Joint reconstruction of PET-MRI by exploiting structural similarity

Matthias J. Ehrhardt, Kris Thielemans, Luis Pizarro, David Atkinson, Sébastien Ourselin, Brian F. Hutton, Simon R. Arridge

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114 Citations (SciVal)


Recent advances in technology have enabled the combination of positron emission tomography (PET) with magnetic resonance imaging (MRI). These PET-MRI scanners simultaneously acquire functional PET and anatomical or functional MRI data. As function and anatomy are not independent of one another the images to be reconstructed are likely to have shared structures. We aim to exploit this inherent structural similarity by reconstructing from both modalities in a joint reconstruction framework. The structural similarity between two modalities can be modelled in two different ways: edges are more likely to be at similar positions and/or to have similar orientations. We analyse the diffusion process generated by minimizing priors that encapsulate these different models. It turns out that the class of parallel level set priors always corresponds to anisotropic diffusion which is sometimes forward and sometimes backward diffusion. We perform numerical experiments where we jointly reconstruct from blurred Radon data with Poisson noise (PET) and under-sampled Fourier data with Gaussian noise (MRI). Our results show that both modalities benefit from each other in areas of shared edge information. The joint reconstructions have less artefacts and sharper edges compared to separate reconstructions and the ℓ2-error can be reduced in all of the considered cases of under-sampling.

Original languageEnglish
Article number015001
JournalInverse Problems
Issue number1
Publication statusPublished - 10 Dec 2014


  • Anisotropic diffusion
  • Compressed sensing
  • Joint inversion
  • Joint reconstruction
  • Magnetic resonance imaging
  • Positron emission tomography
  • Structural similarity

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Mathematical Physics
  • Computer Science Applications
  • Applied Mathematics


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