Image registration guided, sparsity constrained reconstructions for dynamic MRI.

It is generally a challenging task to reconstruct dynamic magnetic resonance (MR) images with high spatial and high temporal resolutions, especially with highly incomplete k-space sampling. In this work, a novel method that combines a non-rigid image registration technique with sparsity-constrained image reconstruction is introduced. Employing a multi-resolution free-form deformation technique with B-spline interpolations, the non-rigid image registration accurately models the complex deformations of the physiological dynamics, and provides artifact-suppressed high spatial-resolution predictions. Based on these prediction images, the sparsity-constrained data fidelity-enforced image reconstruction further improves the reconstruction accuracy. When compared with the k-t FOCUSS with motion estimation/motion compensation (MEMC) technique on volunteer scans, the proposed method consistently outperforms in both the spatial and the temporal accuracy with variously accelerated k-space sampling. High fidelity reconstructions for dynamic systolic phases with reduction factor of 10 and cardiac perfusion series with reduction factor of 3 are presented.

[1]  Marc Teboulle,et al.  A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems , 2009, SIAM J. Imaging Sci..

[2]  N J Pelc,et al.  Temporal resolution improvement in dynamic imaging , 1996, Magnetic resonance in medicine.

[3]  Feng Huang,et al.  k‐t GRAPPA: A k‐space implementation for dynamic MRI with high reduction factor , 2005, Magnetic resonance in medicine.

[4]  Steven A. Orszag,et al.  CBMS-NSF REGIONAL CONFERENCE SERIES IN APPLIED MATHEMATICS , 1978 .

[5]  Zhi-Pei Liang,et al.  SPATIOTEMPORAL IMAGINGWITH PARTIALLY SEPARABLE FUNCTIONS , 2007, 2007 4th IEEE International Symposium on Biomedical Imaging: From Nano to Macro.

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

[7]  Z P Liang,et al.  Fast dynamic imaging using two reference images , 1996, Magnetic resonance in medicine.

[8]  Yoram Bresler,et al.  MR Image Reconstruction From Highly Undersampled k-Space Data by Dictionary Learning , 2011, IEEE Transactions on Medical Imaging.

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

[10]  Zhi-Pei Liang,et al.  An efficient method for dynamic magnetic resonance imaging , 1994, IEEE Trans. Medical Imaging.

[11]  Ling Xia,et al.  Sparsity-constrained SENSE reconstruction: an efficient implementation using a fast composite splitting algorithm. , 2013, Magnetic resonance imaging.

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

[13]  Jürgen Weese,et al.  A comparison of similarity measures for use in 2-D-3-D medical image registration , 1998, IEEE Transactions on Medical Imaging.

[14]  Guy Marchal,et al.  Multimodality image registration by maximization of mutual information , 1997, IEEE Transactions on Medical Imaging.

[15]  G. Wahba Spline models for observational data , 1990 .

[16]  Junzhou Huang,et al.  Efficient MR image reconstruction for compressed MR imaging , 2011, Medical Image Anal..

[17]  Stephen L. Keeling,et al.  An image space approach to Cartesian based parallel MR imaging with total variation regularization , 2012, Medical Image Anal..

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

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

[20]  K. Scheffler,et al.  Analysis and compensation of eddy currents in balanced SSFP , 2005, Magnetic resonance in medicine.

[21]  Bo Liu,et al.  A statistical approach to SENSE regularization with arbitrary k‐space trajectories , 2008, Magnetic resonance in medicine.

[22]  Justin P. Haldar,et al.  Image Reconstruction From Highly Undersampled $( {\bf k}, {t})$-Space Data With Joint Partial Separability and Sparsity Constraints , 2012, IEEE Transactions on Medical Imaging.

[23]  Michael Elad,et al.  Submitted to Ieee Transactions on Image Processing Image Decomposition via the Combination of Sparse Representations and a Variational Approach , 2022 .

[24]  J. C. Ye,et al.  Projection reconstruction MR imaging using FOCUSS , 2007, Magnetic resonance in medicine.

[25]  Suyash P. Awate,et al.  Spatiotemporal dictionary learning for undersampled dynamic MRI reconstruction via joint frame-based and dictionary-based sparsity , 2012, 2012 9th IEEE International Symposium on Biomedical Imaging (ISBI).

[26]  D. Hill,et al.  Medical image registration , 2001, Physics in medicine and biology.

[27]  Sung Yong Shin,et al.  Scattered Data Interpolation with Multilevel B-Splines , 1997, IEEE Trans. Vis. Comput. Graph..

[28]  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.

[29]  Graeme P. Penney,et al.  2007 4TH IEEE INTERNATIONAL SYMPOSIUM ON BIOMEDICAL IMAGING : MACRO TO NANO, VOLS 1-3 , 2007 .

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

[31]  Zhi-Pei Liang,et al.  Real-time cardiac MRI without triggering, gating, or breath holding , 2008, 2008 30th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[32]  Daniel Rueckert,et al.  Nonrigid registration using free-form deformations: application to breast MR images , 1999, IEEE Transactions on Medical Imaging.

[33]  A G Webb,et al.  Applications of reduced‐encoding MR imaging with generalized‐series reconstruction (RIGR) , 1993, Journal of magnetic resonance imaging : JMRI.

[34]  Hong Jiang,et al.  Dynamic imaging by model estimation , 1997 .

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

[36]  J. J. van Vaals,et al.  “Keyhole” method for accelerating imaging of contrast agent uptake , 1993, Journal of magnetic resonance imaging : JMRI.

[37]  Feng Huang,et al.  Improved partial k-space reconstruction technique for dynamic myocardial perfusion MRI , 2005, 2005 IEEE Engineering in Medicine and Biology 27th Annual Conference.

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

[39]  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.

[40]  Peter Boesiger,et al.  Compressed sensing in dynamic MRI , 2008, Magnetic resonance in medicine.

[41]  M Zaitsev,et al.  Shared k‐space echo planar imaging with keyhole , 2001, Magnetic resonance in medicine.

[42]  X Hu,et al.  Continuous Update with Random Encoding (CURE): A New Strategy for Dynamic Imaging , 1995, Magnetic resonance in medicine.

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

[44]  Mathews Jacob,et al.  Accelerated Dynamic MRI Exploiting Sparsity and Low-Rank Structure: k-t SLR , 2011, IEEE Transactions on Medical Imaging.

[45]  Didier Le Gall,et al.  MPEG: a video compression standard for multimedia applications , 1991, CACM.

[46]  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.

[47]  G. Pohost,et al.  Block Regional Interpolation Scheme for k‐Space (BRISK): A Rapid Cardiac Imaging Technique , 1995, Magnetic resonance in medicine.

[48]  D. L. Donoho,et al.  Compressed sensing , 2006, IEEE Trans. Inf. Theory.

[49]  Junfeng Yang,et al.  A New Alternating Minimization Algorithm for Total Variation Image Reconstruction , 2008, SIAM J. Imaging Sci..

[50]  Mark Holden,et al.  A Review of Geometric Transformations for Nonrigid Body Registration , 2008, IEEE Transactions on Medical Imaging.

[51]  Kay Nehrke,et al.  k‐t PCA: Temporally constrained k‐t BLAST reconstruction using principal component analysis , 2009, Magnetic resonance in medicine.

[52]  Feng Huang,et al.  k‐t sparse GROWL: Sequential combination of partially parallel imaging and compressed sensing in k‐t space using flexible virtual coil , 2012, Magnetic resonance in medicine.

[53]  Zhi-Pei Liang,et al.  Real-time cardiac MRI using prior spatial-spectral information , 2009, 2009 Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[54]  O. Haraldseth,et al.  K‐space substitution: A novel dynamic imaging technique , 1993, Magnetic resonance in medicine.

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

[56]  Jong Chul Ye,et al.  Radial k‐t FOCUSS for high‐resolution cardiac cine MRI , 2010, Magnetic resonance in medicine.