Wavelet-domain filtering for photon imaging systems

Many imaging systems rely on photon detection as the basis of image formati on. One of the major sources of error in these systems is Poisson noise due to the quantum nature of the photon detection process. Unlike additive Gau ssian white noise, the variance of Poisson noise is proportional to the und erlying signal intensity, and consequently separating signal from noise is a very difficult task. In this paper, we perform a novel gedankenexperiment to devise a new wavelet-domain filtering procedure for noise removal in ph oton imaging systems, The filter adapts to both the signal and the noise, a nd balances the trade-off between noise removal and excessive smoothing of image details. Designed using the statistical method of cross-validation, t he filter is simultaneously optimal in a small-sample predictive sum of squ ares sense and asymptotically optimal in the mean-square-error sense. The f iltering procedure has a simple interpretation as a joint edge detection/es timation process. Moreover, we derive an efficient algorithm for performing the filtering that has the same order of complexity as the fast wavelet tr ansform itself. The performance of the new filter is assessed with simulate d data experiments and tested with actual nuclear medicine imagery.