In Emission Tomography the design of the Imaging System has a great influence on the quality of the output image. Optimisation of the system design is a difficult problem due to the computational complexity and to the challenges in its mathematical formulation. In order to compare different system designs, an efficient and effective method to calculate the Image Quality is needed. In this thesis the statistical and deterministic methods for the calculation of the uncertainty in the reconstruction are presented. In the deterministic case, the Fisher Information Matrix (FIM) formalism can be employed to characterize such uncertainty. Unfortunately, computing, storing and inverting the FIM is not feasible with 3D imaging systems. In order to tackle the problem of the computational load in calculating the inverse of the FIM a novel approximation, that relies on a sub-sampling of the FIM, is proposed. The FIM is calculated over a subset of voxels arranged in a grid that covers the whole volume. This formulation reduces the computational complexity in inverting the FIM but nevertheless accounts for the global interdependence between the variables, for the acquisition geometry and for the object dependency. Using this approach, the noise properties as a function of the system geometry parameterisation were investigated for three different cases. In the first study, the design of a parallel-hole collimator for SPECT is optimised. The new method can be applied to evaluating problems like trading-off collimator resolution and sensitivity. In the second study, the reconstructed image quality was evaluated in the case of truncated projection data; showing how the subsampling approach is very accurate for evaluating the effects of missing data. Finally, the noise properties of a D-SPECT system were studied for varying acquisition protocols; showing how the new method is well-suited to problems like optimising adaptive data sampling schemes
