Compressed Sensing

Compressed sensing scheme

Compressed sensing may be considered as revolution in the world of signal processing. It is a new paradigm which enables recovering a signal from much fewer measurements than traditionally required by the Nyquist rate. It is particularly important in systems where measurements are costly like, e.g., magnetic resonance imaging (MRI).

Classical sensing devices (e.g., digital cameras) sample a signal at a high resolution and then proceed to source coding (e.g., jpeg) to get a compressed representation of this signal. In other words, a huge amount of data is captured and most of it is thrown away to keep only the most important parts.

Compressed sensing aims at sensing at a low resolution and directly capturing the important parts of a signal, thus, enabling the use of much simpler and cheaper sensors, e.g., low frequency AD converters.

The figure above shows a typical compressed sensing setup.

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