The derivation and verification of a non-stationary, optimal smoothing filter for nuclear medicine image data

A non-stationary optimal smoothing filter for digital nuclear medicine image data, degraded by Poisson noise, has been derived and applied to temporal simulated and clinical gated blood pool study (GBPS) data. The derived filter is automatically calculated from a large group (library) of similar GBPS which are representative of all studies acquired according to the same protocol in a defined patient population (the ensemble). The filter is designed to minimize the mean-square difference between the filtered data and the true image values; it provides an optimal trade-off between noise reduction and signal degradation for members of the ensemble. The filter is evaluated using a computer simulated ensemble of GBPS. Libraries of Poisson-degraded and non-degraded studies were generated. Libraries of up to 400 Poisson-degraded simulated studies were used to estimate optimal temporal filters that, when applied to Poisson-degraded members of the ensemble not included in the libraries, reduced the mean-square error in the raw data by 65%. When the non-degraded studies were used instead to compute the optimal filter values, the corresponding reduction in the error was 83%. Libraries of previously acquired clinical GBPS were then used to estimate optimal temporal filters for an ensemble of similarly acquired studies. These filters were subsequently applied to studies of 13 patients (not in the original libraries) who received multiple sequential repeat studies. Comparisons of both the filtered and raw data to averages of the repeat studies demonstrated that optimal filters calculated from 400 and 800 clinical studies reduced the mean-square error in the clinical data by 56% and 63% respectively.