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IGPM278.pdf January 2007 
TITLE 
A Taste of Compressed Sensing 
AUTHORS 
Albert Cohen, Wolfgang Dahmen, Ronald DeVore 
ABSTRACT 
The usual paradigm for signal processing is to model a signal as a bandlimited
function and capture the signal by means of its time samples. The ShannonNyquist
theory says that the sampling rate needs to be at least twice the bandwidth. For
broadbanded signals, such high sampling rates may be impossible to implement in
circuitry. Compressed Sensing is a new area of signal processing whose aim is to
circumvent this dilemma by sampling signals closer to their information rate instead
of their bandwidth. Rather than model the signal as bandlimited, Compressed
Sensing, assumes the signal can be represented or approximated by a few suitably
chosen terms from a basis expansion of the signal. It also enlarges the concept of
sample to include the application of any linear functional applied to the signal. In
this paper, we shall give a brief introduction to compressed sensing that centers on
the effectiveness and implementation of random sampling.

KEYWORDS 
compressed sensing, best kterm approximation, instance optimality in
probability, efficient decoding, orthogonal matching pursuit.

DOI 
10.1117/12.725193 
PUBLICATION 
Proceedings of SPIE 6576, 65760C (2007) 