Scanning and sequential decision making for multidimensional data - Part I: The noiseless case

Asaf Cohen, Neri Merhav, Tsachy Weissman

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


We investigate the problem of scanning and prediction ("scandiction," for short) of multidimensional data arrays. This problem arises in several aspects of image and video processing, such as predictive coding, for example, where an image is compressed by coding the error sequence resulting from scandicting it. Thus, it is natural to ask what is the optimal method to scan and predict a given image, what is the resulting minimum prediction loss, and whether there exist specific scandiction schemes which are universal in some sense. Specifically, we investigate the following problems: first, modeling the data array as a random field, we wish to examine whether there exists a scandiction scheme which is independent of the field's distribution, yet asymptotically achieves the same performance as if this distribution were known. This question is answered in the affirmative for the set of all spatially stationary random fields and under mild conditions on the loss function. We then discuss the scenario where a nonoptimal scanning order is used, yet accompanied by an optimal predictor, and derive bounds on the excess loss compared to optimal scanning and prediction. This paper is the first part of a two-part paper on sequential decision making for multidimensional data. It deals with clean, noiseless data arrays. The second part deals with noisy data arrays, namely, with the case where the decision maker observes only a noisy version of the data, yet it is judged with respect to the original, clean data.

Original languageEnglish
Pages (from-to)3001-3020
Number of pages20
JournalIEEE Transactions on Information Theory
Issue number9
StatePublished - 1 Dec 2007
Externally publishedYes


  • Individual image
  • Multidimensional data
  • Random field
  • Scandiction
  • Sequential decision making
  • Universal scanning

ASJC Scopus subject areas

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


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