|Stochastic Systems Group|
Wireless Sensing, Active Learning, and Compressive Sampling
University of Wisconsin, Madison
Wireless sensor networks promise a fundamentally new approach for gathering information about the physical world via a distributed network of sensors that can communicate with each other and/or with a (usually distant) fusion center through radio-frequency wireless links. Limited energy resources make power conservation essential in these envisioned sensing systems. Thus, it becomes crucial to strategically decide when, where and how to collect samples and communicate information. Active learning methods adaptively select sample locations based on previous observations in order to "learn" a target function using as few samples as possible, which could clearly be advantageous in sensor network operations. Compressive sampling refers to taking non-traditional samples in the form of randomized projections of data. Recent results show that compressive sampling can allow one to reconstruct signals from very few such samples, again suggesting promising opportunities for wireless sensing. This talk compares the theoretical performance of adaptive and compressive sampling to conventional Shannon-Nyquist sampling, and it is shown that for certain classes of piecewise constant (spatial) signals, both compressive and adaptive schemes can dramatically outperform conventional sampling. Furthermore, we show that in high SNR regimes the performance of compressive sampling approaches that of adaptive sampling, achieving a near-optimal rate of convergence.
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