The idea that signals reside in a union of low dimensional subspaces subsumesmany low dimensional models that have been used extensively in the recentdecade in many fields and applications. Until recently, the vast majority ofworks have studied each one of these models on its own. However, a recentapproach suggests providing general theory for low dimensional models usingtheir Gaussian mean width, which serves as a measure for the intrinsic lowdimensionality of the data. In this work we use this novel approach to study ageneralized version of the popular compressive sampling matching pursuit(CoSaMP) algorithm, and to provide general recovery guarantees for signals froma union of low dimensional linear subspaces, under the assumption that themeasurement matrix is Gaussian. We discuss the implications of our results forspecific models, and use the generalized algorithm as an inspiration for a newgreedy method for signal reconstruction in a combined sparse-synthesis andcosparse-analysis model. We perform experiments that demonstrate the usefulnessof the proposed strategy.
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