Wavelet-domain filtering for photon imaging: a Bayesian estimation approach

Many medical imaging modalities rely on photon detection, including nuclear medicine positron emission tomography. It is well-known that the noise in photon imaging obeys a Poisson distribution and, therefore, is signal-dependent. Consequently, spatially-adaptive filtering is required for optimal noise removal. In this paper the authors develop a new wavelet-domain Bayesian framework for modeling and estimating the intensity of a Poisson process directly from count observations. A new multiscale, multiplicative innovations model is developed as a prior for the underlying intensity function. The new prior model leads to a simple and efficient closed-form estimator which represents a substantial improvement over existing photon image filtering methods. The impact of the new filtering approach on nuclear medicine imaging is illustrated.