Global projection estimation methods for the tomographic reconstruction of images with Poisson noise

Methods for image reconstruction under Poisson noise are proposed. These methods involve filtering the one-dimensional projections and taking into consideration the correlation between points on the nonnoisy projections, both in the filtering and the parameter estimation phases. The results display an improvement in the mean square error for one-dimensional filtering of the projections, as compared to pointwise estimators. The reconstruction of both simulated and real images shows an improvement with respect to simple convolution-backprojection without filtering the projections and a comparable CPU (central processing unit) time. This is due to the fact that the major computational effort for reconstruction is in the convolution-backprojection algorithm. When compared to the ML-EM (maximum-likelihood expectation maximization) algorithm, the proposed method displayed results that were slightly inferior, but with a CPU time that remains one to two orders of magnitude lower on conventional architectures, such as the pointwise estimators