Understanding Gaussian Noise Mismatch: A Hellinger Distance Approach

This paper explores noise-mismatched models using the Hellinger distance. In many applications, the design/training stage often assumes an independent and identically distributed (i.i.d.) Gaussian prior noise, but the real world introduces Gaussian noise with arbitrary covariance, creating a mismatch. We analyze the impact on system output and study optimal injected noise intensity for training/design. While theory assumes Gaussian sources, it provides guidance for non-Gaussian settings too. Experiments with Cycle-GAN for image-to-image translation validate the theory, producing results consistenting with derivations. Overall, this work provides theoretical and empirical insights into designing systems robust to noise uncertainties beyond simplified assumptions.