Realizing Median Based Filter Using Bootstrap Method and its Application in PET Imaging

Image reconstruction in positron emission tomography (PET) demands multiple scan of an object. This is a tedious task and results in noisy artifacts due to long scan time and object movement. Recently proposed MRP algorithm is found to be very useful in PET. MRP algorithm favors locally monotonic images by penalizing the processed pixel with the median of the surrounding neighborhood pixels and hence performs optimal smoothing. But streaking effects are found in median root prior (MRP) reconstructed image. This necessitates better estimation of the median value. In this paper, we have used a relatively new technique called bootstrap technique which generates multiple observations of the data set from the available dataset (neighborhood estimates in the reconstructed image) for better estimation of the desired parameters (here, local median). This helps in better realization of the median filter used in MRP algorithm. Bootstrap technique determines the parameters like, mean, median etc., from the distribution to which the available sample is a single observation and hence efficiently eliminates the contribution from noisy pixels. Quantitative analysis shows that the proposed method is capable of producing good quality reconstruction