Domain independent post-processing with graph U-nets: applications to electrical impedance tomographic imaging⋆.

Area of Science:

• Computer Vision
• Medical Imaging
• Graph Neural Networks

Background:

• U-Net architecture is highly successful for image segmentation but limited to regular pixel/voxel domains.
• Irregular meshes are commonly used in solving inverse problems, such as in electrical impedance tomography (EIT).

Purpose of the Study:

• To extend the U-Net architecture to handle irregular meshes by developing a graph-based equivalent.
• To demonstrate the effectiveness of the proposed graph U-Net for improving EIT reconstructions.

Main Methods:

• Interpreted irregular meshes as graphs to develop a graph U-Net.
• Introduced novel cluster pooling and unpooling layers to mimic max-pooling operations on graphs.
• Evaluated performance on simulated and experimental EIT data from various measurement devices.

Main Results:

• The graph U-Net effectively improved early iterate total variation (TV) reconstructions in EIT, even from the first iteration.
• Demonstrated generalization capabilities, with networks trained on 2D data successfully applied to 3D reconstructions.
• Showed flexibility across different measurement geometries and instrumentation.

Conclusions:

• The graph U-Net offers a flexible solution for processing data on irregular meshes, directly applicable to computational domains.
• This approach significantly reduces computational cost for inverse problems, especially in higher dimensions.
• The dimension-independent graph structure facilitates training on 2D data and application to 3D problems, further optimizing computational efficiency.