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

From variable density sampling to continuous sampling using Markov chains