A Square Root Sampling Law for Signal Recovery

The problem of finding the optimal node density for reconstructing a stochastic signal from its noisy samples in sensor networks is considered. The signal could be nonstationary and nonbandlimited. A weight is assigned to each location that indicates the relative importance of the signal at that location. It is shown that when the number of samples is very large, the optimal density of the samples at each location is proportional to the square root of the weight associated to that location.