  The idea that signals reside in a union of low dimensional subspaces subsumes
many low dimensional models that have been used extensively in the recent
decade in many fields and applications. Until recently, the vast majority of
works have studied each one of these models on its own. However, a recent
approach suggests providing general theory for low dimensional models using
their Gaussian mean width, which serves as a measure for the intrinsic low
dimensionality of the data. In this work we use this novel approach to study a
generalized version of the popular compressive sampling matching pursuit
(CoSaMP) algorithm, and to provide general recovery guarantees for signals from
a union of low dimensional linear subspaces, under the assumption that the
measurement matrix is Gaussian. We discuss the implications of our results for
specific models, and use the generalized algorithm as an inspiration for a new
greedy method for signal reconstruction in a combined sparse-synthesis and
cosparse-analysis model. We perform experiments that demonstrate the usefulness
of the proposed strategy.
