Compressed sensing with super-resolution in magnetic resonance using quadratic phase modulation

In recent years, compressed sensing (CS) has attracted considerable attention in areas of rapid MR imaging. Our group and Y. Wiaux have shown independently that the use of quadratic phase modulation prior to data acquisition can greatly improve the accelerating factor of CS. The use of quadratic phase modulation has distinctive features that the extrapolation of signal by post processing calculation is feasible. In this paper, we propose a novel image reconstruction method in which extrapolation of signal is executed in the CS reconstruction algorithm, resulting in the improvement of spatial resolution. Simulation and experimental studies have revealed that the spatial resolution is fairly improved compared to the images obtained in standard CS based on Fourier transform imaging.