Directed information and causal estimation in continuous time
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
Directed information, causal estimation, and communication in continuous time
WiOPT'09 Proceedings of the 7th international conference on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks
Discrete denoising with shifts
IEEE Transactions on Information Theory
The relationship between causal and noncausal mismatched estimation in continuous-time AWGN channels
IEEE Transactions on Information Theory
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We consider the problem of sequential decision making for 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 scanning and sequentially 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 nonoptimal scanners are used, compared to optimal scanning and filtering. We then discuss the problem of scanning and prediction for 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 suboptimal 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 scanning and sequential decision making on noiseless data arrays.