block-iterative

New Douglas-Rachford algorithmic structures and their convergence analyses

  • Yair Censor
  • Rafiq Mansour
    • Categories Convex Optimization Tags , ,

    In this paper we study new algorithmic structures with Douglas- Rachford (DR) operators to solve convex feasibility problems. We propose to embed the basic two-set-DR algorithmic operator into the String-Averaging Projections (SAP) and into the Block-Iterative Pro- jection (BIP) algorithmic structures, thereby creating new DR algo- rithmic schemes that include the recently proposed cyclic Douglas- … Read more

    String-Averaging Expectation-Maximization for Maximum Likelihood Estimation in Emission Tomography

  • Yair Censor
  • Álvaro Rodolfo De Pierro
  • Elias Salomão Helou
  • Tai-Been Chen
  • I-Liang Chern
  • Ming Jiang
  • Henry Horng-Shing Lu
    • Categories Biomedical Applications, Convex Optimization Tags , , , , , ,

    We study the maximum likelihood model in emission tomography and propose a new family of algorithms for its solution, called String-Averaging Expectation-Maximization (SAEM). In the String-Averaging algorithmic regime, the index set of all underlying equations is split into subsets, called “strings,” and the algorithm separately proceeds along each string, possibly in parallel. Then, the end-points … Read more