CAREER: Toward a Unified Approach to Universality in Information Processing

信号处理、通信和压缩应用中的一个主要挑战是如何构建接近理论性能极限的方案。事实上，在实践中很少有关于源和信道特性的先验知识，这就需要这些方案是通用的。虽然针对不同问题的现有通用方案显然有许多共同的成分，但到目前为止，它们大多是分开考虑的。该项目开发了一个统一的框架，包括普遍性问题的理论、算法和实施方面。我们解决了从降噪、Wyner-Ziv编码、联合源信道编码、扫描和预测到强化学习等问题领域中有关通用方案的问题。我们开发了一个统一的框架来解决这些问题，这有助于为新问题构建通用方案，并对现有问题产生新的见解。在更多的应用方面，我们正在开发具有吸引力的复杂性的新算法范例，并将其应用于实践。我们也在开发分析工具来评估新算法的性能。

A major challenge in signal processing, communication, and compression applications is the construction of schemes that approach the theoretical performance limits. The fact that a priori knowledge of source and channel characteristics is rarely available in practice necessitates that these schemes be universal. While it is clear that existing universal schemes for different problems share many common ingredients, thus far they have been considered mostly separately. This project develops a unified framework encompassing theoretical, algorithmic, and implementation aspects of the universality problem.We address questions concerning universal schemes in problem areas ranging from denoising, Wyner-Ziv coding, joint source-channel coding, scanning and prediction, to reinforcement learning. We develop a unified framework for addressing such questions, which facilitates the construction of universal schemes for new problems, and leads to new insights on existing ones. On the more applied side, we are developing new algorithmic paradigms that have attractive complexity, and applying them in practice. We are also developing analytic tools for assessing the performance of the new algorithms.