Deep Unfolding Network for Nonlinear Multi-Frequency Electrical Impedance Tomography
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909699910139904 |
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| author | Alberti, Giovanni S. Lazzaro, Damiana Morigi, Serena Ratti, Luca Santacesaria, Matteo |
| author_facet | Alberti, Giovanni S. Lazzaro, Damiana Morigi, Serena Ratti, Luca Santacesaria, Matteo |
| contents | Multi-frequency Electrical Impedance Tomography (mfEIT) represents a promising biomedical imaging modality that enables the estimation of tissue conductivities across a range of frequencies. Addressing this challenge, we present a novel variational network, a model-based learning paradigm that strategically merges the advantages and interpretability of classical iterative reconstruction with the power of deep learning. This approach integrates graph neural networks (GNNs) within the iterative Proximal Regularized Gauss Newton (PRGN) framework. By unrolling the PRGN algorithm, where each iteration corresponds to a network layer, we leverage the physical insights of nonlinear model fitting alongside the GNN's capacity to capture inter-frequency correlations. Notably, the GNN architecture preserves the irregular triangular mesh structure used in the solution of the nonlinear forward model, enabling accurate reconstruction of overlapping tissue fraction concentrations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_16678 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deep Unfolding Network for Nonlinear Multi-Frequency Electrical Impedance Tomography Alberti, Giovanni S. Lazzaro, Damiana Morigi, Serena Ratti, Luca Santacesaria, Matteo Numerical Analysis Machine Learning 65K10, 65N20, 68T07 Multi-frequency Electrical Impedance Tomography (mfEIT) represents a promising biomedical imaging modality that enables the estimation of tissue conductivities across a range of frequencies. Addressing this challenge, we present a novel variational network, a model-based learning paradigm that strategically merges the advantages and interpretability of classical iterative reconstruction with the power of deep learning. This approach integrates graph neural networks (GNNs) within the iterative Proximal Regularized Gauss Newton (PRGN) framework. By unrolling the PRGN algorithm, where each iteration corresponds to a network layer, we leverage the physical insights of nonlinear model fitting alongside the GNN's capacity to capture inter-frequency correlations. Notably, the GNN architecture preserves the irregular triangular mesh structure used in the solution of the nonlinear forward model, enabling accurate reconstruction of overlapping tissue fraction concentrations. |
| title | Deep Unfolding Network for Nonlinear Multi-Frequency Electrical Impedance Tomography |
| topic | Numerical Analysis Machine Learning 65K10, 65N20, 68T07 |
| url | https://arxiv.org/abs/2507.16678 |