Coil sketching for computationally efficient MR iterative reconstruction

Purpose: Parallel imaging and compressed sensing reconstructions of large MRI datasets often have a prohibitive computational cost that bottlenecks clinical deployment, especially for three-dimensional (3D) non-Cartesian acquisitions. One common approach is to reduce the number of coil channels actively used during reconstruction as in coil compression. While effective for Cartesian imaging, coil compression inherently loses signal energy, producing shading artifacts that compromise image quality for 3D non-Cartesian imaging. We propose coil sketching, a general and versatile method for computationally-efficient iterative MR image reconstruction. Theory and Methods: We based our method on randomized sketching algorithms, a type of large-scale optimization algorithms well established in the fields of machine learning and big data analysis. We adapt the sketching theory to the MRI reconstruction problem via a structured sketching matrix that, similar to coil compression, considers high-energy virtual coils obtained from principal component analysis. But, unlike coil compression, it also considers random linear combinations of the remaining low-energy coils, effectively leveraging information from all coils. Results: First, we performed ablation experiments to validate the sketching matrix design on both Cartesian and non-Cartesian datasets. The resulting design yielded both improved computatioanal efficiency and preserved signal-to-noise ratio (SNR) as measured by the inverse g-factor. Then, we verified the efficacy of our approach on high-dimensional non-Cartesian 3D cones datasets, where coil sketching yielded up to three-fold faster reconstructions with equivalent image quality. Conclusion: Coil sketching is a general and versatile reconstruction framework for computationally fast and memory-efficient reconstruction.