• Speaker: Dr Victoria Martín-Márquez, Department of Mathematical Analysis, Universidad de Sevilla
  • Title: Solving Convex Split Feasibility Problems and Applications
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Access Grid Venue: UniSA
  • Time and Date: 3:00 pm, Tue, 12th Nov 2013
  • Abstract:

    The split feasibility problem (SFP) consists in finding a point in a closed convex subset of a Hilbert space such that its image under a bounded linear operator belongs to a closed convex subset of another Hilbert space. Since its inception in 1994 by Censor and Elfving, it has received much attention thanks mainly to its applications to signal processing and image reconstruction. Iterative methods can be employed to solve the SFP. One of the most popular iterative method is Byrne's CQ algorithm. However, this algorithm requires prior knowledge (or at least an estimate) of the norm of the bounded linear operator. We introduce a stepsize selection method so that the implementation of the CQ algorithm does not need any prior information regarding the operator norm. Furthermore, a relaxed CQ algorithm, where the two closed convex sets are both level sets of convex functions, and a Halpern-type algorithm are studied under the same stepsize rule, yielding both weak and strong convergence. A more general problem, the Multiple-sets split feasibility problem, will be also presented. Numerical experiments are included to illustrate the applications to signal processing and, in particular, to compressed sensing and wavelet-based signal restoration.

    Based on joint works with G. López and H-K Xu.

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