225 research outputs found
Accelerating two projection methods via perturbations with application to Intensity-Modulated Radiation Therapy
Constrained convex optimization problems arise naturally in many real-world
applications. One strategy to solve them in an approximate way is to translate
them into a sequence of convex feasibility problems via the recently developed
level set scheme and then solve each feasibility problem using projection
methods. However, if the problem is ill-conditioned, projection methods often
show zigzagging behavior and therefore converge slowly.
To address this issue, we exploit the bounded perturbation resilience of the
projection methods and introduce two new perturbations which avoid zigzagging
behavior. The first perturbation is in the spirit of -step methods and uses
gradient information from previous iterates. The second uses the approach of
surrogate constraint methods combined with relaxed, averaged projections.
We apply two different projection methods in the unperturbed version, as well
as the two perturbed versions, to linear feasibility problems along with
nonlinear optimization problems arising from intensity-modulated radiation
therapy (IMRT) treatment planning. We demonstrate that for all the considered
problems the perturbations can significantly accelerate the convergence of the
projection methods and hence the overall procedure of the level set scheme. For
the IMRT optimization problems the perturbed projection methods found an
approximate solution up to 4 times faster than the unperturbed methods while at
the same time achieving objective function values which were 0.5 to 5.1% lower.Comment: Accepted for publication in Applied Mathematics & Optimizatio
The superiorization method with restarted perturbations for split minimization problems with an application to radiotherapy treatment planning
In this paper we study the split minimization problem that consists of two constrained minimization problems in two separate spaces that are connected via a linear operator that maps one space into the other. To handle the data of such a problem we develop a superiorization approach that can reach a feasible point with reduced (not necessarily minimal) objective function values. The superiorization methodology is based on interlacing the iterative steps of two separate and independent iterative processes by perturbing the iterates of one process according to the steps dictated by the other process. We include in our developed method two novel elements. The first one is the permission to restart the perturbations in the superiorized algorithm which results in a significant acceleration and increases the computational efficiency. The second element is the ability to independently superiorize subvectors. This caters to the needs of real-world applications, as demonstrated here for a problem in intensity-modulated radiation therapy treatment planning.The work of Yair Censor was supported by the ISF-NSFC joint research plan Grant Number 2874/19. Francisco Aragón and David Torregrosa were partially supported by the Ministry of Science, Innovation and Universities of Spain and the European Regional Development Fund (ERDF) of the European Commission, Grant PGC2018-097960-B-C22, and the Generalitat Valenciana (AICO/2021/165). David Torregrosa was supported by MINECO and European Social Fund (PRE2019-090751) under the program “Ayudas para contratos predoctorales para la formación de doctores” 2019
The superiorization method with restarted perturbations for split minimization problems with an application to radiotherapy treatment planning
In this paper we study the split minimization problem that consists of two
constrained minimization problems in two separate spaces that are connected via
a linear operator that maps one space into the other. To handle the data of
such a problem we develop a superiorization approach that can reach a feasible
point with reduced (not necessarily minimal) objective function values. The
superiorization methodology is based on interlacing the iterative steps of two
separate and independent iterative processes by perturbing the iterates of one
process according to the steps dictated by the other process. We include in our
developed method two novel elements. The first one is the permission to restart
the perturbations in the superiorized algorithm which results in a significant
acceleration and increases the computational efficiency. The second element is
the ability to independently superiorize subvectors. This caters to the needs
of real-world applications, as demonstrated here for a problem in
intensity-modulated radiation therapy treatment planning.Comment: Revised version, October 10, 2022; accepted for publication in:
Applied Mathematics and Computatio
Application of general semi-infinite Programming to Lapidary Cutting Problems
We consider a volume maximization problem arising in gemstone cutting industry. The problem is formulated as a general semi-infinite program (GSIP) and solved using an interiorpoint method developed by Stein. It is shown, that the convexity assumption needed for the convergence of the algorithm can be satisfied by appropriate modelling. Clustering techniques are used to reduce the number of container constraints, which is necessary to make the subproblems practically tractable. An iterative process consisting of GSIP optimization and adaptive refinement steps is then employed to obtain an optimal solution which is also feasible for the original problem. Some numerical results based on realworld data are also presented
Superiorization: An optimization heuristic for medical physics
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 desired solution (of physically given or otherwise obtained
constraints) by an optimization criterion. Methods: The underlying idea is that
many iterative algorithms for finding such a solution are perturbation
resilient in the sense that, even if certain kinds of changes are made at the
end of each iterative step, the algorithm still produces a
constraints-compatible solution. This property is exploited by using permitted
changes to steer the algorithm to a solution that is not only
constraints-compatible, but is also desirable according to a specified
optimization criterion. The approach is very general, it is applicable to many
iterative procedures and optimization criteria used in medical physics.
Results: The main practical contribution is a procedure for automatically
producing from any given iterative algorithm its superiorized version, which
will supply solutions that are superior according to a given optimization
criterion. It is shown that if the original iterative algorithm satisfies
certain mathematical conditions, then the output of its superiorized version is
guaranteed to be as constraints-compatible as the output of the original
algorithm, but it is superior to the latter according to the optimization
criterion. This intuitive description is made precise in the paper and the
stated claims are rigorously proved. Superiorization is illustrated on
simulated computerized tomography data of a head cross-section and, in spite of
its generality, superiorization is shown to be competitive to an optimization
algorithm that is specifically designed to minimize total variation.Comment: Accepted for publication in: Medical Physic
On the clinical potential of ion computed tomography with different detector systems and ion species
High Performance Optical Computed Tomography for Accurate Three-Dimensional Radiation Dosimetry
Optical computed tomography (CT) imaging of radiochromic gel dosimeters is a method for truly three-dimensional radiation dosimetry. Although optical CT dosimetry is not widely used currently due to previous concerns with speed and accuracy, the complexity of modern radiotherapy is increasing the need for a true 3D dosimeter. This thesis reports technical improvements that bring the performance of optical CT to a clinically useful level. New scanner designs and improved scanning and reconstruction techniques are described.
First, we designed and implemented a new light source for a cone-beam optical CT system which reduced the scatter to primary contribution in CT projection images of gel dosimeters from approximately 25% to approximately 4%. This design, which has been commercially implemented, enables accurate and fast dosimetry.
Second, we designed and constructed a new, single-ray, single-detector parallel-beam optical CT scanner. This system was able to very accurately image both absorbing and scattering objects in large volumes (15 cm diameter), agreeing within ∼1% with independent measurements. It has become a reference standard for evaluation of optical CT geometries and dosimeter formulations.
Third, we implemented and characterized an iterative reconstruction algorithm for optical CT imaging of gel dosimeters. This improved image quality in optical CT by suppressing the effects of noise and artifacts by a factor of up to 5.
Fourth, we applied a fiducial-based ray path measurement scheme, combined with an iterative reconstruction algorithm, to enable optical CT reconstruction in the case of refractive index mismatch between different media in the scanner’s imaged volume. This improved the practicality of optical CT, as time-consuming mixing of liquids can be avoided.
Finally, we applied the new laser scanner to the difficult dosimetry task of small-field measurement. We were able to obtain beam profiles and depth dose curves for 4 fields (3x3 cm2 and below) using one 15 cm diameter dosimeter, within 2 hours. Our gel dosimetry depth-dose curves agreed within ∼1.5% with Monte Carlo simulations.
In conclusion, the developments reported here have brought optical CT dosimetry to a clinically useful level. Our techniques will be used to assist future research in gel dosimetry and radiotherapy treatment techniques
- …