Information theory, which describes the transmission of signals in the presence of noise, has enabled the development of reliable communication systems that underlie the modern world. Imaging systems can also be viewed as a form of communication, in which information about the object is "transmitted" through images. However, the application of information theory to imaging systems has been limited by the challenges of accounting for their physical constraints. Here, we introduce a framework that addresses these limitations by modeling the probabilistic relationship between objects and their measurements. Using this framework, we develop a method to estimate information using only a dataset of noisy measurements, without making any assumptions about the image formation process. We demonstrate that these estimates comprehensively quantify measurement quality across a diverse range of imaging systems and applications. Furthermore, we introduce Information-Driven Encoder Analysis Learning (IDEAL), a technique to optimize the design of imaging hardware for maximum information capture. This work provides new insights into the fundamental performance limits of imaging systems and offers powerful new tools for their analysis and design.

翻译：描述信号在噪声环境中传输的信息论，推动了现代世界所依赖的可靠通信系统的发展。成像系统亦可被视为一种通信形式，其中关于物体的信息通过图像被"传输"。然而，信息论在成像系统中的应用一直受限于如何准确考量其物理约束的挑战。本文提出一个框架，通过建模物体与其测量值之间的概率关系来解决这些局限。利用该框架，我们开发了一种仅需使用含噪测量数据集即可估计信息的方法，且无需对图像形成过程做任何假设。我们证明，这些估计能够全面量化多种成像系统及应用场景下的测量质量。此外，我们引入了信息驱动编码器分析学习（IDEAL），这是一种优化成像硬件设计以实现最大信息捕获的技术。这项工作为理解成像系统的基本性能极限提供了新视角，并为其分析与设计提供了强大的新工具。