Wavelet-Domain Filtering for Photon Imaging Systems
Nowak, Robert David
Baraniuk, Richard G.
Many imaging systems rely on photon detection as the basis of image formation. 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 Gaussian noise, Poisson noise is signal-dependent, and consequently separating signal from noise is a very difficult task. In this paper, we develop a novel wavelet-domain filtering procedure for noise removal in photon imaging systems. The filter adapts to both the signal <i>and</i> the noise and balances the trade-off between noise removal and excessive smoothing of image details. Designed using the statistical method of cross-validation, the filter is simultaneously optimal in a small-sample predictive sum of squares sense and asymptotically optimal in the mean square error sense. The filtering procedure has a simple interpretation as a joint edge detection/estimation process. Moreover, we derive an efficient algorithm for performing the filtering that has the same order of complexity as the fast wavelet transform itself. The performance of the new filter is assessed with simulated data experiments and tested with actual nuclear medicine imagery.