Kesten has observed that the known reconstruction methods of random sceneries seem to strongly depend on the one-dimensional setting of the problem and asked whether a construction still is possible in two dimensions. In this paper we answer this question in the affirmative under the condition that the number of colors in the scenery is large enough.
"Scenery reconstruction in two dimensions with many colors." Ann. Appl. Probab. 12 (4) 1322 - 1347, November 2002. https://doi.org/10.1214/aoap/1037125865