Scanning and sequential decision making for multidimensional data - Part II: The noisy case

Asaf Cohen, Tsachy Weissman, Neri Merhav

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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 andWeissman. 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.

Original languageEnglish
Pages (from-to)5609-5631
Number of pages23
JournalIEEE Transactions on Information Theory
Issue number12
StatePublished - 15 Dec 2008
Externally publishedYes


  • Filtering
  • Hidden Markov model
  • Multidimensional data
  • Prediction
  • Random field
  • Scandiction
  • Scanning
  • Sequential decision making

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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