Nuclear medicine images are degraded by blurring caused by the gamma camera system response function and the inherent Poisson noise of radioactivity. Well known digital filters proposed for the restoration of these images have been investigated in this thesis. Particularly, Metz filter and a two-step filter have been extensively studied by the FROC methodology. The effectiveness and practical limitations of the FROC methodology in the assessment of nuclear medicine images have also been investigated. It was observed from the results that the closeness of test patterns to the real clinical cases was a crucial factor for a successful assessment. Therefore, a method to simulate clinical bone scans with focal abnormalities at a given depth has been developed in this thesis. A binormal model is used for the analysis of the FROC and AFROC results. A method has been developed in this thesis to determine the parameters that completely specify the binormal model. Using this method it has been shown in this work that the two-step filter may be useful in detecting focal abnormalities from complicated structures such as bone scans at strict criteria. It also has been observed in this work, that the Metz filter is useful for the detection of focal abnormalities in flat noise fields, but not in complicated structures such as bone scans.