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Recent advances have illustrated that it is often possible to learn to solve linear inverse problems in imaging using training data that can outperform more traditional regularized least-squares solutions. Along these lines, we present some extensions of the Neumann network, a recently introduced end-to-end learned architecture inspired by a truncated Neumann series expansion of the solution map to a regularized least-squares problem. Here we summarize the Neumann network approach and show that it has a form compatible with the optimal reconstruction function for a given inverse problem. We also investigate an extension of the Neumann network that incorporates a more sample efficient patch-based regularization approach.more » « less
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Many modern approaches to image reconstruction are based on learning a regularizer that implicitly encodes a prior over the space of images. For large-scale images common in imaging domains like remote sensing, medical imaging, astronomy, and others, learning the entire image prior requires an often-impractical amount of training data. This work describes a deep image patch-based regularization approach that can be incorporated into a variety of modern algorithms. Learning a regularizer amounts to learning the a prior for image patches, greatly reducing the dimension of the space to be learned and hence the sample complexity. Demonstrations in a remote sensing application illustrates that learning patch-based regularizers produces high-quality reconstructions and even permits learning from a single ground-truth image.more » « less
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