Compressive Sensing

Sensors and imaging systems and networks are under increasing pressure to accommodate ever larger and higher-dimensional data sets; ever faster capture, sampling, and processing rates; ever lower power consumption; communication over ever more difficult channels; and radically new sensing modalities. The foundation of today’s digital data acquisition systems is the Shannon/Nyquist sampling theorem, which asserts that to avoid losing information when digitizing a signal or image, one must sample at least two times faster than the signal’s bandwidth, at the so-called Nyquist rate. Unfortunately, the physical limitations of current sensing systems combined with inherently high Nyquist rates impose a performance brick wall to a large class of important and emerging applications.

This talk will overview our recent work on compressive sensing, a new approach to data acquisition in which analog signals are digitized for processing not via uniform sampling but via measurements using more general, even random, test functions. In stark contrast with conventional wisdom, the new theory asserts that one can combine “sub-Nyquist-rate sampling” with digital computational power for efficient and accurate signal acquisition. Compressive sensing systems directly translate analog data into a compressed digital form; all we need to do is “decompress” the measured data through an optimization on a digital computer. The implications of compressive sensing are promising for many applications and enable the design of new kinds of analog-to-digital converters, cameras and imaging systems, and sensor networks.