Yair Censor

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

An Improved Method of Total Variation Superiorization Applied to Reconstruction in Proton Computed Tomography

  • Yair Censor
  • Paniz Karbasi
  • Keith E. Schubert
  • Reinhard W. Schulte
  • Blake Schultze
    • Categories Biomedical Applications, Constrained Nonlinear Optimization, Convex Optimization Tags , , , , ,

    Previous work showed that total variation superiorization (TVS) improves reconstructed image quality in proton computed tomography (pCT). The structure of the TVS algorithm has evolved since then and this work investigated if this new algorithmic structure provides additional benefits to pCT image quality. Structural and parametric changes introduced to the original TVS algorithm included: (1) … Read more

    Algorithms and Convergence Results of Projection Methods for Inconsistent Feasibility Problems: A Review

  • Yair Censor
  • Maroun Zaknoon
    • Categories Convex Optimization, Nonlinear Optimization Tags , ,

    The convex feasibility problem (CFP) is to find a feasible point in the intersection of finitely many convex and closed sets. If the intersection is empty then the CFP is inconsistent and a feasible point does not exist. However, algorithmic research of inconsistent CFPs exists and is mainly focused on two directions. One is oriented … Read more

    Convergence Analysis of Processes with Valiant Projection Operators in Hilbert Space

  • Yair Censor
  • Rafiq Mansour
    • Categories Constrained Nonlinear Optimization, Convex Optimization

    Convex feasibility problems require to find a point in the intersection of a finite family of convex sets. We propose to solve such problems by performing set-enlargements and applying a new kind of projection operators called valiant projectors. A valiant projector onto a convex set implements a special relaxation strategy, proposed by Goffin in 1971, … Read more

    Finding a best approximation pair of points for two polyhedra

  • Ron Aharoni
  • Yair Censor
  • Zilin Jiang
    • Categories Convex Optimization, Polyhedra Tags , , ,

    Given two disjoint convex polyhedra, we look for a best approximation pair relative to them, i.e., a pair of points, one in each polyhedron, attaining the minimum distance between the sets. Cheney and Goldstein showed that alternating projections onto the two sets, starting from an arbitrary point, generate a sequence whose two interlaced subsequences converge … Read more

    Sparsity constrained split feasibility for dose-volume constraints in inverse planning of intensity-modulated photon or proton therapy

  • Mark Brooke
  • Margherita Casiraghi
  • Yair Censor
  • Scott Penfold
  • Reinhard W. Schulte
  • Rafal Zalas
    • Categories Biomedical Applications, Convex Optimization Tags , , , , , ,

    A split feasibility formulation for the inverse problem of intensity-modulated radiation therapy (IMRT) treatment planning with dose-volume constraints (DVCs) included in the planning algorithm is presented. It involves a new type of sparsity constraint that enables the inclusion of a percentage-violation constraint in the model problem and its handling by continuous (as opposed to integer) … Read more

    Can linear superiorization be useful for linear optimization problems?

  • Yair Censor
    • Categories Constrained Nonlinear Optimization, Linear Programming, Problem Solving Environments Tags , , , , , , , , ,

    Linear superiorization considers linear programming problems but instead of attempting to solve them with linear optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers them toward reduced (not necessarily minimal) target function values. The two questions that we set out to explore experimentally are (i) Does linear superiorization provide a feasible point whose linear … Read more

    Linear superiorization for infeasible linear programming

  • Yair Censor
  • Yehuda Zur
    • Categories Constrained Nonlinear Optimization, Linear Programming

    Linear superiorization (abbreviated: LinSup) considers linear programming (LP) problems wherein the constraints as well as the objective function are linear. It allows to steer the iterates of a feasibility-seeking iterative process toward feasible points that have lower (not necessarily minimal) values of the objective function than points that would have been reached by the same … Read more

    The implicit convex feasibility problem and its application to adaptive image denoising

  • Yair Censor
  • Aviv Gibali
  • Frank Lenzen
  • Christoph Schnörr
    • Categories Biomedical Applications, Convex and Nonsmooth Optimization Tags , , , , ,

    The implicit convex feasibility problem attempts to find a point in the intersection of a finite family of convex sets, some of which are not explicitly determined but may vary. We develop simultaneous and sequential projection methods capable of handling such problems and demonstrate their applicability to image denoising in a specific medical imaging situation. … 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

    Techniques in Iterative Proton CT Image Reconstruction

  • Yair Censor
  • Scott Penfold
    • Categories Biomedical Applications, Convex Optimization Tags , , , , , ,

    This is a review paper on some of the physics, modeling, and iterative algorithms in proton computed tomography (pCT) image reconstruction. The primary challenge in pCT image reconstruction lies in the degraded spatial resolution resulting from multiple Coulomb scattering within the imaged object. Analytical models such as the most likely path (MLP) have been proposed … Read more