  Consider a continuous signal that cannot be observed directly. Instead, one
has access to multiple corrupted versions of the signal. The available
corrupted signals are correlated because they carry information about the
common remote signal. The goal is to reconstruct the original signal from the
data collected from its corrupted versions. The information theoretic
formulation of the remote reconstruction problem assumes that the corrupted
signals are uniformly sampled and the focus is on optimal compression of the
samples. In this paper we revisit this problem from a sampling perspective. We
look at the problem of finding the best sampling locations for each signal to
minimize the total reconstruction distortion of the remote signal. In finding
the sampling locations, one can take advantage of the correlation among the
corrupted signals. Our main contribution is a fundamental lower bound on the
reconstruction distortion for any arbitrary nonuniform sampling strategy. This
lower bound is valid for any sampling rate. Furthermore, it is tight and
matches the optimal reconstruction distortion in low and high sampling rates.
Moreover, it is shown that in the low sampling rate region, it is optimal to
use a certain nonuniform sampling scheme on all the signals. On the other hand,
in the high sampling rate region, it is optimal to uniformly sample all the
signals. We also consider the problem of finding the optimal sampling locations
to recover the set of corrupted signals, rather than the remote signal. Unlike
the information theoretic formulation of the problem in which these two
problems were equivalent, we show that they are not equivalent in our setting.
