Copyright © 2008 Andrew Thomas Curtis and Christopher Kumar Anand. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

1. T. Knopp, S. Kunis, and D. Potts, “A note on the iterative MRI reconstruction from nonuniform $k$-space data,” International Journal of Biomedical Imaging, vol. 2007, Article ID 24727, 9 pages, 2007. View at Publisher · View at Google Scholar · View at PubMed
2. C. K. Anand, A. T. Curtis, and R. Kumar, “Durga: a heuristically-optimized data collection strategy for volumetric magnetic resonance imaging,” Engineering Optimization, vol. 40, no. 2, pp. 117–136, 2008. View at Publisher · View at Google Scholar
3. K. S. Nayak and D. G. Nishimura, “Randomized trajectories for reduced aliasing artifact,” in Proceedings of the 6th Annual Meeting of the International Society for Magnetic Resonance in Medicine (ISMRM '98), p. 670, Sydney, Australia, April 1998.
4. R. Ahmad, Y. Deng, D. S. Vikram, et al., “Quasi Monte Carlo-based isotropic distribution of gradient directions for improved reconstruction quality of 3D EPR imaging,” Journal of Magnetic Resonance, vol. 184, no. 2, pp. 236–245, 2007. View at Publisher · View at Google Scholar · View at PubMed
5. B. A. Hargreaves, D. G. Nishimura, and S. M. Conolly, “Time-optimal multidimensional gradient waveform design for rapid imaging,” Magnetic Resonance in Medicine, vol. 51, no. 1, pp. 81–92, 2004. View at Publisher · View at Google Scholar · View at PubMed
6. A. Oppelt, R. Graumann, H. Barfuss, H. Fischer, W. Hartl, and W. Shajor, “Fisp—a new fast mri sequence,” Electromedica, vol. 54, no. 1, pp. 15–18, 1986.
7. C. K. Anand, M. Thompson, D. Wu, and T. Cull, “Teardrop, a novel trajectory for truefisp,” in Proceedings of the 9th Annual Meeting of the International Society for Magnetic Resonance in Medicine (ISMRM '01), p. 1804, Glasgow, UK, April 2001.
8. C. K. Anand, T. Ren, and T. Terlaky, “Optimizing Teardrop, an MRI sampling trajectory,” Optimization Methods and Software. In press. View at Publisher · View at Google Scholar
9. K. S. Nayak, B. A. Hargreaves, B. S. Hu, D. G. Nishimura, J. M. Pauly, and C. H. Meyer, “Spiral balanced steady-state free precession cardiac imaging,” Magnetic Resonance in Medicine, vol. 53, no. 6, pp. 1468–1473, 2005. View at Publisher · View at Google Scholar · View at PubMed
10. B. M. Dale, J. S. Lewin, and J. L. Duerk, “Optimal design of $k$-space trajectories using a multi-objective genetic algorithm,” Magnetic Resonance in Medicine, vol. 52, no. 4, pp. 831–841, 2004. View at Publisher · View at Google Scholar · View at PubMed
11. K. K. Vigen, D. C. Peters, T. M. Grist, W. F. Block, and C. A. Mistretta, “Undersampled projection-reconstruction imaging for time-resolved contrast-enhanced imaging,” Magnetic Resonance in Medicine, vol. 43, no. 2, pp. 170–176, 2000. View at Publisher · View at Google Scholar
12. J. Du, S. B. Fain, F. R. Korosec, T. M. Grist, and C. A. Mistretta, “Time-resolved contrast-enhanced carotid imaging using undersampled projection reconstruction acquisition,” Journal of Magnetic Resonance Imaging, vol. 25, no. 5, pp. 1093–1099, 2007. View at Publisher · View at Google Scholar · View at PubMed
13. J. Du, F. J. Thornton, S. B. Fain, et al., “Artifact reduction in undersampled projection reconstruction MRI of the peripheral vessels using selective excitation,” Magnetic Resonance in Medicine, vol. 51, no. 5, pp. 1071–1076, 2004. View at Publisher · View at Google Scholar · View at PubMed
14. R. Mir, A. Guesalaga, J. Spiniak, M. Guarini, and P. Irarrazaval, “Fast three-dimensional $k$-space trajector design using missile guidance ideas,” Magnetic Resonance in Medicine, vol. 52, no. 2, pp. 329–336, 2004. View at Publisher · View at Google Scholar · View at PubMed
15. J. Spiniak, A. Guesalaga, R. Mir, M. Guarini, and P. Irarrazaval, “Undersampling $k$-space using fast progressive 3D trajectories,” Magnetic Resonance in Medicine, vol. 54, no. 4, pp. 886–892, 2005. View at Publisher · View at Google Scholar · View at PubMed
16. A. V. Barger, W. F. Block, Y. Toropov, T. M. Grist, and C. A. Mistretta, “Time-resolved contrast-enhanced imaging with isotropic resolution and broad coverage using an undersampled 3D projection trajectory,” Magnetic Resonance in Medicine, vol. 48, no. 2, pp. 297–305, 2002. View at Publisher · View at Google Scholar · View at PubMed
17. K. P. Pruessmann, M. Weiger, P. Börnert, and P. Boesiger, “Advances in sensitivity encoding with arbitrary $k$-space trajectories,” Magnetic Resonance in Medicine, vol. 46, no. 4, pp. 638–651, 2001. View at Publisher · View at Google Scholar · View at PubMed
18. J. G. Pipe and P. Menon, “Sampling density compensation in MRI: rationale and an iterative numerical solution,” Magnetic Resonance in Medicine, vol. 41, no. 1, pp. 179–186, 1999. View at Publisher · View at Google Scholar
19. F. Wajer, R. Lethmate, J. van Osch, D. Graveron-Demilly, and D. van Ormondt, “Simple formula for the accuracy of gridding,” in Proceedings of the 9th Annual Meeting of the International Society for Magnetic Resonance in Medicine (ISMRM '01), Glasgow, UK, April 2001.
20. V. Rasche, R. Proksa, R. Sinkus, P. Börnert, and H. Eggers, “Resampling of data between arbitrary grids using convolution interpolation,” IEEE Transactions on Medical Imaging, vol. 18, no. 5, pp. 385–392, 1999. View at Publisher · View at Google Scholar
21. J. I. Jackson, C. H. Meyer, D. G. Nishimura, and A. Macovski, “Selection of a convolution function for Fourier inversion using gridding,” IEEE Transactions on Medical Imaging, vol. 10, no. 3, pp. 473–478, 1991. View at Publisher · View at Google Scholar · View at PubMed
22. C. K. Anand, T. Terlaky, and B. Wang, “Rapid, embeddable design method for spiral magnetic resonance image reconstruction resampling kernels,” Optimization and Engineering, vol. 5, no. 4, pp. 485–502, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
23. A. Rosset, L. Spadola, and O. Ratib, “OsiriX: an open-source software for navigating in multidimensional DICOM images,” Journal of Digital Imaging, vol. 17, no. 3, pp. 205–216, 2004. View at Publisher · View at Google Scholar · View at PubMed
24. B. Eicke, A. K. Louis, and R. Plato, “The instability of some gradient methods for ill-posed problems,” Numerische Mathematik, vol. 58, no. 1, pp. 129–134, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
25. Z. Strakoš and P. Tichý, “On error estimation in the conjugate gradient method and why it works in finite precision computations,” Electronic Transactions on Numerical Analysis, vol. 13, pp. 56–80, 2002.
26. M. Lustig, D. Donoho, and J. M. Pauly, “Sparse MRI: the application of compressed sensing for rapid MR imaging,” Magnetic Resonance in Medicine, vol. 58, no. 6, pp. 1182–1195, 2007. View at Publisher · View at Google Scholar · View at PubMed