  Let {\xi (n)}_{n\in Z} be a two-color random scenery, that is, a random
coloring of Z in two colors, such that the \xi (i)'s are i.i.d. Bernoulli
variables with parameter \tfrac12. Let {S(n)}_{n\in N} be a symmetric random
walk starting at 0. Our main result shows that a.s., \xi \circ S (the
composition of \xi and S) determines \xi up to translation and reflection. In
other words, by observing the scenery \xi along the random walk path S, we can
a.s. reconstruct \xi up to translation and reflection. This result gives a
positive answer to the question of H. Kesten of whether one can a.s. detect a
single defect in almost every two-color random scenery by observing it only
along a random walk path.
