Iterative FBP using new families of empirical filters

PET images reconstructed using the filtered backprojection (FBP) algorithm have the advantage of being unbiased but at the cost of exhibiting a high variance. The latter effect is often the dominant factor in clinical practice. Recently we have proposed new families of filters for FBP reconstruction that were designed so that the FBP reconstructions using these filters emulate the error properties of OSEM reconstructions (i.e. exhibiting some level of bias but with reduced variance). In this study these families of filters are used as the reconstruction filters prior to backprojection in iterative FBP (IFBP). Using these filters the convergence rate of the IFBP algorithm can be controlled. Two well known special cases correspond to the conventional IFBP with ramp filter and the Landweber method, reaching the highest and lowest convergence speeds respectively. In addition the range of filters in the filter family allows exploration of a range of bias variance trade-off curves, with the Landweber method reaching the lowest mean squared error (MSE). Additionally optional non-negativity constraints can be included allowing still different bias variance trade-offs. In conclusion it is found that the use of filters with a lower inversion power result in a slower convergence of the IFBP algorithm but the resulting images can reach a lower MSE. It is shown that, for a cold region, adding the non-negativity constraint effectively reduces the variance but at the cost of introducing a bias. For a range of filters from the new filter families, it is found that the IFBP algorithm using these filters can outperform both the conventional IFBP using the ramp filter, FBP and OSEM reconstructions in terms of MSE. The optional non-negativity constraint can aid in further reducing the MSE depending on the ROI and ROI size. Therefore, using the new filters in FBP permits a compromise between reconstruction speed and the reconstruction error.