Dependence of parallel imaging with linear predictability on the undersampling direction

Parallel imaging with linear predictability takes advantage of information present in multiple receive coils to accurately reconstruct the image with fewer samples. Commonly used algorithms based on linear predictability include GRAPPA and SPIRiT. We present a sufficient condition for an accurate reconstruction based on the direction of undersampling and the arrangement of the sensing coils. We show, with examples, that the quality of the reconstruction can be high or low for the same data based on whether this condition is met or not met, respectively. We also propose a metric—the acceleration direction metric (ADM)—that uses a fully sampled region centered on the 0 frequency to identify which direction(s) of undersampling would allow for a good-quality image reconstruction prior to full data collection.