Impact of noise correlation on multimodality

In this paper, we consider the problem of estimating an unknown random scalar observed by two modalities. We study two scenarios using mutual information and mean square error. In the first scenario, we consider that the noise correlation is known and examine its impact on the information content of two modalities. In the second scenario we quantify the information loss when the considered value of the noise correlation is wrong. It is shown that the noise correlation usually enhances the estimation accuracy and increases information. However, the performance declines if the noise correlation is misdefined, and the two modalities may jointly convey less information than one single modality.