string-averaging

Dynamic string-averaging CQ-methods for the split feasibility problem with percentage violation constraints arising in radiation therapy treatment planning

  • Mark Brooke
  • Yair Censor
  • Aviv Gibali
    • Categories Biomedical Applications, Nonlinear Optimization Tags , , , , , , ,

    We study a feasibility-seeking problem with percentage violation constraints. These are additional constraints, that are appended to an existing family of constraints, which single out certain subsets of the existing constraints and declare that up to a specified fraction of the number of constraints in each subset is allowed to be violated by up to … Read more

    Data-compatibility of algorithms

  • Yair Censor
  • Maroun Zaknoon
  • Alexander J. Zaslavski
    • Categories Constrained Nonlinear Optimization, Convex Optimization Tags , , , , , , , ,

    The data-compatibility approach to constrained optimization, proposed here, strives to a point that is “close enough” to the solution set and whose target function value is “close enough” to the constrained minimum value. These notions can replace analysis of asymptotic convergence to a solution point of infinite sequences generated by specific algorithms. We consider a … Read more

    Dynamic string-averaging CQ-methods for the split feasibility problem with percentage violation constraints arising in radiation therapy treatment planning

  • Mark Brooke
  • Yair Censor
  • Aviv Gibali
    • Categories Biomedical Applications, Constrained Nonlinear Optimization, Convex Optimization Tags , , , , , , , , ,

    In this paper we study a feasibility-seeking problem with percentage violation con- straints. These are additional constraints, that are appended to an existing family of constraints, which single out certain subsets of the existing constraints and declare that up to a speci ed fraction of the number of constraints in each subset is allowed to be … Read more

    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

    Block-Iterative and String-Averaging Projection Algorithms in Proton Computed Tomography Image Reconstruction

  • Vladimir Bashkirov
  • Yair Censor
  • Scott McAllister
  • Scott Penfold
  • Anatoly Rosenfeld
  • Keith Schubert
  • Reinhard W. Schulte
    • Categories Applications - Science and Engineering, Biomedical Applications Tags , , ,

    Proton computed tomography (pCT) is an imaging modality that has been suggested as a means for reducing the range uncertainty during proton radiation treatments. By measuring the spatial location of individual protons pre- and post-patient, as well as the energy lost along the proton path, three dimensional maps of patient water equivalent electron densities can … Read more