On the Numerical Distortion-Mutual Information Function of Image Denoising with Deep Convolutional Networks

This paper presents a new perspective on the image denoising problem. The architecture of image denoising algorithm used in this paper is the Deep Convolutional Neural Networks (DCNN). Designing DCNN models relates tuning hyperparameters such as a number of layers of DCNN. To choose suitable hyperparameters, it would has an advantage to examine the best achievable image denoising performance under different a number of DCNN layers. Moreover realizing how close the image denoising algorithm performance to the optimal result allows us to design the efficient image denoising algorithm. The Blahut-Arimoto algorithm is used to derive numerically distortion-mutual information function of image denoising algorithm. The derived function is the distortion lower bound given the mutual information between the original image and the denoised image. The noise environment in this paper is relied on the Poisson noise. The denoised image qualities of different DCNN configurations are compared with the results from the numerical Blahut-Arimoto algorithm. The experimental results indicate that the DCNN models provide near optimal denoised image qualities given mutual information, even though there are some rooms to further improve image denoising algorithm.