Distributed sampling of signals linked by sparse filtering: theory and applications

We study the distributed sampling and centralized reconstruction of two correlated signals, modeled as the input and output of an unknown sparse filtering operation. This is akin to a Slepian-Wolf setup, but in the sampling rather than the lossless compression case. Two different scenarios are considered: In the case of universal reconstruction, we look for a sensing and recovery mechanism that works for all possible signals, whereas in the case of almost sure reconstruction, we allow to have a small set (with measure zero) of unrecoverable signals. We derive achievability bounds on the number of samples needed for both scenarios. Our results show that, only in the almost sure setup can we effectively exploit the signal correlations to achieve effective gains in sampling efficiency. In addition to the above theoretical analysis, we propose an efficient and robust distributed sensing and reconstruction algorithm based on annihilating filters. Finally, we evaluate the performance of our...

• Type: Journal
• Year: 2010
• Where: TSP
• Authors: Ali Hormati, Olivier Roy, Yue M. Lu, Martin Vetterli
• Keywords: Artificial Intelligence, Lossless Compression Case, Scenario, Sparse Filtering Operation, TSP 2010