Compressive sensing: Principles and hardware implementations

Abstract

Compressive sensing (CS) [1]-[3] has emerged in the last decade as a powerful tool and paradigm for acquiring signals of interest from fewer measurements than was thought possible. CS capitalizes on the the fact that many real-world signals inherently have far fewer degrees of freedom than the signal size might indicate. For instance, a signal with a sparse spectrum depends upon fewer degrees of freedom than the total bandwidth it may cover. CS theory then asserts that one can use very efficient randomized sensing protocols, which would sample such signals in proportion to their degrees of freedom rather than in proportion to the dimension of the larger space they occupy (e.g., Nyquist-rate sampling). An overview and mathematical description of CS can be found in [4].