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Constrained Regularization by Denoising with Automatic Parameter Selection

Pasquale Cascarano, Alessandro Benfenati, Ulugbek S. Kamilov, Xiaojian Xu

TL;DR

The Constrained Regularization by Denoising (CRED) method is introduced that reformulates RED as a constrained optimization problem where the regularization parameter corresponds directly to the amount of noise in the measurements.

Abstract

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.

Constrained Regularization by Denoising with Automatic Parameter Selection

TL;DR

The Constrained Regularization by Denoising (CRED) method is introduced that reformulates RED as a constrained optimization problem where the regularization parameter corresponds directly to the amount of noise in the measurements.

Abstract

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.
Paper Structure (8 sections, 6 equations, 3 figures, 3 tables, 1 algorithm)

This paper contains 8 sections, 6 equations, 3 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Constrained RED
  3. Numerical Results
  4. Settings, evaluation metrics, and baseline methods
  5. On the choice of the threshold
  6. On the choice of the ADMM penalties and denoiser
  7. Comparisons with RED and RED-PRO
  8. Conclusions

Figures (3)

  • Figure 1: Distribution of $\sigma_{\mathbf{x}^{\ast}}$ (a) and PSNR (b) by varying $\tau$ for idealized and realistic scenarios on the whole Set5.
  • Figure 2: PSNR behaviour by varying $\lambda$ for RED (a), $(\alpha,\mu)$ and $\mu$ for RED-PRO (b), $(\beta_{\mathbf{r}},\beta_{\mathbf{t}})$ for CRED (c). In (b) for each $\alpha$ we present the PSNR distribution (average $\pm$ std) wrt $\mu$; in (c) for each $\beta_\mathbf{r}$ we present the PSNR distribution (average $\pm$ std) wrt $\beta_\mathbf{t}$.
  • Figure 3: Restoration of the Baby image. From left to right: two close-ups of ground truth, degraded image, RED, RED-PRO, and CRED.

Theorems & Definitions (1)

  • Remark 1