Holographic representations of data encode information in packets of equal importance that enable progressive recovery. The quality of recovered data improves as more and more packets become available. This progressive recovery of the information is independent of the order in which packets become available. Such representations are ideally suited for distributed storage and for the transmission of data packets over networks with unpredictable delays and or erasures.

Several methods for holographic representations of signals and images have been proposed over the years and multiple description information theory also deals with such representations. Surprisingly, however, these methods had not been considered in the classical framework of optimal least-squares estimation theory, until very recently. We develop a least-squares approach to the design of holographic representation for stochastic data vectors, relying on the framework widely used in modeling signals and images.

数据的全息表示将信息编码在同等重要的数据包中，从而能够逐步恢复。随着越来越多的数据包变得可用，恢复的数据的质量将提高。信息的这种逐步恢复与数据包变得可用的顺序无关。这样的表示理想地适合于分布式存储以及通过不可预测的延迟和/或擦除在网络上传输数据分组。

多年来，已经提出了几种用于信号和图像的全息表示的方法，并且多描述信息理论也处理这种表示。然而，令人惊讶的是，直到最近，还没有在最佳最小二乘估计理论的经典框架中考虑这些方法。我们基于在信号和图像建模中广泛使用的框架，开发了一种最小二乘方法来设计随机数据向量的全息表示。