多维数据的扫描和顺序决策.第II部分：噪声情况
Scanning and Sequential Decision Making for Multi-Dimensional Data - Part II: the Noisy Case
摘要：
本文研究了随机域上受噪声污染的序贯决策问题。在这种情况下，决策者观察到数据的噪声版本，但相对于干净的数据进行判断。特别是，我们首先考虑顺序扫描和过滤噪声随机场的问题。在这种情况下，顺序滤波器被给予选择其遍历随机场的路径的自由（例如，嘈杂的图像或视频序列），因此很自然地会询问可实现的最佳性能是什么以及该性能对扫描选择的敏感程度。我们正式定义的问题，扫描和过滤，得出一个最佳的可实现的性能和量化的超额损失时，使用非最佳扫描仪，相比，最佳的扫描和过滤。然后，我们讨论的问题，顺序扫描和预测的噪声随机场。该设置是用于诸如噪声图像的恢复和编码的应用的自然模型。我们正式定义的问题的扫描和预测的一个嘈杂的多维数组，并与最佳性能的清洁scandictability定义的Merhav和Weissman。此外，由于次优扫描的超额损失的界限推导，并建议一个通用的预测算法。本文件是一份两部分文件的第二部分。第一篇论文讨论了无噪声数据阵列上的序贯决策，即当决策者根据它所观察到的同一数据阵列进行判断时。
英文摘要：
We consider the problem of sequential decision making on random fields corrupted by noise. In this scenario, the decision maker observes a noisy version of the data, yet judged with respect to the clean data. In particular, we first consider the problem of sequentially scanning and filtering noisy random fields. In this case, the sequential filter is given the freedom to choose the path over which it traverses the random field (e.g., noisy image or video sequence), thus it is natural to ask what is the best achievable performance and how sensitive this performance is to the choice of the scan. We formally define the problem of scanning and filtering, derive a bound on the best achievable performance and quantify the excess loss occurring when non-optimal scanners are used, compared to optimal scanning and filtering. We then discuss the problem of sequential scanning and prediction of noisy random fields. This setting is a natural model for applications such as restoration and coding of noisy images. We formally define the problem of scanning and prediction of a noisy multidimensional array and relate the optimal performance to the clean scandictability defined by Merhav and Weissman. Moreover, bounds on the excess loss due to sub-optimal scans are derived, and a universal prediction algorithm is suggested. This paper is the second part of a two-part paper. The first paper dealt with sequential decision making on noiseless data arrays, namely, when the decision maker is judged with respect to the same data array it observes.
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