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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.

Our goal is to decrease the importance of beam- hardening artifacts in X-ray computed tomography by address- ing the polyenergetic nature of the X-ray source. We use the same physical model as De Man and al [1]. We next adopt an estimation framework for the reconstruction: the attenuation coefficients are determined by a likelihood-based estimator. This approach leads to minimization of an objective function which exhibits a complex structure. Nonetheless, we develop a numerical procedure with satisfactory numerical efficiency : we use a nonlinear conjugate gradient method. The three major contributions of this communication are : the positivity of the solution ensured by a change of variables, the convergence properties of the algorithm, and a satisfying computation time.

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The equivalent magnetic currents method can be used to characterize radiating structures and to obtain information about the current distribution on the radiating device under test (DUT). In order to do so, the system is assumed to be linear and inversion from near-field measurements can be carried out using numerical techniques such as the singular value decomposition. However this approach is very sensitive to modeling and measurement errors, which is a consequence of the ill-conditioned nature of the inversion process. Here, we propose to account for the ill-conditioning by using a Tikhonov regularization technique to perform the inversion. This technique requires a regularization parameter to be set to an appropriate value, and we show that a generalized cross-validation approach yields adequate determination of the regularization parameter directly from the measured data. The proposed method can be tailored to account for specific characteristics of the DUT. This point is illustrated by the estimation of the current distribution of a bidimensional radiating structure for which prior information about the orientation of radiating edges is incorporated into the inversion method.Index Terms-Antenna measurements, equivalent magnetic currents (EqMC), generalized cross validation, ill-posed problems, inverse problems, near field (NF), Tikhonov regularization technique (TRT).