Self-Supervised Reference-Free Penalty Selection for Regularised PET Image Reconstruction

The use of penalised maximum likelihood methods allows theoretically justified, convergent noise reduction in PET image reconstruction. However, the choice of penalty function and penalty strength are design parameters and the output images are strongly dependent on the user’s choice. Previous work has aimed to address this issue by using bootstrap methods to automatically calculate the penalty strength on-the-fly during the reconstruction. This bootstrap-optimised method was shown to provide near-optimal values of penalty strength across a range of noise levels, but with the restriction that the functional form of the penalty had to be specified. In this work we extend this methodology to enable selection of the penalty function alongside optimisation of the penalty strength. Assuming appropriately normalised penalty functions, we hypothesise that the penalty strengths returned by the bootstrap-optimised reconstructions are indicative of image quality, with higher values reflecting more optimal reconstructions. This hypothesis was tested in 2D simulation studies using the weighted quadratic penalty. Specifically, various guided and unguided penalties were considered, and the relationship between reconstruction error and output penalty strength was investigated. Results showed that when using the bootstrap-optimised framework, guided reconstructions produced higher penalty strengths, correlating with reduced reconstruction error. When the guidance information was intentionally mis-aligned, the bootstrap-optimised reconstruction produced lower penalty strengths, corresponding to higher reconstruction error. These results suggest that the penalty strength output from bootstrap-optimised penalised PET image reconstruction may be a reference-free surrogate for reconstruction error, allowing self-supervised penalty selection. Future work includes acceleration and application to a wider range of penalty functions.