Fast $\ell_1$ -SPIRiT Compressed Sensing Parallel Imaging MRI: Scalable Parallel Implementation and Clinically Feasible Runtime

We present l1 -SPIRiT, a simple algorithm for auto calibrating parallel imaging (acPI) and compressed sensing (CS) that permits an efficient implementation with clinically-feasible runtimes. We propose a CS objective function that minimizes cross-channel joint sparsity in the wavelet domain. Our reconstruction minimizes this objective via iterative soft-thresholding, and integrates naturally with iterative self-consistent parallel imaging (SPIRiT). Like many iterative magnetic resonance imaging reconstructions, l1-SPIRiT's image quality comes at a high computational cost. Excessively long runtimes are a barrier to the clinical use of any reconstruction approach, and thus we discuss our approach to efficiently parallelizing l1 -SPIRiT and to achieving clinically-feasible runtimes. We present parallelizations of l1 -SPIRiT for both multi-GPU systems and multi-core CPUs, and discuss the software optimization and parallelization decisions made in our implementation. The performance of these alternatives depends on the processor architecture, the size of the image matrix, and the number of parallel imaging channels. Fundamentally, achieving fast runtime requires the correct trade-off between cache usage and parallelization overheads. We demonstrate image quality via a case from our clinical experimentation, using a custom 3DFT spoiled gradient echo (SPGR) sequence with up to 8× acceleration via Poisson-disc undersampling in the two phase-encoded directions.

[1]  Robert D. Nowak,et al.  An EM algorithm for wavelet-based image restoration , 2003, IEEE Trans. Image Process..

[2]  Peter Boesiger,et al.  Array compression for MRI with large coil arrays , 2007, Magnetic resonance in medicine.

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

[4]  T. Hohage,et al.  Image reconstruction by regularized nonlinear inversion—Joint estimation of coil sensitivities and image content , 2008, Magnetic resonance in medicine.

[5]  Leslie Ying,et al.  Joint image reconstruction and sensitivity estimation in SENSE (JSENSE) , 2007, Magnetic resonance in medicine.

[6]  Dwight G. Nishimura,et al.  Rapid gridding reconstruction with a minimal oversampling ratio , 2005, IEEE Transactions on Medical Imaging.

[7]  Xiaoping P. Hu,et al.  Iterative GRAPPA (iGRAPPA) for improved parallel imaging reconstruction , 2008, Magnetic resonance in medicine.

[8]  Samuel Williams,et al.  The Landscape of Parallel Computing Research: A View from Berkeley , 2006 .

[9]  Wei Lin,et al.  A rapid and robust numerical algorithm for sensitivity encoding with sparsity constraints: Self‐feeding sparse SENSE , 2010, Magnetic resonance in medicine.

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

[11]  David Atkinson,et al.  Real-Time Reconstruction of Sensitivity Encoded Radial Magnetic Resonance Imaging Using a Graphics Processing Unit , 2009, IEEE Transactions on Medical Imaging.

[12]  Philip J. Bones,et al.  Prior estimate‐based compressed sensing in parallel MRI , 2011, Magnetic resonance in medicine.

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

[14]  Pradeep Dubey,et al.  High-Performance 3D Compressive Sensing MRI Reconstruction Using Many-Core Architectures , 2011, Int. J. Biomed. Imaging.

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

[16]  Eero P. Simoncelli,et al.  Image compression via joint statistical characterization in the wavelet domain , 1999, IEEE Trans. Image Process..

[17]  Tobias Schaeffter,et al.  Accelerating the Nonequispaced Fast Fourier Transform on Commodity Graphics Hardware , 2008, IEEE Transactions on Medical Imaging.

[18]  J. Pauly,et al.  Array Compression for 3 D Cartesian Sampling , 2010 .

[19]  L. Axel,et al.  Combination of Compressed Sensing and Parallel Imaging with Respiratory Motion Correction for Highly-Accelerated First-Pass Cardiac Perfusion MRI , 2010 .

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

[21]  D. Noll,et al.  Homodyne detection in magnetic resonance imaging. , 1991, IEEE transactions on medical imaging.

[22]  V. Tarokh,et al.  A GPU Implementation of Compressed Sensing Reconstruction of 3 D Radial ( Kooshball ) Acquisition for High-Resolution Cardiac MRI , 2010 .

[23]  Justin P. Haldar,et al.  Accelerating advanced MRI reconstructions on GPUs , 2008, J. Parallel Distributed Comput..

[24]  John L. Gustafson,et al.  Reevaluating Amdahl's law , 1988, CACM.

[25]  A. C. Brau,et al.  Efficient L 1 SPIRiT Reconstruction ( ESPIRiT ) for Highly Accelerated 3 D Volumetric MRI with Parallel Imaging and Compressed Sensing , 2009 .

[26]  Armando Manduca,et al.  Sparse‐CAPR: Highly accelerated 4D CE‐MRA with parallel imaging and nonconvex compressive sensing , 2011, Magnetic resonance in medicine.

[27]  Sébastien Roujol,et al.  Online real‐time reconstruction of adaptive TSENSE with commodity CPU/GPU hardware , 2009, Magnetic resonance in medicine.

[28]  D. Donoho,et al.  SPIR-iT : Autocalibrating Parallel Imaging Compressed Sensing , 2008 .

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

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

[31]  K. T. Block,et al.  Undersampled radial MRI with multiple coils. Iterative image reconstruction using a total variation constraint , 2007, Magnetic resonance in medicine.

[32]  K. Bredies,et al.  Parallel imaging with nonlinear reconstruction using variational penalties , 2012, Magnetic resonance in medicine.

[33]  A. C. Brau,et al.  A Method for Autocalibrating 2-D Accelerated Volumetric Parallel Imaging with Clinically Practical Reconstruction Times , 2007 .

[34]  M. Lustig,et al.  Improved pediatric MR imaging with compressed sensing. , 2010, Radiology.

[35]  K. Thulborn,et al.  GPU-Accelerated Gridding for Rapid Reconstruction of Non-Cartesian MRI , 2010 .

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

[37]  Ching-Hua Chang,et al.  Compressed sensing MRI with multichannel data using multicore processors , 2010, Magnetic resonance in medicine.

[38]  P. Boesiger,et al.  Advances in sensitivity encoding with arbitrary k‐space trajectories , 2001, Magnetic resonance in medicine.

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

[40]  Justin P. Haldar,et al.  Impatient MRI: Illinois Massively Parallel Acceleration Toolkit for image reconstruction with enhanced throughput in MRI , 2011, 2011 IEEE International Symposium on Biomedical Imaging: From Nano to Macro.

[41]  D. L. Donoho,et al.  Ideal spacial adaptation via wavelet shrinkage , 1994 .

[42]  M. Lustig,et al.  Clinically Feasible Reconstruction Time for L 1-SPIRiT Parallel Imaging and Compressed Sensing MRI , 2009 .

[43]  Kurt Keutzer,et al.  Practical parallel imaging compressed sensing MRI: Summary of two years of experience in accelerating body MRI of pediatric patients , 2011, 2011 IEEE International Symposium on Biomedical Imaging: From Nano to Macro.

[44]  Justin P. Haldar,et al.  Multi-GPU Implementation for Iterative MR Image Reconstruction with Field Correction , 2011 .