  Since its discovery over the last decade, Compressed Sensing (CS) has been
successfully applied to Magnetic Reso- nance Imaging (MRI). It has been shown
to be a powerful way to reduce scanning time without sacrificing image quality.
MR images are actually strongly compressible in a wavelet basis, the latter
being largely incoherent with the k-space or spatial Fourier domain where
acquisition is performed. Nevertheless, since its first application to MRI [1],
the theoretical justification of actual k-space sampling strategies is
questionable. Indeed, the vast majority of k-space sampling distributions have
been heuris- tically designed (e.g., variable density) or driven by
experimental feasibility considerations (e.g., random radial or spiral sampling
to achieve smoothness k-space trajectory). In this paper, we try to reconcile
very recent CS results with the MRI specificities (mag- netic field gradients)
by enforcing the measurements, i.e. samples of k-space, to fit continuous
trajectories. To this end, we propose random walk continuous sampling based on
Markov chains and we compare the reconstruction quality of this scheme to the
state- of-the art.
