figueiredo, M.A.T., Nowak, R.D., Wright, S.J.: Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems. IEEE J. Sel. Top. Signal Process. 1(4), 586–597 (2007)CrossRefGoogle Scholar
- 10.Bioucas-Dias, J.M., Figueiredo, M.A.T.: A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration. IEEE Trans. Image Process. 16(12), 2992–3004 (2007)MathSciNetCrossRefGoogle Scholar