Regularization by Denoising via Fixed-Point Projection (RED-PRO)

@article{Cohen2021RegularizationBD,
  title={Regularization by Denoising via Fixed-Point Projection (RED-PRO)},
  author={Regev Cohen and Michael Elad and Peyman Milanfar},
  journal={SIAM J. Imaging Sci.},
  year={2021},
  volume={14},
  pages={1374-1406}
}
Inverse problems in image processing are typically cast as optimization tasks, consisting of data fidelity and stabilizing regularization terms. A recent regularization strategy of great interest utilizes the power of denoising engines. Two such methods are the Plug-and-Play Prior (PnP) and Regularization by Denoising (RED). While both have shown state-of-the-art results in various recovery tasks, their theoretical justification is incomplete. In this paper, we aim to enrich the understanding… 
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27 Citations
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27 Citations

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TLDR
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ASYNC-RED: A PROVABLY CONVERGENT ASYN-
TLDR
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References

SHOWING 1-10 OF 117 REFERENCES
Image Restoration by Iterative Denoising and Backward Projections
  • Tom Tirer, R. Giryes
  • Computer Science, Mathematics
    IEEE Transactions on Image Processing
  • 2019
TLDR
An alternative method for solving inverse problems using off-the-shelf denoisers, which requires less parameter tuning and is competitiveness with task-specific techniques and the P&P approach for image inpainting and deblurring is proposed.
Regularization by Denoising: Clarifications and New Interpretations
TLDR
This work proposes a new framework called Score-Matching by Denoising (SMD), which aims to match a “score” (i.e., the gradient of a log-prior) and shows tight connections between SMD, kernel density estimation, and constrained minimum mean-squared error denoising.
Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problems
TLDR
This paper studies the possibility of replacing the proximal operator of the regularization used in many convex energy minimization algorithms by a denoising neural network, and obtains state-of-the-art reconstruction results.
Block Coordinate Regularization by Denoising
TLDR
A new block coordinate RED algorithm is developed that decomposes a large-scale estimation problem into a sequence of updates over a small subset of the unknown variables and theoretically analyzes the convergence of the algorithm and discusses its relationship to the traditional proximal optimization.
The Little Engine That Could: Regularization by Denoising (RED)
TLDR
This paper provides an alternative, more powerful, and more flexible framework for achieving Regularization by Denoising (RED): using the denoising engine in defining the regulariza...
Performance Analysis of Plug-and-Play ADMM: A Graph Signal Processing Perspective
  • Stanley H. Chan
  • Computer Science
    IEEE Transactions on Computational Imaging
  • 2019
TLDR
This paper restricts the denoisers to the class of graph filters under a linearity assumption, or more specifically the symmetric smoothing filters, and introduces a new analysis technique via the concept of consensus equilibrium to provide interpretations to problems involving multiple priors.
Plug-and-Play ADMM for Image Restoration: Fixed-Point Convergence and Applications
TLDR
It is shown that for any denoising algorithm satisfying an asymptotic criteria, called bounded denoisers, Plug-and-Play ADMM converges to a fixed point under a continuation scheme.
A Convergent Image Fusion Algorithm Using Scene-Adapted Gaussian-Mixture-Based Denoising
TLDR
This work proposes using a scene-adapted denoiser plugged into the iterations of the alternating direction method of multipliers, which yields state-of-the-art results but also allows proving convergence of the resulting algorithm.
DeepRED: Deep Image Prior Powered by RED
TLDR
This work proposes to bring-in the concept of Regularization by Denoising (RED), which leverages existing denoisers for regularizing inverse problems, and shows how the two can be merged into a highly effective unsupervised recovery process while avoiding the need to differentiate the chosen denoiser, and leading to very effective results.
Boosting the Performance of Plug-and-Play Priors via Denoiser Scaling
TLDR
A scaling parameter is introduced that adjusts the magnitude of the denoiser input and output so that the performance of plug-and-play prirs for denoising CNN priors that do not have explicitly tunable parameters is improved.
...
1
2
3
4
5
...