On global and local convergence of half-quadratic algorithms.
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.
Allain
Marc
M
Institut de Recherche en Communications et en Cybernétique de Nantes (IRCCyN), BP 92 101-44321 Nantes Cedex 03, France. marc.allain@irccyn.ec-nantes.fr
Idier
Jerôme
J
Goussard
Yves
Y