From variable density sampling to continuous sampling using Markov chains

Nicolas Chauffert 1, * Philippe Ciuciu 1 Pierre Weiss 2 Fabrice Gamboa 3
* Corresponding author
1 PARIETAL - Modelling brain structure, function and variability based on high-field MRI data
NEUROSPIN - Service NEUROSPIN, Inria Saclay - Ile de France
2 PRIMO, ITAV, UMS3039
ITAV - Institut des Technologies Avancées en sciences du Vivant
Abstract : Since its discovery over the last decade, Compressed Sensing (CS) has been successfully applied to Magnetic Resonance 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 (magnetic 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.
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  • HAL Id : hal-00848286, version 1
  • ARXIV : 1307.6960

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Nicolas Chauffert, Philippe Ciuciu, Pierre Weiss, Fabrice Gamboa. From variable density sampling to continuous sampling using Markov chains. SampTA - 10th Conference International Conference on Sampling Theory and Applications, Jul 2013, Bremen, Germany. pp.200-203. ⟨hal-00848286⟩

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