Spread spectrum for compressed sensing techniques in magnetic resonance imaging

  • Authors:

  • Y. Wiaux;G. Puy;R. Gruetter;J.-Ph. Thiran;D. Van De Ville;P. Vandergheynst

  • Affiliations:

  • Inst. of Electrical Eng., Ecole Polytechnique Fédérale de Lausanne, Switzerland and Inst. of Bioeng., Ecole Polytechnique Fédérale de Lausanne, Switzerland and Dept. of Radiolo ...;Institute of Electrical Engineering, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland and Institute of the Physics of Biological Systems, Ecole Polytechnique Fédé ...;Institute of the Physics of Biological Systems, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland;Institute of Electrical Engineering, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland;Institute of Bioengineering, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland and Department of Radiology and Medical Informatics, University of Geneva, Geneva, Switzerlan ...;Institute of Electrical Engineering, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

  • Venue:
  • ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
  • Year:
  • 2010

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Abstract

Magnetic resonance imaging (MRI) probes signals through Fourier measurements. Accelerating the acquisition process is of major interest for various MRI applications. The recent theory of compressed sensing shows that sparse or compressible signals may be reconstructed from a small number of random measurements in a sensing basis incoherent with the sparsity basis. In this context, we advocate the use of a chirp modulation of MRI signals prior to probing an incomplete Fourier coverage, in the perspective of accelerating the acquisition process relative to a standard setting with complete coverage. We analyze the spread spectrum phenomenon related to the modulation and we prove its effectiveness in enhancing the overall quality of image reconstruction. We also study its impact at each scale of decomposition in a wavelet sparsity basis. Our preliminary results rely both on theoretical considerations related to the mutual coherence between the sparsity and sensing bases, as well as on numerical simulations from synthetic signals.