Reconstructing a piece of scenery with polynomially many observations

Heinrich Matzinger, Silke W.W. Rolles

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


Benjamini asked whether the scenery reconstruction problem can be solved using only polynomially many observations. In this article, we answer his question in the affirmative for an i.i.d. uniformly colored scenery on ℤ observed along a random walk path with bounded jumps. We assume the random walk is recurrent, can reach every integer with positive probability, and the number of possible single steps for the random walk exceeds the number of colors. For infinitely many l, we prove that a finite piece of scenery of length l around the origin can be reconstructed up to reflection and a small translation from the first p(l) observations with high probability; here p is a polynomial and the probability that the reconstruction succeeds converges to 1 as l→∞.

Original languageEnglish
Pages (from-to)289-300
Number of pages12
JournalStochastic Processes and their Applications
Issue number2
StatePublished - 1 Oct 2003
Externally publishedYes


  • Polynomially many observations
  • Random walk
  • Scenery reconstruction


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