Multimodality and multichannel monitoring have become increasingly popular and accessible in engineering, Internet of Things, wearable devices, and biomedical applications. In these contexts, given the diverse and complex nature of data modalities, the relevance of sensor fusion and sensor selection is heightened. In this note, we study the problem of channel/modality selection and fusion from an information theoretical perspective, focusing on linear and nonlinear signal mixtures corrupted by additive Gaussian noise. We revisit and extend well-known properties of linear noisy data models in estimation and information theory, providing practical insights that assist in the decision-making process between channel (modality) selection and fusion. Using the notion of multichannel signal-to-noise ratio, we derive conditions under which, selection or fusion of multimodal/multichannel data can be beneficial or redundant. This contributes to a better understanding of how to optimize sensor fusion and selection from a theoretical standpoint, aiming to enhance multimodal/multichannel system design, especially for biomedical multichannel/multimodal applications.

翻译：多模态和多通道监测在工程、物联网、可穿戴设备及生物医学应用中日益普及且易于实现。在这些场景中，由于数据模态的多样性和复杂性，传感器融合与传感器选择的相关性愈发凸显。本文从信息论视角研究通道/模态选择与融合问题，重点关注被加性高斯噪声破坏的线性和非线性信号混合。我们重新审视并拓展了估计理论与信息论中线性噪声数据模型的经典性质，为通道（模态）选择与融合的决策过程提供实用见解。利用多通道信噪比概念，我们推导出多模态/多通道数据选择或融合可能产生效益或冗余的条件。这有助于从理论层面深入理解如何优化传感器融合与选择，旨在改进多模态/多通道系统设计，尤其适用于生物医学多通道/多模态应用场景。