Improving the Generalisation of Learned Reconstruction Frameworks
This work improves generalization for inverse problems in medical imaging, particularly CT reconstruction, by reducing parameter counts and enhancing robustness to unseen acquisition variations, though it is incremental as it builds on existing neural network methods.
The paper tackles the challenge of poor generalization in data-driven reconstruction for X-ray CT by addressing the mismatch between grid-based CNNs and the line manifold of sinogram data, introducing a graph representation for CT geometries and a hybrid GLM architecture that outperforms CNNs in metrics like structural similarity and peak signal-to-noise ratio with fewer parameters and better scaling.
Ensuring proper generalization is a critical challenge in applying data-driven methods for solving inverse problems in imaging, as neural networks reconstructing an image must perform well across varied datasets and acquisition geometries. In X-ray Computed Tomography (CT), convolutional neural networks (CNNs) are widely used to filter the projection data but are ill-suited for this task as they apply grid-based convolutions to the sinogram, which inherently lies on a line manifold, not a regular grid. The CNNs, unaware of the geometry, are implicitly tied to it and require an excessive amount of parameters as they must infer the relations between measurements from the data rather than from prior information. The contribution of this paper is twofold. First, we introduce a graph data structure to represent CT acquisition geometries and tomographic data, providing a detailed explanation of the graph's structure for circular, cone-beam geometries. Second, we propose GLM, a hybrid neural network architecture that leverages both graph and grid convolutions to process tomographic data. We demonstrate that GLM outperforms CNNs when performance is quantified in terms of structural similarity and peak signal-to-noise ratio, despite the fact that GLM uses only a fraction of the trainable parameters. Compared to CNNs, GLM also requires significantly less training time and memory, and its memory requirements scale better. Crucially, GLM demonstrates robust generalization to unseen variations in the acquisition geometry, like when training only on fully sampled CT data and then testing on sparse-view CT data.