Optimal single-shot k-space trajectory design for non-Cartesian sparse MRI

Introduction: Sparse MRI [1] is able to reduce the acquisition time and raw data size by significantly undersampling the k-space. However, the issue on how to design an optimal k-space trajectory on sparse k-space is technically challenging and has not been addressed. In this work, we use graphic theory to design an optimized non-Cartesian k-trajectory which can further decrease the acquisition time. The k-space is firstly sampled using the Monto-Carlo sampling schemes [1] and then an optimal single-shot k-trajectory traveling through all these samples is designed using the simulated annealing (SA) algorithm [2]. Finally the corresponding gradient waveforms are designed using the time-optimal gradient algorithm [3]. For comparison, conventional single-shot Cartesian EPI trajectory and spiral trajectory traveling through all the same k-space samples as well as their corresponding gradients are designed. Theory and method: The k-space sampling followed Monte-Carlo incoherent sampling strategy used in Ref. [1]. The SA was then used to design an optimal singleshot k-space trajectory traveling through all these samples. The k-space trajectory was initiated by connecting all the samples using a continuous curve and the cost function of SA was defined as the curve length: