Practical Bounds on Image Denoising: From Estimation to Information
Recently, in a previous work, we proposed a way to bound how well any given image can be denoised. The bound was computed directly from the noise-free image that was assumed to be available. In this work, we extend the formulation to the more practical case where no ground truth is available. We show that the parameters of the bounds, namely the cluster covariances and level of redundancy for patches in the image, can be estimated directly from the noise corrupted image. Further, we analyze the bounds formulation to show that these two parameters are interdependent and they, along with the bounds formulation as a whole, have a nice information-theoretic interpretation as well. The results are verified through a variety of well-motivated experiments.
image denoising bayesian cramer-rao lower bound image clustering image patch model mutual information renyi entropy shannon entropy