Markovian reconstruction in computed imaging and Fourier synthesis

In computed imaging an object which is not directly observable has to be imaged from some deficient projection data; the authors suppose that the image-data relation is linearised. Recovering the image is an ill-posed inverse problem and requires the use of prior information. The currently used quadratic regularisation is not satisfactory. The authors propose a class of reconstruction algorithms permitting the introduction of various scene features as priors for an MAP estimation, by means of Markov random fields with implicit line processes. The resulting optimisation problem, numerically not feasible by stochastic algorithms, is solved in a sub-optimal but very efficient manner with graduated non-convexity algorithms. The proposed technique is directly applicable to any ill-posed inverse problem whose log-likelihood is convex