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Purpose: Parallel imaging and compressed sensing reconstructions of large MRIdatasets often have a prohibitive computational cost that bottlenecks clinicaldeployment, especially for 3D non-Cartesian acquisitions. One common approachis to reduce the number of coil channels actively used during reconstruction asin coil compression. While effective for Cartesian imaging, coil compressioninherently loses signal energy, producing shading artifacts that compromiseimage quality for 3D non-Cartesian imaging. We propose coil sketching, ageneral and versatile method for computationally-efficient iterative MR imagereconstruction.  Theory and Methods: We based our method on randomized sketching algorithms, atype of large-scale optimization algorithms well established in the fields ofmachine learning and big data analysis. We adapt the sketching theory to theMRI reconstruction problem via a structured sketching matrix that, similar tocoil compression, considers high-energy virtual coils obtained from principalcomponent analysis. But, unlike coil compression, it also considers randomlinear combinations of the remaining low-energy coils, effectively leveraginginformation from all coils.  Results: First, we performed ablation experiments to validate the sketchingmatrix design on both Cartesian and non-Cartesian datasets. The resultingdesign yielded both improved computational efficiency and preservedsignal-to-noise ratio (SNR) as measured by the inverse g-factor. Then, weverified the efficacy of our approach on high-dimensional non-Cartesian 3Dcones datasets, where coil sketching yielded up to three-fold fasterreconstructions with equivalent image quality.  Conclusion: Coil sketching is a general and versatile reconstructionframework for computationally fast and memory-efficient reconstruction.

Coil Sketching for computationally-efficient MR iterative reconstruction