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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
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)
Nayak, K.S., Nishimura, D.G.: Randomized trajectories for reduced aliasing artifact. In: Proceedings of the Scientific Meeting and Exhibition of ISMRM. Sydney (1998)
Sersa, I., Macura, S.: Excitation of arbitrary shapes by gradient optimized random walk in discrete k-space. Magn. Reson. Med. 37, 920–931 (1997)
Usman, M., Batchelor, P.G.: Optimized sampling patterns for practical compressed MRI. In: International Conference on Sampling Theory and Applications (SAMPTA’09), Marseille (2009)
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)
Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press (2004)
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)
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)
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)
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)
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.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer India
About this chapter
Cite this chapter
Deka, B., Datta, S. (2015). A Practical Under-Sampling Pattern for Compressed Sensing MRI. In: Bora, P., Prasanna, S., Sarma, K., Saikia, N. (eds) Advances in Communication and Computing. Lecture Notes in Electrical Engineering, vol 347. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2464-8_9
Download citation
DOI: https://doi.org/10.1007/978-81-322-2464-8_9
Published:
Publisher Name: Springer, New Delhi
Print ISBN: 978-81-322-2463-1
Online ISBN: 978-81-322-2464-8
eBook Packages: EngineeringEngineering (R0)