Sparsity-Enforced Slice-Selective MRI RF Excitation Pulse Design

We introduce a novel algorithm for the design of fast slice-selective spatially-tailored magnetic resonance imaging (MRI) excitation pulses. This method, based on sparse approximation theory, uses a second-order cone optimization to place and modulate a small number of slice-selective sine-like radio-frequency (RF) pulse segments ("spokes") in excitation fc-space, enforcing sparsity on the number of spokes allowed while si multaneously encouraging those that remain to be placed and modulated in a way that best forms a user-defined in-plane target magnetization. Pulses are designed to mitigate B1 inhomogeneity in a water phantom at 7 T and to produce highly-structured excitations in an oil phantom on an eight-channel parallel excitation system at 3 T. In each experiment, pulses generated by the spar- sity-enfoldquoced method outperform those created via conventional Fourier-based techniques, e.g., when attempting to produce a uniform magnetization in the presence of severe B1 inhomogeneity, a 5.7-ms 15-spoke pulse generated by the sparsity-enforced method produces an excitation with 1.28 times lower root mean square error than conventionally-designed 15-spoke pulses. To achieve this same level of uniformity, the conventional methods need to use 29-spoke pulses that are 7.8 ms long.

[1]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[2]  Michael Elad,et al.  Image Denoising with Shrinkage and Redundant Representations , 2006, 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06).

[3]  Bhaskar D. Rao,et al.  Sparse signal reconstruction from limited data using FOCUSS: a re-weighted minimum norm algorithm , 1997, IEEE Trans. Signal Process..

[4]  Jürgen Hennig,et al.  Experimental analysis of parallel excitation using dedicated coil setups and simultaneous RF transmission on multiple channels , 2005, Magnetic resonance in medicine.

[5]  T. Ibrahim,et al.  B1 field homogeneity and SAR calculations for the birdcage coil , 2001 .

[6]  I. Johnstone.  On Minimax Estimation of a Sparse Normal Mean Vector , 1994 .

[7]  D. Luenberger.  Optimization by Vector Space Methods , 1968 .

[8]  Michael B. Smith,et al.  Central brightening due to constructive interference with, without, and despite dielectric resonance , 2005, Journal of magnetic resonance imaging : JMRI.

[9]  S. Souza,et al.  Multiecho magnetic resonance angiography , 1987, Magnetic resonance in medicine.

[10]  D. Donoho.  For most large underdetermined systems of equations, the minimal 𝓁1‐norm near‐solution approximates the sparsest near‐solution , 2006 .

[11]  J. Tropp.  Algorithms for simultaneous sparse approximation. Part II: Convex relaxation , 2006, Signal Process..

[12]  Dmitry M. Malioutov,et al.  A sparse signal reconstruction perspective for source localization with sensor arrays , 2005, IEEE Transactions on Signal Processing.

[13]  Zhifeng Zhang,et al.  Adaptive Nonlinear Approximations , 1994 .

[14]  H. Smith,et al.  Magnetic Resonance Angiography: Techniques, Indications and Practical Applications , 2000, Tidsskrift for den Norske laegeforening : tidsskrift for praktisk medicin, ny raekke.

[15]  Jianming Jin,et al.  On the SAR and field inhomogeneity of birdcage coils loaded with the human head , 1997, Magnetic resonance in medicine.

[16]  Jeffrey A. Fessler,et al.  Advanced three-dimensional tailored RF pulse for signal recovery in T-weighted functional MRI , 2006 .

[17]  Ravi S. Menon,et al.  A transmit‐only/receive‐only (TORO) RF system for high‐field MRI/MRS applications , 2000, Magnetic resonance in medicine.

[18]  I. Daubechies,et al.  An iterative thresholding algorithm for linear inverse problems with a sparsity constraint , 2003, math/0307152.

[19]  Kawin Setsompop,et al.  Parallel RF transmission with eight channels at 3 Tesla , 2006, Magnetic resonance in medicine.

[20]  Joel A. Tropp,et al.  Algorithms for simultaneous sparse approximation. Part I: Greedy pursuit , 2006, Signal Process..

[21]  Joel A. Tropp,et al.  Just relax: convex programming methods for identifying sparse signals in noise , 2006, IEEE Transactions on Information Theory.

[22]  Arkadi Nemirovski,et al.  Lectures on modern convex optimization - analysis, algorithms, and engineering applications , 2001, MPS-SIAM series on optimization.

[23]  X Hu,et al.  Reduction of field of view for dynamic imaging , 1994, Magnetic resonance in medicine.

[24]  Balas K. Natarajan,et al.  Sparse Approximate Solutions to Linear Systems , 1995, SIAM J. Comput..

[25]  P A Bottomley,et al.  RF magnetic field penetration, phase shift and power dissipation in biological tissue: implications for NMR imaging. , 1978, Physics in medicine and biology.

[26]  R. R. Ernst,et al.  Application of Fourier Transform Spectroscopy to Magnetic Resonance , 1966 .

[27]  S. Junge,et al.  Parallel Excitation Experiments Using a Novel Direct Calibration Technique for RF-Pulse Determination , 2007 .

[28]  Yudong Zhu,et al.  Parallel excitation with an array of transmit coils , 2004, Magnetic resonance in medicine.

[29]  Xiaoming Huo,et al.  Uncertainty principles and ideal atomic decomposition , 2001, IEEE Trans. Inf. Theory.

[30]  Aharon Ben-Tal,et al.  Lectures on modern convex optimization , 1987 .

[31]  P. Börnert,et al.  Transmit SENSE , 2003, Magnetic resonance in medicine.

[32]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[33]  Tropp.  Mutual Inductance in the Bird-Cage Resonator , 1997, Journal of magnetic resonance.

[34]  Douglas C Noll,et al.  Spatial domain method for the design of RF pulses in multicoil parallel excitation , 2006, Magnetic resonance in medicine.

[35]  Peter Börnert,et al.  Theoretical and numerical aspects of transmit SENSE , 2004, IEEE Transactions on Medical Imaging.

[36]  Kim-Chuan Toh,et al.  SDPT3 -- A Matlab Software Package for Semidefinite Programming , 1996 .

[37]  V. K. Goyal,et al.  DESIGNING FAST 3-D RF EXCITATIONS BY OPTIMIZING THE NUMBER , PLACEMENT AND WEIGHTING OF SPOKES IN K-SPACE VIA A SPARSITY-ENFORCEMENT ALGORITHM , 2007 .

[38]  Vivek K. Goyal,et al.  Comparison of Three Algorithms for Solving Linearized Systems of Parallel Excitation RF Waveform Design Equations: Experiments on an Eight-Channel System at 3 Tesla , 2007 .

[39]  R. Goebel,et al.  7T vs. 4T: RF power, homogeneity, and signal‐to‐noise comparison in head images , 2001, Magnetic resonance in medicine.

[40]  Douglas C Noll,et al.  Iterative RF pulse design for multidimensional, small‐tip‐angle selective excitation , 2005, Magnetic resonance in medicine.

[41]  Steen Moeller,et al.  B1 destructive interferences and spatial phase patterns at 7 T with a head transceiver array coil , 2005, Magnetic resonance in medicine.

[42]  Per Christian Hansen,et al.  REGULARIZATION TOOLS: A Matlab package for analysis and solution of discrete ill-posed problems , 1994, Numerical Algorithms.

[43]  Kawin Setsompop,et al.  An 8 Channel Transmit Coil for Transmit Sense at 3T , 2006 .

[44]  W. Manning,et al.  Simultaneous acquisition of spatial harmonics (SMASH): Fast imaging with radiofrequency coil arrays , 1997, Magnetic resonance in medicine.

[45]  Michael A. Saunders,et al.  LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares , 1982, TOMS.

[46]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[47]  R. Constable,et al.  Measurement and correction of transmitter and receiver induced nonuniformities in vivo , 2005, Magnetic resonance in medicine.

[48]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

[49]  Alan V. Oppenheim,et al.  Discrete-Time Signal Pro-cessing , 1989 .

[50]  Joel A. Tropp,et al.  Topics in sparse approximation , 2004 .

[51]  P. Röschmann,et al.  Spectroscopy and imaging with a 4 tesla whole‐body mr system , 1988, NMR in biomedicine.

[52]  M. J. D. Powell,et al.  A fast algorithm for nonlinearly constrained optimization calculations , 1978 .

[53]  I. Johnstone,et al.  Ideal spatial adaptation by wavelet shrinkage , 1994 .

[54]  Douglas C Noll,et al.  Fast‐kz three‐dimensional tailored radiofrequency pulse for reduced B1 inhomogeneity , 2006, Magnetic resonance in medicine.

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

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

[57]  L. L. Wald,et al.  Sparse spokes slice selective design for B 1 inhomogeneity correction at 7 T , 2007 .

[58]  Michael B. Smith,et al.  SAR and B1 field distributions in a heterogeneous human head model within a birdcage coil , 1998, Magnetic resonance in medicine.

[59]  S. P. Souza,et al.  Phase-contrast magnetic resonance angiography , 1989, Images of the Twenty-First Century. Proceedings of the Annual International Engineering in Medicine and Biology Society,.

[60]  Douglas C Noll,et al.  Joint design of trajectory and RF pulses for parallel excitation , 2007, Magnetic resonance in medicine.

[61]  Ingmar Graesslin,et al.  Whole Body 3T MRI System with Eight Parallel RF Transmission Channels , 2006 .