Generalized sampling , infinite-dimensional compressed sensing , and semi-random sampling for asymptotically incoherent dictionaries

Recent developments in sampling in abstract Hilbert spaces have led to a new theory of compressed sensing for infinitedimensional signals. In this paper, we continue with this theme by introducing a new type of subsampling for infinite-dimensional sparse recovery problems, known as semi-random sampling. As we demonstrate, this allows for subsampling in problems which previously had not been amenable to more conventional compressed sensing tools. More specifically, semi-random sampling allows one to overcome the so-called incoherence barrier, which limits the potential for subsampling via standard random sampling techniques. The key to this improvement is a property known as asymptotic incoherence. In the final part of this paper we provide specific estimates for this property in several important cases, and illustrate via numerical example the benefit of semi-random sampling.

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