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This paper provides original results on the global and local convergence properties of half-quadratic (HQ) algorithms resulting from the Geman and Yang (GY) and Geman and Reynolds (GR) primal-dual constructions. First, we show that the convergence domain of the GY algorithm can be extended with the benefit of an improved convergence rate. Second, we provide a precise comparison of the convergence rates for both algorithms. This analysis shows that the GR form does not benefit from a better convergence rate in general. Moreover, the GY iterates often take advantage of a low cost implementation. In this case, the GY form is usually faster than the GR form from the CPU time viewpoint.

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Considering the image quality and execution times, this method may be useful for reconstruction of low-dose clinical acquisitions. It may be of particular benefit to patients who undergo multiple acquisitions by reducing the overall imaging radiation dose and associated risks.

This paper provides a complete characterization of stationary Markov random fields on a finite rectangular (nontoroidal) lattice in the basic case of a second-order neighborhood system. Equivalently, it characterizes stationary Markov fields on 2 whose restrictions to finite rectangular subsets are still Markovian (i.e., even on the boundaries). Until now, Pickard random fields formed the only known class of such fields. First, we derive a necessary and sufficient condition for Markov random fields on a finite lattice to be stationary. It is shown that their joint distribution factors in terms of the marginal distribution on a generic (2 2 2) cell which must fulfill some consistency constraints. Second, we solve the consistency constraints and provide a complete characterization of such measures in three cases. Symmetric measures and Gaussian measures are shown to necessarily belong to the Pickard class, whereas binary measures belong either to the Pickard class, or to a new nontrivial class which is further studied. In particular, the corresponding fields admit a simple parameterization and may be simulated in a simple, although nonunilateral manner.