Poisson statistic and half-quadratic regularization for emission tomography reconstruction algorithm

In emission computerized tomography, the use of realistic constraints such as edge-preserving smoothing lead to nonlinear regularisation. Charbonnier et al. (see IEEE Trans. on Image Processing, 1994) used the half-quadratic regularization in order to solve this problem. Applied together with a Gaussian likelihood, it formed the ARTUR algorithm. We propose a new regularized algorithm called MOISE which takes into account the Poisson nature of the statistical noise and uses this half-quadratic regularization. For that reason, MOISE differ from the MAP EM (maximum a posteriori expectation maximization) algorithm developed by P.J. Green (1990) which uses the one step late technique. We tested MOISE and compared it with ARTUR, on numerical simulation and real data. The results show that, despite the slowness of convergence, the half-quadratic regularization can be applied in the case of a Poisson statistic.