A unified treatment of some iterative algorithms in signal processing and image reconstruction

Let T be a (possibly nonlinear) continuous operator on Hilbert space. If, for some starting vector x, the orbit sequence Tkx, k = 0, 1,. . . converges, then the limit z is a fixed point of T; that is, Tz = z. An operator N on a Hilbert space is nonexpansive (ne) if, for each x and y in, Even when N has fixed points the orbit sequence Nkx need not converge; consider the example N = −I, where I denotes the identity operator. However, for any the iterative procedure defined by converges (weakly) to a fixed point of N whenever such points exist. This is the Krasnoselskii–Mann (KM) approach to finding fixed points of ne operators.