Ill-posed image recovery requires regularisation to ensure stability. The presented open-source regularisation toolkit consists of state-of-the-art variational algorithms which can be embedded in a plug-and-play fashion into the general framework of proximal splitting methods. The packaged regularisers aim to satisfy various prior expectations of the investigated objects, e.g., their structural characteristics, smooth or non-smooth surface morphology. The flexibility of the toolkit helps with the design of more advanced model-based iterative reconstruction methods for different imaging modalities while operating with simpler building blocks. The toolkit is written for CPU and GPU architectures and wrapped for Python/MATLAB. We demonstrate the functionality of the toolkit in application to Positron Emission Tomography (PET) and X-ray synchrotron computed tomography (CT).
The effect of random coincidences estimation methods on the quantitative accuracy of iterative and analytic reconstruction methods to determine myocardial blood flow (MBF) in PET studies using H<sub>2</sub> <sup>15</sup>O has been investigated. Dynamic scans were acquired on the EXACT3D PET scanner on pigs after H<sub>2</sub> <sup>15</sup>O injection (resting and dipyridamoleinduced stress). Radioactive microspheres (MS) were used to provide a "gold standard" of MBF values. The online subtraction (OS) and maximum likelihood (ML) methods for estimating randoms were combined with (i) 3D-RP, (ii) FORE + attenuation-weighted OSEM, (iii) FORE-FBP and (iv) 3D-OSEM. Factor images were generated and resliced to short axis images; 16 ROIs were defined in the left myocardium and 2 ROIs in the left and right cavities. ROIs were projected onto the dynamic images to extract time-activity-curves, which were then fitted to a single compartment model to estimate absolute MBF. Microsphere measurements were obtained in a similar way and 64 pairs of measurements were made. The ML method improved the SNR of 3D-RP, FORE-FBP, FORE-OSEM, and 3D-OSEM by 8%, 8%, 7% and 3% respectively. Compared to the OS method, the ML method improved the accuracy of coronary flow reserve values of 3DOSEM, 3D-RP, FORE-OSEM and FORE-FBP by 9%, 7%, 1% and 3% respectively. Regression analysis provided better correlation with 3D-OSEM and FORE-OSEM when combined with the ML method. We conclude that the ML method for estimating randoms combined with 3D-OSEM and FORE-OSEM delivers the best performance for absolute quantification of MBF using H<sub>2</sub> <sup>15</sup>O when compared with microsphere measurements.