Graph Convolutional Networks for Model-Based Learning in Nonlinear Inverse Problems

Herzberg, William; Rowe, Daniel B.; Hauptmann, Andreas; Hamilton, Sarah J.

doi:10.1109/tci.2021.3132190

Cited by 30 publications

(29 citation statements)

References 57 publications

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“…Here, datadriven approaches are a powerful alternative to compensate for modelling errors [194,234,302] or reducing computational cost of iterative optimization schemes by model approximations [32,303]. Finally, we note that recent developments in geometric learning extend deep networks on Euclidean meshes to general meshes, such as finite elements, by a embedding them into graph structures essentially using the underlying geometry [304,305]. This opens the possibility to extend many data-driven approaches to complex structural problems.…”

Section: (A) Machine-learned Inversionmentioning

confidence: 99%

Structural engineering from an inverse problems perspective

et al. 2022

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The field of structural engineering is vast, spanning areas from the design of new infrastructure to the assessment of existing infrastructure. From the onset, traditional entry-level university courses teach students to analyse structural responses given data including external forces, geometry, member sizes, restraint, etc.—characterizing a forward problem (structural causalities → structural response). Shortly thereafter, junior engineers are introduced to structural design where they aim to, for example, select an appropriate structural form for members based on design criteria, which is the inverse of what they previously learned. Similar inverse realizations also hold true in structural health monitoring and a number of structural engineering sub-fields (response → structural causalities). In this light, we aim to demonstrate that many structural engineering sub-fields may be fundamentally or partially viewed as inverse problems and thus benefit via the rich and established methodologies from the inverse problems community. To this end, we conclude that the future of inverse problems in structural engineering is inexorably linked to engineering education and machine learning developments.

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Section: (A) Machine-learned Inversionmentioning

confidence: 99%

Structural engineering from an inverse problems perspective

et al. 2022

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“…Since CNNs operate on uniform pixel domains, the images drawn in the mesh basis were interpolated to the image basis for the application of the CNN and back for simulation of (1)-( 3). Alternatively, one can use graph structures to formulate the problem on the FE mesh directly [43].…”

Section: B Training the Deep Gauss-newtonmentioning

confidence: 99%

A Model-Based Iterative Learning Approach for Diffuse Optical Tomography

Mozumder

Hauptmann

Nissilä

et al. 2022

IEEE Trans. Med. Imaging

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Diffuse optical tomography (DOT) utilises near-infrared light for imaging spatially distributed optical parameters, typically the absorption and scattering coefficients. The image reconstruction problem of DOT is an ill-posed inverse problem, due to the non-linear light propagation in tissues and limited boundary measurements. The ill-posedness means that the image reconstruction is sensitive to measurement and modelling errors. The Bayesian approach for the inverse problem of DOT offers the possibility of incorporating prior information about the unknowns, rendering the problem less ill-posed. It also allows marginalisation of modelling errors utilising the socalled Bayesian approximation error method. A more recent trend in image reconstruction techniques is the use of deep learning , which has shown promising results in various applications from image processing to tomographic reconstructions. In this work, we study the non-linear DOT inverse problem of estimating the (absolute) absorption and scattering coefficients utilising a 'model-based' learning approach, essentially intertwining learned components with the model equations of DOT. The proposed approach was validated with 2D simulations and 3D experimental data.We demonstrated improved absorption and scattering estimates for targets with a mix of smooth and sharp image features, implying that the proposed approach could learn image features that are difficult to model using standard Gaussian priors. Furthermore, it was shown that the approach can be utilised in compensating for modelling errors due to coarse discretisation enabling computationally efficient solutions. Overall, the approach provided improved computation times compared to a standard Gauss-Newton iteration.

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“…To generalize deep learning approaches to graph-structured data, Graph Neural Networks (GNNs) have been proposed and applied in many areas, such as molecular fingerprints [34], recommender system [35], and traffic forecasting [36]. A recent work [37] employed graph structures to construct the finite element mesh and proposed a GNN to solve the mono-frequency EIT inverse problem. Our work extends the GNN to solve the mfEIT image reconstruction problem with the assistance of auxiliary structural information.…”

Section: B Graph Neural Networkmentioning

confidence: 99%

Mask-Guided Spatial–Temporal Graph Neural Network for Multifrequency Electrical Impedance Tomography

Chen

Liu

et al. 2022

IEEE Trans. Instrum. Meas.

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Multi-frequency Electrical Impedance Tomography (mfEIT) is an emerging biomedical imaging modality that exploits frequency-dependent electrical properties. The mfEITimage-reconstruction problem for cell imaging is particularly challenging due to weak signals from miniaturized sensors and high sensitivity to modelling errors. Existing approaches are primarily based on the linearized model and few are applied to the miniaturized setup. Here we report a Mask-guided Spatial-Temporal Graph Neural Network (M-STGNN) to reconstruct mfEIT images in cell culture imaging. The M-STGNN captures simultaneously spatial and frequency correlations, and the spatial correlation is further constrained by geometric structures from auxiliary binary masks, such as CT or microscopic images. We validate the mfEIT approach through numerical simulations and experiments on MCF-7 human breast cancer cell aggregates. The results demonstrate the superiority of M-STGNN over the state of the art with an improvement of approximately 10.7% under the experimental setup. It can be readily extended to multi-modal biomedical imaging applications.

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Graph Convolutional Networks for Model-Based Learning in Nonlinear Inverse Problems

Cited by 30 publications

References 57 publications

Structural engineering from an inverse problems perspective

Structural engineering from an inverse problems perspective

A Model-Based Iterative Learning Approach for Diffuse Optical Tomography

Mask-Guided Spatial–Temporal Graph Neural Network for Multifrequency Electrical Impedance Tomography

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