Speeding up Magnetic Resonance Image Acquisition by Bayesian Multi-Slice Adaptive Compressed Sensing

We show how to sequentially optimize magnetic resonance imaging measurement designs over stacks of neighbouring image slices, by performing convex variational inference on a large scale non-Gaussian linear dynamical system, tracking dominating directions of posterior covariance without imposing any factorization constraints. Our approach can be scaled up to high-resolution images by reductions to numerical mathematics primitives and parallelization on several levels. In a first study, designs are found that improve significantly on others chosen independently for each slice or drawn at random.

[1]  P. Lauterbur,et al.  Image Formation by Induced Local Interactions: Examples Employing Nuclear Magnetic Resonance , 1973, Nature.

[2]  J Velikina,et al.  Highly constrained backprojection for time‐resolved MRI , 2006, Magnetic resonance in medicine.

[3]  W. Freeman,et al.  Understanding Camera Trade-Offs through a Bayesian Analysis of Light Field Projections , 2008, ECCV.

[4]  William T. Freeman,et al.  Informative Sensing , 2009, ArXiv.

[5]  P. Boesiger,et al.  SENSE: Sensitivity encoding for fast MRI , 1999, Magnetic resonance in medicine.

[6]  L D Cromwell,et al.  Filtering noise from images with wavelet transforms , 1991, Magnetic resonance in medicine.

[7]  Henrik Madsen,et al.  On the construction of a reduced rank square-root Kalman filter for efficient uncertainty propagation , 2005, Future Gener. Comput. Syst..

[8]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[9]  Marseille,et al.  Nonuniform Phase-Encode Distributions for MRI Scan Time Reduction , 1996, Journal of magnetic resonance. Series B.

[10]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[11]  Michael K. Schneider,et al.  Krylov Subspace Estimation , 2000, SIAM J. Sci. Comput..

[12]  Frank T. A. W. Wajer,et al.  Non-Cartesian MRI scan time reduction through sparse sampling , 2001 .

[13]  Bernhard Schölkopf,et al.  Bayesian Experimental Design of Magnetic Resonance Imaging Sequences , 2008, NIPS.

[14]  Mark A. Girolami,et al.  A Variational Method for Learning Sparse and Overcomplete Representations , 2001, Neural Computation.

[15]  M. Lustig,et al.  SPIRiT: Iterative self‐consistent parallel imaging reconstruction from arbitrary k‐space , 2010, Magnetic resonance in medicine.

[16]  P. Mansfield,et al.  Image formation in NMR by a selective irradiative process , 1974 .

[17]  K. W. Cattermole.  The Fourier Transform and its Applications , 1965 .

[18]  D. Donoho,et al.  Sparse MRI: The application of compressed sensing for rapid MR imaging , 2007, Magnetic resonance in medicine.

[19]  N J Pelc,et al.  Unaliasing by Fourier‐encoding the overlaps using the temporal dimension (UNFOLD), applied to cardiac imaging and fMRI , 1999, Magnetic resonance in medicine.

[20]  Wilson Fong.  Handbook of MRI Pulse Sequences , 2005 .

[21]  Dmitry M. Malioutov,et al.  Low-Rank Variance Estimation in Large-Scale Gmrf Models , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

[22]  A. S. Willsky,et al.  Krylov subspace algorithms for space-time oceanography data assimilation , 2000, IGARSS 2000. IEEE 2000 International Geoscience and Remote Sensing Symposium. Taking the Pulse of the Planet: The Role of Remote Sensing in Managing the Environment. Proceedings (Cat. No.00CH37120).

[23]  Gene H. Golub,et al.  Matrix computations , 1983 .

[24]  Matthias W. Seeger,et al.  Compressed sensing and Bayesian experimental design , 2008, ICML '08.

[25]  Robin M Heidemann,et al.  Generalized autocalibrating partially parallel acquisitions (GRAPPA) , 2002, Magnetic resonance in medicine.

[26]  Peter Boesiger,et al.  k‐t BLAST and k‐t SENSE: Dynamic MRI with high frame rate exploiting spatiotemporal correlations , 2003, Magnetic resonance in medicine.