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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.
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Deep Equilibrium Learning of Explicit Regularization Functionals for Imaging Inverse Problems
There has been significant recent interest in the use of deep learning for regularizing imaging inverse problems. Most work in the area has focused on regularization imposed implicitly by convolutional neural networks (CNNs) pre-trained for image reconstruction. In this work, we follow an alternative line of work based on learning explicit regularization functionals that promote preferred solutions. We develop the Explicit Learned Deep Equilibrium Regularizer (ELDER) method for learning explicit regularization functionals that minimize a mean-squared error (MSE) metric. ELDER is based on a regularization functional parameterized by a CNN and a deep equilibrium learning (DEQ) method for training the functional to be MSE-optimal at the fixed points of the reconstruction algorithm. The explicit regularizer enables ELDER to directly inherit fundamental convergence results from optimization theory. On the other hand, DEQ training enables ELDER to improve over existing explicit regularizers without prohibitive memory complexity during training. We use ELDER to train several approaches to parameterizing explicit regularizers and test their performance on three distinct imaging inverse problems. Our results show that ELDER can greatly improve the quality of explicit regularizers compared to existing methods, and show that learning explicit regularizers does not compromise performance relative to methods based on implicit regularization.
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- Award ID(s):
- 2043134
- PAR ID:
- 10504934
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- IEEE Open Journal of Signal Processing
- Volume:
- 4
- ISSN:
- 2644-1322
- Page Range / eLocation ID:
- 390 to 398
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1109/OJSP.2023.3296036
