Rethinking Signal Processing

By Kirk L. Kroeker

Compressed sensing, which draws on information theory, probability theory, and other fields, has generated a great deal of excitement with its nontraditional approach to signal processing.

For many years, traditional signal processing has relied on the Shannon-Nyquist theory, which states that the number of samples required to capture a signal must be determined by the signal’s bandwidth. An alternative sampling theory, called compressed sensing or compressive sampling, turns the Shannon-Nyquist theory on its head. The idea behind compressed sensing is to accurately acquire signals from relatively few samples. The theory was so revolutionary when it was created a few years ago that an early paper outlining it was initially rejected on the basis that its claims appeared impossible to substantiate.

(This article appeared in CACM, vol. 52, no. 5, May 2009, pp. 13-15.)

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