Analysis of generalized rosette trajectory for compressed sensing MRI

Purpose: The application of compressed sensing (CS) technology in magnetic resonance imaging (MRI) is to accelerate the MRI scan speed by incoherent undersampling of k-space data and nonlinear iterative reconstruction of MRI images. This paper generalizes the existing rosette trajectories to configure the sampling patterns for undersampled k-space data acquisition in MRI scans. The arch and curvature characteristics of the generalized rosette trajectories are analysed to explore their feasibility and advantages for CS reconstruction of MRI images. Methods: Two key properties crucial to the CS MRI application, the scan speed and sampling incoherence of the generalized rosette trajectories, are analyzed. The analysis on the scan speed of generalized rosette trajectories is based on the transversal time derived from the curvature of the trajectories,
and the sampling incoherence is based on the evaluation of the point spread function for the measurement matrix. The results of analysis are supported by extensive simulations where the performances of rosette, spiral, and radial sampling patterns at different acceleration factors are compared. Results: It is shown that compared with spiral trajectories, the arch and curvature characteristics of the generalized rosette trajectories are more feasible to meet the physical requirements of undersampled k-space data acquisition in terms of time shortness and scan area. It is further shown that the sampling pattern of the rosette trajectory as higher incoherence than that of the other trajectories and can thus achieve higher reconstruction performance. Reconstruction
performances llustrate that the rosette trajectory can achieve about 10% higher peak signal-to-noise ratio than radial and spiral trajectories under the high acceleration factor R = 10. Conclusions: The generalized rosette trajectories can be a desirable candidate for CS reconstruction of MRI.