Noise and signal decoupling in maximum likelihood reconstructions and Metz filters for PET images

The authors have chosen some Metz filters for FBP (filtered backprojection) reconstructions based on matching the mean signal amplitude spectra of FBP images with those of ML (maximum likelihood) reconstructions. It is demonstrated that, for the mean signal behavior, FBP with Metz filters of various orders can achieve similar performance to ML over a range of image resolution. However, for images with resolution beyond the intrinsic detector resolution, the variance as shown by the noise power spectrum increased significantly for FBP compared to ML. This suggested that the noise was decoupled from the signal in the process of signal recovery for ML due to its noise model and nonlinearity. Such decoupling is not possible with FBP. However, ML has very limited advantages over FBP for most images with resolution equivalent to or lower than the intrinsic resolution, or if mean signals are obtained from a large number of noisy ensembles