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Efficient gradient-based optimization for reconstructing binary images in applications to electrical impedance tomography

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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.

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Parts of data generated or analyzed during this study are included in this published article. The rest data that support the findings of this study are available from the corresponding author upon request.

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Acknowledgements

We wish to thank the anonymous reviewers for their valuable comments and suggestions to improve the clarity of the presented approach and the overall readability of this paper.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Florida Institute of Technology, 150 W. University Blvd., Melbourne, FL, 32901, USA

    Paul R. Arbic II

  2. Department of Mathematics and Systems Engineering, Florida Institute of Technology, 150 W. University Blvd, Melbourne, FL, 32901, USA

    Vladislav Bukshtynov

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  1. Paul R. Arbic II
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Correspondence to Vladislav Bukshtynov.

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Arbic II, P.R., Bukshtynov, V. Efficient gradient-based optimization for reconstructing binary images in applications to electrical impedance tomography. Comput Optim Appl 88, 379–403 (2024). https://doi.org/10.1007/s10589-024-00553-z

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