Lower variance FBP image reconstruction via new filter families

Linear one-step reconstruction algorithms such as filtered backprojection (FBP) have some advantages compared to EM iterative reconstruction: linearity, reduced reconstruction time and more accurate quantification in low count regions (i.e. lower bias). As such, FBP is often preferred for dynamic PET imaging, which requires both the reconstruction of many image frames and accurate quantification. However, FBP algorithms often exhibit high variance in the reconstructed images (i.e. low precision). Whilst this can be countered by projection or image-space smoothing, these operations degrade the resolution of the final image. In contrast, EM reconstruction can reduce image variance with better resolution preservation via early stopping of the algorithm, where the reconstruction error (bias and variance) is minimised well before convergence. Despite the bias, these low-variance early iterations often result in lower overall reconstruction error compared to regular FBP reconstruction. This work investigates new families of filters for FBP which seek to emulate these benefits of early EM iterates, by reducing variance and preserving a higher-level of spatial resolution compared to conventional smoothing (but at the cost of increased bias) using a linear and fast one-step reconstruction algorithm. The proposal is that, for some imaging tasks, images possessing lower reconstruction error with improved resolution (but biased) are preferable. Initial results show contrast-noise performance which is competitive with OSEM, and in the case of colder regions a performance which is superior to OSEM.