Y. Censor
In this paper we propose an approach for solving systems of nonlinear equations without computing function derivatives. Motivated by the application area of tomographic absorption spectroscopy, which is a highly-nonlinear problem with…
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…
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…
We investigate projected scaled gradient (PSG) methods for convex minimization problems. These methods perform a descent step along a diagonally scaled gradient direction followed by a feasibility regaining step via orthogonal projection…
Purpose: To describe and mathematically validate the superiorization methodology, which is a recently-developed heuristic approach to optimization, and to discuss its applicability to medical physics problem formulations that specify the…
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…
We apply the recently proposed superiorization methodology (SM) to the inverse planning problem in radiation therapy. The inverse planning problem is represented here as a constrained minimization problem of the total variation (TV) of the…
We consider constrained minimization problems and propose to replace the projection onto the entire feasible region, required in the Projected Subgradient Method (PSM), by projections onto the individual sets whose intersection forms the…
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…
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.…