Motion-Adaptive Spatio-Temporal Regularization ( MASTeR ) for Accelerated Dynamic MRI

Accelerated MRI techniques reduce signal acquisition time by undersampling k-space. A fundamental problem in accelerated MRI is the recovery of quality images from undersampled k-space data. Current state-of-the-art recovery algorithms exploit the spatial and temporal structures in underlying images to improve the reconstruction quality. In recent years, compressed sensing theory has helped formulate mathematical principles and conditions that ensure recovery of (structured) sparse signals from undersampled, incoherent measurements. In this paper, a new recovery algorithm, motion-adaptive spatio-temporal regularization (MASTeR), is presented. MASTeR, which uses compressed sensing principles to recover dynamic MR images from highly undersampled kspace data, takes advantage of spatial and temporal structured sparsity in MR images. In contrast to existing algorithms, MASTeR models temporal sparsity using motion-adaptive linear transformations between neighboring images. The efficiency of MASTeR is demonstrated with experiments on cardiac MRI for a range of reduction factors. Results are also compared with k-t FOCUSS with motion estimation and compensation—another recently proposed recovery algorithm for dynamic MRI.

[1]  Yin Zhang,et al.  Fixed-Point Continuation for l1-Minimization: Methodology and Convergence , 2008, SIAM J. Optim..

[2]  Ajay Luthra,et al.  Overview of the H.264/AVC video coding standard , 2003, IEEE Trans. Circuits Syst. Video Technol..

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

[4]  Anil K. Jain,et al.  Displacement Measurement and Its Application in Interframe Image Coding , 1981, IEEE Trans. Commun..

[5]  Julian Magarey,et al.  Motion estimation using a complex-valued wavelet transform , 1998, IEEE Trans. Signal Process..

[6]  Emmanuel J. Candès,et al.  Decoding by linear programming , 2005, IEEE Transactions on Information Theory.

[7]  A. A. Samsonov,et al.  Design of Temporally Constrained Compressed Sensing Methods for Accelerated Dynamic MRI , 2009 .

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

[9]  Michael Lustig,et al.  k-t SPARSE: High frame rate dynamic MRI exploiting spatio-temporal sparsity , 2006 .

[10]  R. Srinivasan,et al.  Predictive Coding Based on Efficient Motion Estimation , 1985, IEEE Trans. Commun..

[11]  Bruno Madore,et al.  UNFOLD‐SENSE: A parallel MRI method with self‐calibration and artifact suppression , 2004, Magnetic resonance in medicine.

[12]  David J. Fleet,et al.  Performance of optical flow techniques , 1994, International Journal of Computer Vision.

[13]  Jong Chul Ye,et al.  Motion estimated and compensated compressed sensing dynamic magnetic resonance imaging: What we can learn from video compression techniques , 2010, Int. J. Imaging Syst. Technol..

[14]  Berthold K. P. Horn,et al.  Determining Optical Flow , 1981, Other Conferences.

[15]  A TroppJoel Corrigendum in "Just relax: Convex programming methods for identifying sparse signals in noise" , 2009 .

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

[17]  Michael B. Wakin,et al.  A multiscale framework for Compressive Sensing of video , 2009, 2009 Picture Coding Symposium.

[18]  Thomas Brox,et al.  High Accuracy Optical Flow Estimation Based on a Theory for Warping , 2004, ECCV.

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

[20]  Michael T. Orchard,et al.  Overlapped block motion compensation: an estimation-theoretic approach , 1994, IEEE Trans. Image Process..

[21]  F. Sebert,et al.  SparseSENSE: Randomly-Sampled Parallel Imaging using Compressed Sensing , 2007 .

[22]  Rama Chellappa,et al.  P2C2: Programmable pixel compressive camera for high speed imaging , 2011, CVPR 2011.

[23]  Richard Baraniuk,et al.  The Dual-tree Complex Wavelet Transform , 2007 .

[24]  Jong Chul Ye,et al.  k‐t FOCUSS: A general compressed sensing framework for high resolution dynamic MRI , 2009, Magnetic resonance in medicine.

[25]  José Millet-Roig,et al.  Noquist: Reduced field‐of‐view imaging by direct Fourier inversion , 2004, Magnetic resonance in medicine.

[26]  Gary J. Sullivan,et al.  Video Compression - From Concepts to the H.264/AVC Standard , 2005, Proceedings of the IEEE.

[27]  Leon Axel,et al.  Combination of Compressed Sensing and Parallel Imaging for Highly-Accelerated 3 D First-Pass Cardiac Perfusion MRI , 2009 .

[28]  Ce Liu,et al.  Exploring new representations and applications for motion analysis , 2009 .

[29]  Axthonv G. Oettinger,et al.  IEEE Transactions on Information Theory , 1998 .

[30]  D. Kacher,et al.  Sensitivity profiles from an array of coils for encoding and reconstruction in parallel (SPACE RIP) , 2000, Magnetic resonance in medicine.

[31]  Emmanuel J. Candès,et al.  Templates for convex cone problems with applications to sparse signal recovery , 2010, Math. Program. Comput..

[32]  Robert H. Halstead,et al.  Matrix Computations , 2011, Encyclopedia of Parallel Computing.

[33]  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.

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

[35]  L. Ying,et al.  Accelerating SENSE using compressed sensing , 2009, Magnetic resonance in medicine.

[36]  David Moratal,et al.  “PINOT”: Time‐resolved parallel magnetic resonance imaging with a reduced dynamic field of view , 2011, Magnetic resonance in medicine.

[37]  Emmanuel J. Candès,et al.  NESTA: A Fast and Accurate First-Order Method for Sparse Recovery , 2009, SIAM J. Imaging Sci..

[38]  Mário A. T. Figueiredo,et al.  Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems , 2007, IEEE Journal of Selected Topics in Signal Processing.

[39]  E. Candès,et al.  Sparsity and incoherence in compressive sampling , 2006, math/0611957.

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

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

[42]  F H Epstein,et al.  Adaptive sensitivity encoding incorporating temporal filtering (TSENSE) † , 2001, Magnetic resonance in medicine.