The little Engine that Could: Regularization by Denoising (RED)


Image denoising has reached impressive heights in performance and quality -- almost as good as it can ever get. But is this the only way in which tasks in image processing can exploit the image denoising engine? In this paper we offer Regularization by Denoising (RED): using the denoising engine in defining the regularization of the inverse problem. We propose an explicit image-adaptive Laplacian-based regularization functional, making the overall objective functional clear and well-defined. With a complete flexibility to choose the iterative optimization procedure for minimizing the above functional, RED is capable of incorporating any image denoising algorithm, treat general inverse problems very effectively, and is guaranteed to converge to the globally optimal result. As examples of its utility, we test this approach and demonstrate state-of-the-art results in the image deblurring and super-resolution problems.