  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.
