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Adaptive Sensing of Sparse Signals

Robert Nowak

Recorded 10 July 2013 in Lausanne, Vaud, Switzerland

Event: Spars 2013 - Signal Processing with Adaptive Sparse Structured Representations

Abstract

Compressed sensing has had a tremendous impact on signal processing, machine learning, and statistics, fundamentally changing the way we think about sensing and data acquisition. Beyond the standard compressed sensing methods that gave birth to the ?eld, the compressive framework naturally suggests an ability to make measurements in an on-line and adaptive manner. Adaptive sensing uses previously collected measurements to guide the design and selection of the next measurement in order to optimize the gain of new information. There is now a reasonably complete understanding of the potential advantages of adaptive sensing over non-adaptive sensing, the main one being that adaptive sensing can reliably recover sparse signals at lower SNRs than non-adaptive sensing. Roughly speaking, to recover a k-sparse signal of length n, standard (non-adaptive) sensing requires the SNR to grow like log(n). Adaptive sensing, on the other hand, succeeds as long as the SNR scales like log(k). This is a signi?cant improvement, especially in high-dimensional regimes. This talk will cover theory, methods, and applications of adaptive sensing of sparse signals.

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