A Note on the Size of Denoising Neural Networks

Patch based denoising algorithms seek to approximate the conditional expectation of clean patches given their related noisy observations. In this note, we give a probabilistic account of how various algorithms approach this problem and in particular, we argue that small neural networks can denoise small-scale texture patterns almost as well as their large counterparts. The analysis further indicates that self-similarity and Bayesian approaches such as neural networks are complementary paradigms for patch denoising, which we illustrate with an algorithm that effectively complements BM3D with small neural networks, thereby outperforming BM3D with minor additional cost.