Computing Null Space Hallucinations on Simulated SPECT Image Reconstructions

Iterative reconstruction techniques have been integrated into clinical practice for emission tomography reconstruction. While these techniques have shown promising results in image reconstruction, there remains a lack of clarity regarding which parts of the image are reliably estimated and which are not. Currently, there is a missing measure to differentiate between epistemic and aleatoric errors. One approach to address this issue is to estimate the null space of the imaging model for a given object. In this study, we utilize a previously proposed adaptation of the Landweber iteration, known as the Wilson-Barret method, for calculating the null space of a noiseless reference phantom and for a corresponding reconstruction of a simulated phantom. Using the calculated null spaces we can apply a method for creating hallucination maps, that allow derivation of the epistemic error. Our findings suggest that the hallucinated components of the image are primarily attributable to the edges or high-frequency components of the phantom as well as the center of the phantom, which is consistent with expectations.