On Retrospective $k$-space Subsampling schemes For Deep MRI Reconstruction

$\textbf{Purpose:}$ The MRI $k$-space acquisition is time consuming. Traditional techniques aim to acquire accelerated data, which in conjunction with recent DL methods, aid in producing high-fidelity images in truncated times. Conventionally, subsampling the $k$-space is performed by utilizing Cartesian-rectilinear trajectories, which even with the use of DL, provide imprecise reconstructions, though, a plethora of non-rectilinear or non-Cartesian trajectories can be implemented in modern MRI scanners. This work investigates the effect of the $k$-space subsampling scheme on the quality of reconstructed accelerated MRI measurements produced by trained DL models. $\textbf{Methods:}$ The RecurrentVarNet was used as the DL-based MRI-reconstruction architecture. Cartesian fully-sampled multi-coil $k$-space measurements from three datasets with different accelerations were retrospectively subsampled using eight distinct subsampling schemes (four Cartesian-rectilinear, two Cartesian non-rectilinear, two non-Cartesian). Experiments were conducted in two frameworks: Scheme-specific, where a distinct model was trained and evaluated for each dataset-subsampling scheme pair, and multi-scheme, where for each dataset a single model was trained on data randomly subsampled by any of the eight schemes and evaluated on data subsampled by all schemes. $\textbf{Results:}$ In the scheme-specific setting RecurrentVarNets trained and evaluated on non-rectilinearly subsampled data demonstrated superior performance especially for high accelerations, whilst in the multi-scheme setting, reconstruction performance on rectilinearly subsampled data improved when compared to the scheme-specific experiments. $\textbf{Conclusion:}$ Training DL-based MRI reconstruction algorithms on non-rectilinearly subsampled measurements can produce more faithful reconstructions.