Reducing data acquisition times in phase-encoded velocity imaging using compressed sensing

We present a method for accelerating the acquisition of phase-encoded velocity images by the use of compressed sensing (CS), a technique that exploits the observation that an under-sampled signal can be accurately reconstructed by utilising the prior knowledge that it is sparse or compressible. We present results of both simulated and experimental measurements of liquid flow through a packed bed of spherical glass beads. For this system, the best image reconstruction used a spatial finite-differences transform. The reconstruction was further improved by utilising prior knowledge of the liquid distribution within the image. Using this approach, we demonstrate that for a sampling fraction of ∼30% of the full k-space data set, the velocity can be recovered with a relative error of 11%, which is below the visually detectable limit. Furthermore, the error in the total flow measured using the CS reconstruction is