A single site update algorithm for nonlinear diffraction tomography

We focus on the nonlinear inverse problem of diffraction tomography. We set the problem as one of estimation within the Bayesian framework and define the solution as the maximum a posteriori (MAP) estimate which corresponds to the global minimum of a multimodal criterion. The objective of this paper is to present a new deterministic single site update algorithm specially designed to compute this solution. The term of fidelity to the data, function of one pixel value, can be written as a second order rational fraction. Thus, the 1-D MAP criterion can be evaluated and minimized-at a very low computational cost. Moreover, for certain MRF models the global minimum can even be computed explicitly as roots of a polynomial. The proposed algorithm turns these properties to advantage and moreover performs the updates of intermediate quantities at a particularly low cost compared to the criterion evaluation. Even if not guaranteed to converge towards the global minimum, the algorithm has shown itself to give satisfactory practical results.