nips nips2008 nips2008-30 nips2008-30-reference knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Hannes Nickisch, Rolf Pohmann, Bernhard Schölkopf, Matthias Seeger
Abstract: We show how improved sequences for magnetic resonance imaging can be found through optimization of Bayesian design scores. Combining approximate Bayesian inference and natural image statistics with high-performance numerical computation, we propose the first Bayesian experimental design framework for this problem of high relevance to clinical and brain research. Our solution requires large-scale approximate inference for dense, non-Gaussian models. We propose a novel scalable variational inference algorithm, and show how powerful methods of numerical mathematics can be modified to compute primitives in our framework. Our approach is evaluated on raw data from a 3T MR scanner. 1
[1] M.A. Bernstein, K.F. King, and X.J. Zhou. Handbook of MRI Pulse Sequences. Elsevier Academic Press, 1st edition, 2004.
[2] A. Garroway, P. Grannell, and P. Mansfield. Image formation in NMR by a selective irradiative pulse. J. Phys. C: Solid State Phys., 7:L457–L462, 1974.
[3] M. Girolami. A variational method for learning sparse and overcomplete representations. N. Comp., 13:2517–2532, 2001.
[4] G. Golub and C. Van Loan. Matrix Computations. Johns Hopkins University Press, 3rd edition, 1996.
[5] A. Haase, J. Frahm, D. Matthaei, W. H¨ nicke, and K. Merboldt. FLASH imaging: Rapid NMR imaging a using low flip-angle pulses. J. Magn. Reson., 67:258–266, 1986.
[6] J. Hennig, A. Nauerth, and H. Friedburg. RARE imaging: A fast imaging method for clinical MR. Magn. Reson. Med., 3(6):823–833, 1986.
[7] P. Lauterbur. Image formation by induced local interactions: Examples employing nuclear magnetic resonance. Nature, 242:190–191, 1973.
[8] M. Lustig, D. Donoho, and J. Pauly. Sparse MRI: The application of compressed sensing for rapid MR imaging. Magn. Reson. Med., 85(6):1182–1195, 2007.
[9] P. Mansfield. Multi-planar image formation using NMR spin-echoes. J. Phys. C, 10:L50–L58, 1977.
[10] M. Schneider and A. Willsky. Krylov subspace estimation. SIAM J. Comp., 22(5):1840–1864, 2001.
[11] M. Seeger. Bayesian inference and optimal design for the sparse linear model. JMLR, 9:759–813, 2008.
[12] M. Seeger and H. Nickisch. Compressed sensing and Bayesian experimental design. In ICML 25, 2008.
[13] M. Seeger and H. Nickisch. Large scale variational inference and experimental design for sparse generalized linear models. Technical Report TR-175, Max Planck Institute for Biological Cybernetics, T¨ bingen, u Germany, September 2008.
[14] M. Tipping and A. Faul. Fast marginal likelihood maximisation for sparse Bayesian models. In AI and Statistics 9, 2003.
[15] Y. Weiss, H. Chang, and W. Freeman. Learning compressed sensing. Snowbird Learning Workshop, Allerton, CA, 2007.
[16] D. Wipf and S. Nagarajan. A new view of automatic relevance determination. In NIPS 20, 2008. 14 Some common problems with spirals are discussed in [1, ch. 17.6.3], together with remedies. 8