Compressive sensing and filter-bank signal models

A compressible signal can often be modeled as a sum of outputs of subband filters of a synthesis filter bank. This model allows one to find compressive sampling schemes, whereby the original continuous signal can directly be acquired by sampling at a very low (sub-Nyquist) rate. This paper revisits this result from the view point of filter bank theory. This is motivated by recent work by Mishali and Eldar on the so-called Xampling techniques for compressible signals. The viewpoint presented here emphasizes the simplicity and directness of the compressive sensing idea and also places in evidence the framework which can be used to formulate optimal compressive sampling problems.