Stationary wavelet-based intensity models for photon-limited imaging

This paper develops a new statistical modeling and analysis method for photon-limited imaging based on two recent developments in wavelet-domain image processing. Non-Gaussian mixture densities provide very good Bayesian priors for wavelet coefficients and show great promise for statistical image processing. Shift-invariant wavelet transforms are also very useful for signal processing since the usual shift dependency of the wavelet transform is circumvented. In this paper we provide a unified Bayesian framework that unites these two approaches. A novel shift-invariant prior for Poisson intensity estimation is developed that significantly improves upon our previously proposed shift-variant method. Furthermore, we characterize the correlation behavior of the new prior and show that it has 1/f-like fractal characteristics