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. This work explores the Neumann network architecture to solve linear inverse problems, which can be interpreted as an approximation of the MSE optimal reconstruction according to our Proposition 1. The Neumann network architecture also permits a learned patchwise regularizer, which learns the low-dimensional conditional distributions over image patches instead of the whole image. The Neumann network is empirically competitive with other state-of-the-art methods for inverse problems in imaging, and we demonstrate the ability to learn to regularize from a single training pair.
Neumann networks are an end-to-end, sample-efficient learning approach to solving linear inverse problems in imaging that are compatible with the MSE optimal approach and admit an extension to patch-based learning.
{"src": "scitldr-AIC_train", "paper_id": "SyxYnQ398H"}