ABSTRACT
This chapter discusses sparse models, compressive measurement protocols, and the recovery of sparse signals from compressive measurements. Sparsity is manifestation of the fact that many high-dimensional signals actually have a small number of degrees of freedom. The choice of whether a signal is better described using a synthesis sparsity model or an analysis sparsity model can depend on the context. Synthesis sparsity can be preferable in cases where one views the dictionary elements as ingredients that actually comprise the signal; analysis sparsity can be preferable in cases where the dictionary is merely a set of vectors used for looking at the signal. Greedy algorithms for compressive sensing (CS) reconstruction are an alternative to optimization-based recovery methods. Algorithms can be adopted to exploit the structure of exclusions reduced union of subspaces, and when these algorithms are successfully employed, the CS reconstruction problem can be solved using fewer measurements than would be required using a conventional algorithm suitable for unstructured sparsity models.
