Acceleration of high angular and spatial resolution diffusion imaging using compressed sensing

Achieving simultaneously high angular and spatial resolution in diffusion imaging is challenging because of the long acquisition times involved. We propose a novel compressed sensing method to acquire high angular and spatial resolution diffusion imaging data, while keeping the scan time reasonable. We show that joint under sampling of 6-D k-q space is more efficient than undersampling only one of the dimensions. We use a sparse Gaussian mixture model and an iterative reconstruction scheme to recover the peaks of the orientation distribution functions (ODF) with high accuracy. We show that at least 6-fold acceleration of acquisition is possible, thereby enabling high angular and spatial resolution diffusion imaging in a reasonable scan time.

[1]  Brendt Wohlberg,et al.  An Iteratively Reweighted Norm Algorithm for Minimization of Total Variation Functionals , 2007, IEEE Signal Processing Letters.

[2]  Jerry L. Prince,et al.  Resolution of crossing fibers with constrained compressed sensing using traditional diffusion tensor MRI , 2010, Medical Imaging.

[3]  T. Nishimura,et al.  Diffusion Anisotropy Measurement of Brain White Matter Is Affected by Voxel Size: Underestimation Occurs in Areas with Crossing Fibers , 2007, American Journal of Neuroradiology.

[4]  E. Stejskal Use of Spin Echoes in a Pulsed Magnetic‐Field Gradient to Study Anisotropic, Restricted Diffusion and Flow , 1965 .

[5]  D. Tuch Q‐ball imaging , 2004, Magnetic resonance in medicine.

[6]  Jens Frahm,et al.  Inverse reconstruction method for segmented multishot diffusion‐weighted MRI with multiple coils , 2009, Magnetic resonance in medicine.

[7]  Oleg V. Michailovich,et al.  Rician compressed sensing for fast and stable signal reconstruction in diffusion MRI , 2012, Medical Imaging.

[8]  José M. Bioucas-Dias,et al.  An Augmented Lagrangian Approach to the Constrained Optimization Formulation of Imaging Inverse Problems , 2009, IEEE Transactions on Image Processing.

[9]  Jeffrey A. Fessler,et al.  Regularization Parameter Selection for Nonlinear Iterative Image Restoration and MRI Reconstruction Using GCV and SURE-Based Methods , 2012, IEEE Transactions on Image Processing.

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

[11]  Nicolai Bissantz,et al.  Convergence Analysis of Generalized Iteratively Reweighted Least Squares Algorithms on Convex Function Spaces , 2008, SIAM J. Optim..

[12]  S. Skare,et al.  Robust GRAPPA‐accelerated diffusion‐weighted readout‐segmented (RS)‐EPI , 2009, Magnetic resonance in medicine.

[13]  P. Basser,et al.  In vivo fiber tractography using DT‐MRI data , 2000, Magnetic resonance in medicine.

[14]  Mark W. Woolrich,et al.  Probabilistic diffusion tractography with multiple fibre orientations: What can we gain? , 2007, NeuroImage.

[15]  Y. Zhuo,et al.  A Navigated non-CPMG Turbo Spin Echo Pulse Sequence for High Resolution Diffusion Imaging , 2007 .

[16]  P. Basser,et al.  Diffusion tensor MR imaging of the human brain. , 1996, Radiology.

[17]  Rachid Deriche,et al.  Spherical Polar Fourier EAP and odf reconstruction via compressed sensing in diffusion mri , 2011, 2011 IEEE International Symposium on Biomedical Imaging: From Nano to Macro.

[18]  L. Ying,et al.  Accelerated MR diffusion tensor imaging using distributed compressed sensing , 2014, Magnetic resonance in medicine.

[19]  Michael Elad,et al.  Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ1 minimization , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[20]  C. Pierpaoli,et al.  Diffusion‐weighted radial fast spin‐echo for high‐resolution diffusion tensor imaging at 3T , 2008, Magnetic resonance in medicine.

[21]  Ashish Raj,et al.  Spatial HARDI: Improved visualization of complex white matter architecture with Bayesian spatial regularization , 2011, NeuroImage.

[22]  Stéphane Mallat,et al.  Matching pursuits with time-frequency dictionaries , 1993, IEEE Trans. Signal Process..

[23]  Thomas R. Knösche,et al.  k-space and q-space: Combining ultra-high spatial and angular resolution in diffusion imaging using ZOOPPA at 7T , 2012, NeuroImage.

[24]  Roland Bammer,et al.  Simultaneous phase correction and SENSE reconstruction for navigated multi‐shot DWI with non‐cartesian k‐space sampling , 2005, Magnetic resonance in medicine.

[25]  Norbert Schuff,et al.  Improved diffusion imaging through SNR‐enhancing joint reconstruction , 2013, Magnetic resonance in medicine.

[26]  Ross T. Whitaker,et al.  Rician Noise Removal in Diffusion Tensor MRI , 2006, MICCAI.

[27]  Ludovico Minati,et al.  Physical foundations, models, and methods of diffusion magnetic resonance imaging of the brain: A review , 2007 .

[28]  Thierry Blu,et al.  Monte-Carlo Sure: A Black-Box Optimization of Regularization Parameters for General Denoising Algorithms , 2008, IEEE Transactions on Image Processing.

[29]  N. Makris,et al.  High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity , 2002, Magnetic resonance in medicine.

[30]  Dae-Shik Kim,et al.  Spatial resolution dependence of DTI tractography in human occipito-callosal region , 2006, NeuroImage.

[31]  G. Sapiro,et al.  Reconstruction of the orientation distribution function in single‐ and multiple‐shell q‐ball imaging within constant solid angle , 2010, Magnetic resonance in medicine.

[32]  Yogesh Rathi,et al.  Spatially Regularized Compressed Sensing for High Angular Resolution Diffusion Imaging , 2011, IEEE Transactions on Medical Imaging.

[33]  C. Hardy,et al.  Accelerated diffusion spectrum imaging in the human brain using compressed sensing , 2011, Magnetic resonance in medicine.

[34]  R. Stollberger,et al.  Improved diffusion‐weighted single‐shot echo‐planar imaging (EPI) in stroke using sensitivity encoding (SENSE) , 2001, Magnetic resonance in medicine.

[35]  Norbert Schuff,et al.  Denoising diffusion-weighted MR magnitude image sequences using low rank and edge constraints , 2012, 2012 9th IEEE International Symposium on Biomedical Imaging (ISBI).

[36]  Derek K. Jones,et al.  Estimating the number of fiber orientations in diffusion MRI voxels : a constrained spherical deconvolution study , 2010 .

[37]  A. Anderson,et al.  Reduction of noise in diffusion tensor images using anisotropic smoothing , 2005, Magnetic resonance in medicine.

[38]  M. Moseley,et al.  Self‐navigated interleaved spiral (SNAILS): Application to high‐resolution diffusion tensor imaging , 2004, Magnetic resonance in medicine.

[39]  M. Lustig,et al.  Compressed Sensing MRI , 2008, IEEE Signal Processing Magazine.

[40]  Timothy Edward John Behrens,et al.  Characterization and propagation of uncertainty in diffusion‐weighted MR imaging , 2003, Magnetic resonance in medicine.

[41]  Andrew L. Alexander,et al.  Computation of Diffusion Function Measures in $q$ -Space Using Magnetic Resonance Hybrid Diffusion Imaging , 2008, IEEE Transactions on Medical Imaging.

[42]  Rémi Gribonval,et al.  Sparse representations in unions of bases , 2003, IEEE Trans. Inf. Theory.

[43]  Guy B. Williams,et al.  Inference of multiple fiber orientations in high angular resolution diffusion imaging , 2005, Magnetic resonance in medicine.

[44]  Rachid Deriche,et al.  Compressed Sensing for Accelerated EAP Recovery in Diffusion MRI , 2010, MICCAI 2010.

[45]  Mariano Rivera,et al.  Diffusion Basis Functions Decomposition for Estimating White Matter Intravoxel Fiber Geometry , 2007, IEEE Transactions on Medical Imaging.

[46]  Mathews Jacob,et al.  Efficient NUFFT algorithm for non-Cartesian MRI reconstruction , 2009, 2009 IEEE International Symposium on Biomedical Imaging: From Nano to Macro.

[47]  Jan Sijbers,et al.  Super‐resolution for multislice diffusion tensor imaging , 2013, Magnetic resonance in medicine.

[48]  D. Parker,et al.  Analysis of partial volume effects in diffusion‐tensor MRI , 2001, Magnetic resonance in medicine.

[49]  C.P. Lin,et al.  Reduced encoding of diffusion spectrum imaging with cross-term correction , 2003, First International IEEE EMBS Conference on Neural Engineering, 2003. Conference Proceedings..

[50]  D. Tuch,et al.  Boosting the sampling efficiency of q‐ball imaging using multiple wavevector fusion , 2007, Magnetic resonance in medicine.

[51]  Emmanuel J. Candès,et al.  Unbiased Risk Estimates for Singular Value Thresholding and Spectral Estimators , 2012, IEEE Transactions on Signal Processing.

[52]  Paul M. Thompson,et al.  How does angular resolution affect diffusion imaging measures? , 2010, NeuroImage.

[53]  I. Daubechies,et al.  Iteratively reweighted least squares minimization for sparse recovery , 2008, 0807.0575.

[54]  Jens Frahm,et al.  Diffusion tensor imaging using partial Fourier STEAM MRI with projection onto convex subsets reconstruction , 2005, Magnetic resonance in medicine.

[55]  E. Miller,et al.  Efficient determination of multiple regularization parameters in a generalized L-curve framework , 2002 .

[56]  Julien Cohen-Adad,et al.  Accelerated diffusion spectrum imaging with compressed sensing using adaptive dictionaries , 2012, MICCAI.

[57]  Wotao Yin,et al.  Bregman Iterative Algorithms for (cid:2) 1 -Minimization with Applications to Compressed Sensing ∗ , 2008 .

[58]  Mathews Jacob,et al.  Sparse spectral deconvolution algorithm for noncartesian MR spectroscopic imaging , 2014, Magnetic resonance in medicine.

[59]  Otmar Scherzer,et al.  The use of Morozov's discrepancy principle for Tikhonov regularization for solving nonlinear ill-posed problems , 1993, Computing.

[60]  Mathews Jacob,et al.  Accelerating non-Cartesian sense for large coil arrays: Application to motion compensation in multishot DWI , 2012, 2012 9th IEEE International Symposium on Biomedical Imaging (ISBI).

[61]  K. Trinkaus,et al.  Quantification of increased cellularity during inflammatory demyelination. , 2011, Brain : a journal of neurology.

[62]  Anh T Van,et al.  High‐resolution diffusion tensor imaging of the human pons with a reduced field‐of‐view, multishot, variable‐density, spiral acquisition at 3 T , 2009, Magnetic resonance in medicine.

[63]  P. Grenier,et al.  MR imaging of intravoxel incoherent motions: application to diffusion and perfusion in neurologic disorders. , 1986, Radiology.