  We consider the problem of identifying a linear deterministic operator from
its response to a given probing signal. For a large class of linear operators,
we show that stable identifiability is possible if the total support area of
the operator's spreading function satisfies D<=1/2. This result holds for an
arbitrary (possibly fragmented) support region of the spreading function, does
not impose limitations on the total extent of the support region, and, most
importantly, does not require the support region to be known prior to
identification. Furthermore, we prove that stable identifiability of almost all
operators is possible if D<1. This result is surprising as it says that there
is no penalty for not knowing the support region of the spreading function
prior to identification. Algorithms that provably recover all operators with
D<=1/2, and almost all operators with D<1 are presented.
