Yair Censor

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

On diagonally-relaxed orthogonal projection methods

  • Yair Censor
  • Tommy Elfving
  • Gabor T. Herman
  • Touraj Nikazad
    • Categories Biomedical Applications, Unconstrained Optimization Tags , , , ,

    We propose and study a block-iterative projections method for solving linear equations and/or inequalities. The method allows diagonal component-wise relaxation in conjunction with orthogonal projections onto the individual hyperplanes of the system, and is thus called diagonally-relaxed orthogonal projections (DROP). Diagonal relaxation has proven useful in accelerating the initial convergence of simultaneous and block-iterative projection … Read more

    Perturbed projections and subgradient projections for the multiple-sets split feasibility problem

  • Yair Censor
  • Avi Motova
  • Alexander Segal
    • Categories Convex and Nonsmooth Optimization, Unconstrained Optimization

    We study the multiple-sets split feasibility problem that requires to find a point closest to a family of closed convex sets in one space such that its image under a linear transformation will be closest to another family of closed convex sets in the image space. By casting the problem into an equivalent problem in … Read more

    A unified approach for inversion problems in intensity-modulated radiation therapy

  • Thomas Bortfeld
  • Yair Censor
  • Benjamin Martin
  • Alexei Trofimov
    • Categories Biomedical Applications, Nonlinear Optimization

    We propose and study a unified model for handling dose constraints (physical dose, equivalent uniform dose (EUD), etc.) and radiation source constraints in a single mathematical framework based on the split feasibility problem. The model does not impose on the constraints an exogenous objective (merit) function. The optimization algorithm minimizes a weighted proximity function that … Read more

    The Application of an Oblique-Projected Landweber Method to a Model of Supervised Learning

  • Yair Censor
  • Tommy Elfving
  • Per-Erik Forssen
  • Gosta Granlund
  • Bjorn Johansson
  • Vladimir Kozlov
    • Categories Applications - Science and Engineering Tags , , , ,

    This paper brings together a novel information representation model for use in signal processing and computer vision problems, with a particular algorithmic development of the Landweber iterative algorithm. The information representation model allows a representation of multiple values for a variable as well as expression of confidence. Both properties are important for effective computation using … Read more

    The multiple-sets split feasibility problem and its applications for inverse problems

  • Thomas Bortfeld
  • Yair Censor
  • Tommy Elfving
  • Nirit Kopf
    • Categories Applications - Science and Engineering, Biomedical Applications, Convex Optimization

    The multiple-sets split feasibility problem requires to find a point closest to a family of closed convex sets in one space such that its image under a linear transformation will be closest to another family of closed convex sets in the image space. It can be a model for many inverse problems where constraints are … Read more

    Computational acceleration of projection algorithms for the linear best approximation problem

  • Yair Censor
    • Categories Convex Optimization

    This is an experimental computational account of projection algorithms for the linear best approximation problem. We focus on the sequential and simultaneous versions of Dykstra’s algorithm and the Halpern-Lions-Wittmann-Bauschke algorithm for the best approximation problem from a point to the intersection of closed convex sets in the Euclidean space. These algorithms employ different iterative approaches … Read more

    Algorithms for the quasiconvex feasibility problem

  • Yair Censor
  • Alexander Segal
    • Categories Convex and Nonsmooth Optimization Tags , , , , ,

    We study the behavior of subgradient projection algorithms for the quasiconvex feasibility problem of finding a point x^* in R^n that satisfies the inequalities f_i(x^*) less or equal 0, for all i=1,2,…,m, where all functions are continuous and quasiconvex. We consider the consistent case when the solution set is nonempty. Since the Fenchel-Moreau subdifferential might … Read more

    Best approximation to common fixed points of a semigroup of nonexpansive operators

  • Arkady Aleyner
  • Yair Censor
    • Categories Constrained Nonlinear Optimization, Convex and Nonsmooth Optimization Tags , , , ,

    We study a sequential algorithm for finding the projection of a given point onto the common fixed points set of a semigroup of nonexpansive operators in Hilbert space. The convergence of such an algorithm was previously established only for finitely many nonexpansive operators. Algorithms of this kind have been applied to the best approximation and … Read more

    Steered sequential projections for the inconsistent convex feasibility problem

  • Yair Censor
  • Álvaro Rodolfo De Pierro
  • Maroun Zaknoon
    • Categories Convex Optimization, Nonlinear Systems and Least-Squares Tags , ,

    We study a steered sequential gradient algorithm which minimizes the sum of convex functions by proceeding cyclically in the directions of the negative gradients of the functions and using steered step-sizes. This algorithm is applied to the convex feasibility problem by minimizing a proximity function which measures the sum of the Bregman distances to the … Read more

    Inherent smoothness of intensity patterns for intensity modulated radiation therapy generated by simultaneous projection algorithms

  • Yair Censor
  • James M. Galvin
  • Darek Michalski
  • Ying Xiao
    • Categories Biomedical Applications, Convex Optimization Tags , , , ,

    The efficient delivery of intensity modulated radiation therapy (IMRT) depends on finding optimized beam intensity patterns that produce dose distributions, which meet given constraints for the tumor as well as any critical organs to be spared. Many optimization algorithms that are used for beamlet-based inverse planning are susceptible to large variations of neighboring intensities. Accurately … Read more