In this paper, we extend a multiscale Bayesian approach to modeling and estimation of general Poisson processes previously developed in Timmermann and Nowak (1997), and apply it to the emission computed tomography (ECT) image reconstruction problem. We develop a practical prior model for the sinogram image, which we use to estimate the underlying sinogram intensity from the raw projection data prior reconstruction. This sinogram estimate is then used in conjunction with the standard filtered-backprojection algorithm to produce an improved image reconstruction. The impact of the new filtering approach on ECT imaging is illustrated with simulated and clinical data.

Many important problems in engineering and science are well-modeled by Poisson processes. In many applications it is of great interest to accurately estimate the intensities underlying observed Poisson data. In particular, this work is motivated by photon-limited imaging problems. This paper studies a new Bayesian approach to Poisson intensity estimation based on the Haar wavelet transform. It is shown that the Haar transform provides a very natural and powerful framework for this problem. Using this framework, a novel multiscale Bayesian prior to model intensity functions is devised. The new prior leads to a simple Bayesian intensity estimation procedure. Furthermore, we characterize the correlation behavior of the new prior and show that it has 1/f spectral characteristics. The new framework is applied to photon-limited image estimation, and its potential to improve nuclear medicine imaging is examined.

This paper develops 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 that requires O(N) computations, where N is the dimension of the intensity function. We compare the new method with previously proposed wavelet-based approaches to this problem.

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.