Regularization by denoising (RED) is a widely-used framework for solving inverse problems by leveraging image de-noisers as image priors. Recent work has reported the state-of-the-art performance of RED in a number of imaging applications using pre-trained deep neural nets as denoisers. Despite the recent progress, the stable convergence of RED algorithms remains an open problem. The existing RED theory only guarantees stability for convex data-fidelity terms and nonexpansive denoisers. This work addresses this issue by developing a new monotone RED (MRED) algorithm, whose convergence does not require nonexpansiveness of the deep denoising prior. Simulations on image deblurring and compressive sensing recovery from random matrices show the stability of MRED even when the traditional RED diverges.
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This content will become publicly available on January 1, 2025
Constrained Regularization by Denoising With Automatic Parameter Selection
Regularization by Denoising (RED) is a well-known method for solving image restoration problems by using learned image denoisers as priors. Since the regularization parameter in the traditional RED does not have any physical interpretation, it does not provide an approach for automatic parameter selection. This letter addresses this issue by introducing the Constrained Regularization by Denoising (CRED) method that reformulates RED as a constrained optimization problem where the regularization parameter corresponds directly to the amount of noise in the measurements. The solution to the constrained problem is solved by designing an efficient method based on alternating direction method of multipliers (ADMM). Our experiments show that CRED outperforms the competing methods in terms of stability and robustness, while also achieving competitive performances in terms of image quality.
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- Award ID(s):
- 2043134
- NSF-PAR ID:
- 10504937
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- IEEE Signal Processing Letters
- Volume:
- 31
- ISSN:
- 1070-9908
- Page Range / eLocation ID:
- 556 to 560
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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