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

Optimization problems in electron microscopy of single particles

The final publication is available at Springer via http://dx.doi.org/10.1007/s10479-006-0078-8Electron Microscopy is a valuable tool for the elucidation of the three-dimensional structure of macromolecular complexes. Knowledge about the macromolecular structure provides important information about its function and how it is carried out. This work addresses the issue of three-dimensional reconstruction of biological macromolecules from electron microscopy images. In particular, it focuses on a methodology known as “single-particles” and makes a thorough review of all those steps that can be expressed as an optimization problem. In spite of important advances in recent years, there are still unresolved challenges in the field that offer an excellent testbed for new and more powerful optimization techniques.We acknowledge partial support from the “Comunidad Autónoma de Madrid” through grants CAM-07B-0032-2002, GR/SAL/0653/2004 and GR/SAL/0342/2004, the “Comisión Interministerial de Ciencia yTecnologia” of Spain through grants BIO2001-1237, BIO2001-4253-E, BIO2001-4339-E, BIO2002- 10855-E, BFU2004-00217/BMC, the Spanish FIS grant (G03/185), the European Union through grants QLK2- 2000-00634, QLRI-2000-31237, QLRT-2000-0136, QLRI-2001-00015, FP6-502828 and the NIH through grant HL70472. Alberto Pascual and Roberto Marabini acknowledge support by the Spanish Ramon y Cajal Program

Multiobjective Sparse Ensemble Learning by Means of Evolutionary Algorithms

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Ensemble learning can improve the performance of individual classifiers by combining their decisions. The sparseness of ensemble learning has attracted much attention in recent years. In this paper, a novel multiobjective sparse ensemble learning (MOSEL) model is proposed. Firstly, to describe the ensemble classifiers more precisely the detection error trade-off (DET) curve is taken into consideration. The sparsity ratio (sr) is treated as the third objective to be minimized, in addition to false positive rate (fpr) and false negative rate (fnr) minimization. The MOSEL turns out to be augmented DET (ADET) convex hull maximization problem. Secondly, several evolutionary multiobjective algorithms are exploited to find sparse ensemble classifiers with strong performance. The relationship between the sparsity and the performance of ensemble classifiers on the ADET space is explained. Thirdly, an adaptive MOSEL classifiers selection method is designed to select the most suitable ensemble classifiers for a given dataset. The proposed MOSEL method is applied to well-known MNIST datasets and a real-world remote sensing image change detection problem, and several datasets are used to test the performance of the method on this problem. Experimental results based on both MNIST datasets and remote sensing image change detection show that MOSEL performs significantly better than conventional ensemble learning methods

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

Threshold Identification for Micro-Tomographic Damage Characterisation in a Short-Fibre-Reinforced Polymer

The micro-tomographic technique represents an important tool for the analysis of the internal structure in short-fibre-reinforced polymers samples. For the investigation of damage mechanisms, detection of the micro-voids within the matrix can be facilitated by applying a tensile load in-situ during the scan. The investigations here described started from two micro-CT acquisitions, at different strain levels, of the same PA6.6GF10 sample. An original procedure for micro-voids identification is proposed, based on the statistical elaboration of the matrix grey-tone range. In order to validate the suggested procedure beyond visual inspection, an independent method based on an optimisation approach, which puts to use the two available micro-tomographic sets, was developed and applied. The effect of the tensile load, which can induce a progression of the damage within the specimen, was investigated, and the relations among strain, fibre distribution and micro-voids volumetric fraction were studied. Our findings point out that the mechanisms of damage progression, even under static loading as in this case, appear to be more complex than those related to the fibre-density-induced stress concentrations alone and require further investigation