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 MRI 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.

For the last two years, we have been experimenting with applying compressed sensing parallel imaging for body imaging of pediatric patients. It is a joint-effort by teams from UC Berkeley, Stanford University and GE Healthcare. This paper aims to summarize our experience so far. We describe our acquisition approach: 3D spoiled-gradient-echo with poisson-disc random undersampling of the phase encodes. Our re-construction approach: ℓ1-SPIRiT, an iterative autocalibrating parallel imaging reconstruction that enforces both data consistency and joint-sparsity in the wavelet domain. Our implementation: an on-line parallelized implementation of ℓ1-SPIRiT on multi-core CPU and General Purpose Graphics Processors (GPGPU) that achieves sub-minute 3D reconstructions with 8-channels. Clinical results showing higher quality reconstruction and better diagnostic confidence than parallel imaging alone at accelerations on the order of number of coils.

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