期刊
IEEE TRANSACTIONS ON COMPUTATIONAL IMAGING
卷 6, 期 -, 页码 328-343出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCI.2019.2948732
关键词
Image reconstruction; inverse problems; convergence; iterative algorithms; deconvolution; machine learning; estimation
资金
- National Science Foundation [1740707, 1447449, 0353079]
- AFOSR [FA9550-18-1-0166]
- Direct For Computer & Info Scie & Enginr
- Division of Computing and Communication Foundations [0353079] Funding Source: National Science Foundation
- Division of Computing and Communication Foundations
- Direct For Computer & Info Scie & Enginr [1740707] Funding Source: National Science Foundation
- Div Of Information & Intelligent Systems
- Direct For Computer & Info Scie & Enginr [1447449] Funding Source: National Science Foundation
Many challenging image processing tasks can be described by an ill-posed linear inverse problem: deblurring, deconvolution, inpainting, compressed sensing, and superresolution all lie in this framework. Traditional inverse problem solvers minimize a cost function consisting of a data-fit term, which measures how well an image matches the observations, and a regularizer, which reflects prior knowledge and promotes images with desirable properties like smoothness. Recent advances in machine learning and image processing have illustrated that it is often possible to learn a regularizer from training data that can outperform more traditional regularizers. We present an end-to-end, data-driven method of solving inverse problems inspired by the Neumann series, which we call a Neumann network. Rather than unroll an iterative optimization algorithm, we truncate a Neumann series which directly solves the linear inverse problem with a data-driven nonlinear regularizer. The Neumann network architecture outperforms traditional inverse problem solution methods, model-free deep learning approaches, and state-of-the-art unrolled iterative methods on standard datasets. Finally, when the images belong to a union of subspaces and under appropriate assumptions on the forward model, we prove there exists a Neumann network configuration that well-approximates the optimal oracle estimator for the inverse problem and demonstrate empirically that the trained Neumann network has the form predicted by theory.
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