Joint Sampling and Recovery of Correlated Sources

Sampling enables physical signals to be processed using digital hardware. When multiple signals are sampled, the spatial correlation between them may be utilized to reduce the overall reconstruction error. In this work we study joint sampling and reconstruction of multiple correlated stochastic sources, exploiting their correlation to improve recovery. We derive the achievable reconstruction error and the corresponding sampling system for arbitrary sampling rates and spectral structures. The proposed system minimizes the error when sampling below the Nyquist rate by preserving only the most dominant spatial eigenmodes aliased to each frequency. Using this characterization, we obtain sufficient conditions for error free recovery. We also discuss a distributed sampling setting, where each signal is acquired separately, while reconstruction is performed jointly. We characterize conditions under which distributed sampling performs as well as joint sampling. Our numerical results illustrate that joint sampling can achieve negligible reconstruction error using low sampling rates when the signals exhibit notable spatial correlation, and demonstrate that properly exploiting this correlation can dramatically improve reconstruction accuracy.