{"title":"Efficient gradient-based optimization for reconstructing binary images in applications to electrical impedance tomography","authors":"","doi":"10.1007/s10589-024-00553-z","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>A novel and highly efficient computational framework for reconstructing binary-type images suitable for models of various complexity seen in diverse biomedical applications is developed and validated. Efficiency in computational speed and accuracy is achieved by combining the advantages of recently developed optimization methods that use sample solutions with customized geometry and multiscale control space reduction, all paired with gradient-based techniques. The control space is effectively reduced based on the geometry of the samples and their individual contributions. The entire 3-step computational procedure has an easy-to-follow design due to a nominal number of tuning parameters making the approach simple for practical implementation in various settings. Fairly straightforward methods for computing gradients make the framework compatible with any optimization software, including black-box ones. The performance of the complete computational framework is tested in applications to 2D inverse problems of cancer detection by electrical impedance tomography (EIT) using data from models generated synthetically and obtained from medical images showing the natural development of cancerous regions of various sizes and shapes. The results demonstrate the superior performance of the new method and its high potential for improving the overall quality of the EIT-based procedures.</p>","PeriodicalId":55227,"journal":{"name":"Computational Optimization and Applications","volume":"20 1","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Optimization and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10589-024-00553-z","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
A novel and highly efficient computational framework for reconstructing binary-type images suitable for models of various complexity seen in diverse biomedical applications is developed and validated. Efficiency in computational speed and accuracy is achieved by combining the advantages of recently developed optimization methods that use sample solutions with customized geometry and multiscale control space reduction, all paired with gradient-based techniques. The control space is effectively reduced based on the geometry of the samples and their individual contributions. The entire 3-step computational procedure has an easy-to-follow design due to a nominal number of tuning parameters making the approach simple for practical implementation in various settings. Fairly straightforward methods for computing gradients make the framework compatible with any optimization software, including black-box ones. The performance of the complete computational framework is tested in applications to 2D inverse problems of cancer detection by electrical impedance tomography (EIT) using data from models generated synthetically and obtained from medical images showing the natural development of cancerous regions of various sizes and shapes. The results demonstrate the superior performance of the new method and its high potential for improving the overall quality of the EIT-based procedures.
摘要 开发并验证了一种新颖高效的计算框架，用于重建二值型图像，适用于各种生物医学应用中出现的各种复杂模型。通过结合最近开发的优化方法的优势，实现了高效的计算速度和准确性，这些优化方法使用具有定制几何形状和多尺度控制空间缩减的样本解决方案，并与基于梯度的技术相结合。根据样本的几何形状及其各自的贡献，控制空间被有效缩小。整个三步计算程序的设计简单易懂，只需标称数量的调整参数，使该方法易于在各种环境中实际应用。相当简单的梯度计算方法使该框架与任何优化软件（包括黑盒软件）兼容。完整计算框架的性能在电阻抗断层扫描（EIT）癌症检测的二维逆问题应用中进行了测试，使用的数据来自合成生成的模型，以及从显示不同大小和形状的癌症区域自然发展的医学图像中获取的数据。结果表明，新方法性能优越，在提高基于 EIT 的程序的整体质量方面潜力巨大。
期刊介绍：
Computational Optimization and Applications is a peer reviewed journal that is committed to timely publication of research and tutorial papers on the analysis and development of computational algorithms and modeling technology for optimization. Algorithms either for general classes of optimization problems or for more specific applied problems are of interest. Stochastic algorithms as well as deterministic algorithms will be considered. Papers that can provide both theoretical analysis, along with carefully designed computational experiments, are particularly welcome.
Topics of interest include, but are not limited to the following:
Large Scale Optimization,
Unconstrained Optimization,
Linear Programming,
Quadratic Programming Complementarity Problems, and Variational Inequalities,
Constrained Optimization,
Nondifferentiable Optimization,
Integer Programming,
Combinatorial Optimization,
Stochastic Optimization,
Multiobjective Optimization,
Network Optimization,
Complexity Theory,
Approximations and Error Analysis,
Parametric Programming and Sensitivity Analysis,
Parallel Computing, Distributed Computing, and Vector Processing,
Software, Benchmarks, Numerical Experimentation and Comparisons,
Modelling Languages and Systems for Optimization,
Automatic Differentiation,
Applications in Engineering, Finance, Optimal Control, Optimal Design, Operations Research,
Transportation, Economics, Communications, Manufacturing, and Management Science.
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