Multi-modal weighted quadratic priors for robust intensity independent synergistic PET-MR reconstruction

In this work, a robust methodology is presented for synergistic PET-MR image reconstruction, irrespective of their relative signal intensities and contrasts. Mutually-weighted quadratic priors were devised to encourage the formation of common boundaries between PET and MR images while reducing noise, PET Gibbs and MR under-sampling artefacts. These priors are iteratively reweighted using normalized multi-modal Gaussian similarity kernels to modulate smoothing across common boundaries. Synergistic reconstruction was performed using a 3-step optimization: i) maximum a posteriori expectation maximization (MAP-EM) for regularized PET reconstruction, ii) penalized weighted least squares with the conjugate gradient algorithm (PWLS-CG) for regularized sensitivity encoding (SENSE) parallel MR reconstruction and iii) update of joint Gaussian kernels. The performance of the proposed prior was compared against standard reconstruction, separate total variation (TV) regularization and prior-image guided reconstruction using 3D realistic simulations and a real PET-MR dataset. Our results showed that TV regularization reduces noise and artifacts in PET and MR images, but at the expense of resolution degradation, while prior-image guided reconstructions, which exploit high quality fully-sampled MR data, notably improve the image quality but at the expense of suppressing unique lesions. Whereas the proposed method, which exploits information obtained from PET and undersampled MR images, leads to noise and artefact reduction while recovery the details and preserving unique lesions. In conclusion, the proposed algorithm was found promising for multi-modal synergistic image reconstruction.