The Global Convergence of the GMED Iterative Algorithm

In the late 1970's, Wiggins proposed a minimum entropy deconvolution (MED) which has become one of the most important deconvolution methods. He gave a varimax norm $V^4_2$ and a MED iterative procedure. Fortunately, for the last ten years in the practical using, the MED algorithm has never failed to reach a maximizer of the varimax norm. But so far, no theoretical proof has been given to show the convergence of the MED procedure. In this paper, we prove the global convergence of a generalized MED iterative procedure with respect to a generalized varimax norm $V^p_q(q=2,p \gt 2)$.