Yair Censor

A multiprojection algorithm using Bregman projections in a product space

Generalized distances give rise to generalized projections into convex sets. An important question is whether or not one can use within the same projection algorithm different types of such generalized projections. This question has practical consequences in the area of signal detection and image recovery in situations that can be formulated mathematically as a convex feasibility problem. Using an extension of Pierras product space formalism, we show here that a multiprojection algorithm converges. Our algorithm is fully simultaneous, i.e., it uses in each iterative stepall sets of the convex feasibility problem. Different multiprojection algorithms can be derived from our algorithmic scheme by a judicious choice of the Bregman functions which govern the process. As a by-product of our investigation we also obtain blockiterative schemes for certain kinds of linearly constraned optimization problems.

Finite series-expansion reconstruction methods

Series-expansion reconstruction methods made their first appearance in the scientific literature and in the CT scanner industry around 1970. Great research efforts have gone into them since but many questions still wait to be answered. These methods, synonymously known as algebraic methods, iterative algorithms, or optimization theory techniques, are based on the discretization of the image domain prior to any mathematical analysis and thus are rooted in a completely different branch of mathematics than the transform methods which are discussed in this issue by Lewitt [51]. How is the model set up? What is the methodology of the approach? Where does mathematical optimization theory enter? What do these reconstruction algorithms look like? How are quadratic optimization, entropy optimization, and Bayesian analysis used in image reconstruction? Finally, why study series expansion methods if transform methods are so much faster? These are some of the questions that are answered in this paper.

Row-Action Methods for Huge and Sparse Systems and Their Applications

This paper brings together and discusses theory and applications of methods, identified and labelled as row-action methods, for linear feasibility problems (find

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

x \in {\bf R}^n

An iterative row-action method for interval convex programming

, such that

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

Ax \leqq b

Pareto optimality in multiobjective problems

), linearly constrained optimization problems (minimize

Algorithms for the Split Variational Inequality Problem

f(x)

Component averaging: An efficient iterative parallel algorithm for large and sparse unstructured problems

, subject to

Strong underrelaxation in Kaczmarz's method for inconsistent systems

Ax \leqq b