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We consider the problem of constructing a linear map from a Hilbert space$\mathcal{H}$ (possibly infinite dimensional) to $\mathbb{R}^m$ that satisfiesa restricted isometry property (RIP) on an arbitrary signal model $\mathcal{S}\subset \mathcal{H}$. We present a generic framework that handles a large classof low-dimensional subsets but also unstructured and structured linear maps. Weprovide a simple recipe to prove that a random linear map satisfies a generalRIP on $\mathcal{S}$ with high probability. We also describe a generictechnique to construct linear maps that satisfy the RIP. Finally, we detail howto use our results in several examples, which allow us to recover and extendmany known compressive sampling results.

Recipes for stable linear embeddings from Hilbert spaces to R^m