Joint Alignment from Pairwise Differences with a Noisy Oracle.

In this work we consider the problem of recovering n discrete random variables x(i) is an element of {0, . . . , k-i}, 1 <= i <= n with the smallest possible number of queries to a noisy oracle that returns for a given query pair (x(i), x(j)) a noisy measurement of their modulo k pairwise difference, i.e., y(ij) = x(i) - x(j) (mod k). This is a joint discrete alignment problem with important applications in computer vision [12,23], graph mining [20], and spectroscopy imaging [22]. Our main result is a recovery algorithm (up to some offset) that solves with high probability the non convex maximum likelihood estimation problem using O(n(1+o(1))) queries.