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We apply the event-chain Monte Carlo algorithm to classical continuum spin models on a lattice and clarify the condition for its validity. In the two-dimensional XY model, it outperforms the local Monte Carlo algorithm by two orders of magnitude, although it remains slower than the Wolff cluster algorithm. In the three-dimensional XY spin glass model at low temperature, the event-chain algorithm is far superior to the other algorithms.

The combination of positron emission tomography (PET) with magnetic resonance (MR) imaging opens the way to more accurate diagnosis and improved patient management. At present, the data acquired by PET and MR scanners are essentially processed separately, and the search for ways to improve accuracy of the tomographic reconstruction via synergy of the two imaging techniques is an active area of research. The aim of the collaborative computational project on PET and MR (CCP-PETMR), supported by the UK engineering and physical sciences research council (EPSRC), is to accelerate research in synergistic PET-MR image reconstruction by providing an open access software platform for efficient implementation and validation of novel reconstruction algorithms.

Purpose Respiratory motion‐compensated (MC) 3D cardiac fat‐water imaging at 7T. Methods Free‐breathing bipolar 3D triple‐echo gradient‐recalled‐echo (GRE) data with radial phase‐encoding (RPE) trajectory were acquired in 11 healthy volunteers (7M\4F, 21–35 years, mean: 30 years) with a wide range of body mass index (BMI; 19.9–34.0 kg/m2) and volunteer tailored B1+ shimming. The bipolar‐corrected triple‐echo GRE‐RPE data were binned into different respiratory phases (self‐navigation) and were used for the estimation of non‐rigid motion vector fields (MF) and respiratory resolved (RR) maps of the main magnetic field deviations (ΔB0). RR ΔB0 maps and MC ΔB0 maps were compared to a reference respiratory phase to assess respiration‐induced changes. Subsequently, cardiac binned fat‐water images were obtained using a model‐based, respiratory motion‐corrected image reconstruction. Results The 3D cardiac fat‐water imaging at 7T was successfully demonstrated. Local respiration‐induced frequency shifts in MC ΔB0 maps are small compared to the chemical shifts used in the multi‐peak model. Compared to the reference exhale ΔB0 map these changes are in the order of 10 Hz on average. Cardiac binned MC fat‐water reconstruction reduced respiration induced blurring in the fat‐water images, and flow artifacts are reduced in the end‐diastolic fat‐water separated images. Conclusion This work demonstrates the feasibility of 3D fat‐water imaging at UHF for the entire human heart despite spatial and temporal B1+ and B0 variations, as well as respiratory and cardiac motion.

SIRF is a powerful PET/MR image reconstruction research tool for processing data and developing new algorithms. In this research, new developments to SIRF are presented, with focus on motion estimation and correction. SIRF’s recent inclusion of the adjoint of the resampling operator allows gradient propagation through resampling, enabling the MCIR technique. Another enhancement enabled registering and resampling of complex images, suitable for MRI. Furthermore, SIRF’s integration with the optimization library CIL enables the use of novel algorithms. Finally, SPM is now supported, in addition to NiftyReg, for registration. Results of MR and PET MCIR reconstructions are presented, using FISTA and PDHG, respectively. These demonstrate the advantages of incorporating motion correction and variational and structural priors. This article is part of the theme issue ‘Synergistic tomographic image reconstruction: part 2’.