A Taste of Compressed Sensing

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 Shannon-Nyquist 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.