Regularization in multiplexed PET image reconstruction

Multiplexed PET (mPET) using one tracer labeled with a positron plus prompt gamma ray emitter is limited by low sensitivity to triple-photon coincidences (two annihilation photons and one prompt gamma photon), leading to high noise in the reconstructed images.

The use of regularization has been previously shown to increase the image quality of single tracer PET images under low signal-to-noise ratio conditions. We will demonstrate the use of regularization in simultaneously acquired multi-tracer mPET data reconstruction.

First, we present how a maximum a posteriori expectation maximization solution can be obtained for simultaneously acquired multi-isotope PET data. Next, we use a Monte Carlo simulation of an image quality phantom mPET acquisition with a pure positron (¹⁸F) and a positron plus prompt gamma (⁴⁴Sc) emitter to evaluate the performance of different regularization methods.

For a baseline regularization method to simultaneously reconstruct both activity distributions, we show that a relative difference penalty (RDP) provides the best tradeoff of the penalty functions tested in image quality and quantitative accuracy for a simulated hot sphere phantom compared to quadratic and log-cosh penalty functions, with a contrast-to-noise ratio (CNR) in ¹⁸F/⁴⁴Sc of over 60% higher on average for the RDP compared to the quadratic penalty in the largest spheres. However, this regularization approach has up to 2x worse reconstructed inter-tracer crosstalk ratio compared to unregularized reconstruction. Finally, we present a further optimization by alternating reconstruction of the two individual tracer images with regularization to achieve a CNR in the largest ¹⁸F/⁴⁴Sc spheres with an up to 35% improvement on average over the simultaneous RDP-based regularization reconstruction results described above, while maintaining a 10%-20% lower inter-tracer crosstalk ratio over the unregularized reconstruction.

For the selected radionuclides, simulated system and phantom, we demonstrate proof-of-principle that using regularization applied to an alternating update form of EM achieves significantly higher CNR in both tracers compared to unregularized alternating update OSEM and regularized simultaneous OSEM, with significantly lower crosstalk in the prompt gamma emitter reconstruction than the regularized simultaneous OSEM.