We study the problem of remote reconstruction of a continuous signal from its multiple corrupted versions. We are interested in the optimal number of samples and their locations for each corrupted signal to minimize the total reconstruction distortion of the remote signal. The correlation among the corrupted signals can be utilized to reduce the sampling rate.
For a class of Gaussian signals, we show 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 show that both of these sampling strategies are optimal if we are interested in recovering the set of corrupted signals, rather than the remote signal.