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On global and local convergence of half-quadratic algorithms

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3 Author(s)
M. Allain ; Inst. de Recherche en Commun. et en Cybernetique de Nantes, France ; J. Idier ; Y. Goussard

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.

Published in:

IEEE Transactions on Image Processing  (Volume:15 ,  Issue: 5 )