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Deep learning is the current de facto state of the art in tomographic imaging. A common approach is to feed the result of a simple inversion, for example the backprojection, to a convolutional neural network (CNN) which then computes the reconstruction. Despite strong results on "in-distribution" test data similar to the training data, backprojection from sparse-view data delocalizes singularities, so these approaches require a large receptive field to perform well. As a consequence, they overfit to certain global structures which leads to poor generalization on out-of-distribution (OOD) samples. Moreover, their memory complexity and training time scale unfavorably with image resolution, making them impractical for application at realistic clinical resolutions, especially in 3D: a standard U-Net requires a substantial 140GB of memory and 2600 seconds per epoch on a research-grade GPU when training on 1024 × 1024 images. In this paper, we introduce GLIMPSE, a local processing neural network for computed tomography which reconstructs a pixel value by feeding only the measurements associated with the neighborhood of the pixel to a simple MLP. While achieving comparable or better performance with successful CNNs like the U-Net on in-distribution test data, GLIMPSE significantly outperforms them on OOD samples while maintaining a memory footprint almost independent of image resolution; 5GB memory suffices to train on 1024 × 1024 images. Further, we built GLIMPSE to be fully differentiable, which enables feats such as recovery of accurate projection angles if they are out of calibration.

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In electromagnetic inverse scattering, we aim to reconstruct object permittivity from scattered waves. Deep learning is a promising alternative to traditional iterative solvers, but it has been used mostly in a supervised framework to regress the permittivity patterns from scattered fields or back-projections. While such methods are fast at test-time and achieve good results for specific data distributions, they are sensitive to the distribution drift of the scattered fields, common in practice. If the distribution of the scattered fields changes due to changes in frequency, the number of transmitters and receivers, or any other real-world factor, an end-to-end neural network must be re-trained or finetuned on a new dataset. In this paper, we propose a new datadriven framework for inverse scattering based on deep generative models. We model the target permittivities by a low-dimensional manifold which acts as a regularizer and learned from data. Unlike supervised methods which require both scattered fields and target signals, we only need the target permittivities for training; it can then be used with any experimental setup. We show that the proposed framework significantly outperforms the traditional iterative methods especially for strong scatterers while having comparable reconstruction quality to state-of-the-art deep learning methods like U-Net. I. INTRODUCTIONE LECTROMAGNETIC inverse scattering is the problem of determining the electromagnetic properties of unknown objects from how they scatter incident fields. As it is nondestructive, it has a variety of applications in different areas, such as early detection of breast cancer [1], mineral prospecting [2], detecting defects and cracks inside objects [3], imaging through the wall [4] and remote sensing [5].We consider the reconstruction of the finite number of parameters of the object from the scattered fields. While inverse scattering is well-posed and Lipschitz stable in theory, when full-aperture continuous measurements are available [6], it is Manuscript