Yair Censor

Bio-sketch and research interests appear at: http://math.haifa.ac.il/YAIR/censor-interests.html

Weak and Strong Convergence of Algorithms for the Split Common Null Point Problem

  • Charles Byrne
  • Yair Censor
  • Aviv Gibali
  • Simeon Reich
    • Categories Complementarity and Variational Inequalities, Convex Optimization, Nonlinear Optimization

    We introduce and study the Split Common Null Point Problem (SCNPP) for set-valued maximal monotone mappings in Hilbert space. This problem generalizes our Split Variational Inequality Problem (SVIP) [Y. Censor, A. Gibali and S. Reich, Algorithms for the split variational inequality problem, Numerical Algorithms, accepted for publication, DOI 10.1007/s11075-011-9490-5]. The SCNPP with only two set-valued … Read more

    Total variation superiorization schemes in proton computed tomography image reconstruction

  • Yair Censor
  • Scott Penfold
  • Anatoly Rosenfeld
  • Reinhard W. Schulte
    • Categories Biomedical Applications, Constrained Nonlinear Optimization, Other Topics Tags ,

    Purpose: Iterative projection reconstruction algorithms are currently the preferred reconstruction method in proton computed tomography (pCT). However, due to inconsistencies in the measured data arising from proton energy straggling and multiple Coulomb scattering, noise in the reconstructed image increases with successive iterations. In the current work, we investigated the use of total variation superiorization (TVS) … Read more

    The Split Variational Inequality Problem

  • Yair Censor
  • Aviv Gibali
  • Simeon Reich
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization Tags , , , ,

    We propose a new variational problem which we call the Split Variational Inequality Problem (SVIP). It entails finding a solution of one Variational Inequality Problem (VIP), the image of which under a given bounded linear transformation is a solution of another VIP. We construct iterative algorithms that solve such problems, under reasonable conditions, in Hilbert … Read more

    Perturbation resilience and superiorization of iterative algorithms

  • Yair Censor
  • Ran Davidi
  • Gabor T. Herman
    • Categories Biomedical Applications, Constrained Nonlinear Optimization Tags , , , ,

    Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little demand on computer resources. For other problems, such as finding that point in the intersection at which the … Read more

    On the Effectiveness of Projection Methods for Convex Feasibility

  • Yair Censor
  • Patrick L. Combettes
  • Wei Chen
  • Ran Davidi
  • Gabor T. Herman
    • Categories Applications - Science and Engineering, Biomedical Applications, Linear, Cone and Semidefinite Programming

    The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications. This is supported by experimental evidence provided in this paper on problems of various sizes (up to tens of thousands of … Read more

    On String-Averaging for Sparse Problems and On the Split Common Fixed Point Problem

  • Yair Censor
  • Alexander Segal
    • Categories Nonlinear Optimization, Parallel Algorithms Tags , ,

    We review the common fixed point problem for the class of directed operators. This class is important because many commonly used nonlinear operators in convex optimization belong to it. We present our recent definition of sparseness of a family of operators and discuss a string-averaging algorithmic scheme that favorably handles the common fixed points problem … Read more

    A Note on the Behavior of the Randomized Kaczmarz Algorithm of Strohmer and Vershynin

  • Yair Censor
  • Gabor T. Herman
  • Ming Jiang
    • Categories Biomedical Applications, Convex Optimization Tags , ,

    In a recent paper by Strohmer and Vershynin (J. Fourier Anal. Appl. 15:262–278, 2009) a “randomized Kaczmarz algorithm” is proposed for solving consistent systems of linear equations {ai, x = bi }m i=1. In that algorithm the next equation to be used in an iterative Kaczmarz process is selected with a probability proportional to ai2. … Read more

    Seminorm-induced oblique projections for sparse nonlinear convex feasibility problems

  • Yair Censor
  • Alexander Segal
    • Categories Nonlinear Optimization, Nonlinear Systems and Least-Squares Tags , , ,

    Simultaneous subgradient projection algorithms for the convex feasibility problem use subgradient calculations and converge sometimes even in the inconsistent case. We devise an algorithm that uses seminorm-induced oblique projections onto super half-spaces of the convex sets, which is advantageous when the subgradient-Jacobian is a sparse matrix at many iteration points of the algorithm. Using generalized … 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

    Projections Onto Super-Half-Spaces for Monotone Variational Inequality Problems in Finite-Dimensional Spaces

  • Yair Censor
  • Aviv Gibali
    • Categories Complementarity and Variational Inequalities Tags , ,

    The variational inequality problem (VIP) is considered here. We present a general algorithmic scheme which employs projections onto hyperplanes that separate balls from the feasible set of the VIP instead of projections onto the feasible set itself. Our algorithmic scheme includes the classical projection method and Fukushima’s subgradient projection method as special cases. Citation Technical … Read more