On the size of incoherent systems Original Research Article

This paper concerns systems with small coherence parameter. Simple greedy-type algorithms perform well on these systems, which are also useful in the construction of compressed sensing matrices. We discuss the following problems for both RnRn and CnCn. How large can a dictionary be, if we prescribe the coherence parameter? How small could the resulting coherence parameter be, if we impose a size on the dictionary? How could we construct such a system? Several fundamental results from different areas of mathematics shed light on these important problems with far-reaching implications in approximation theory.