  Many inverse problems in signal processing deal with the robust estimation of
unknown data from underdetermined linear observations. Low dimensional models,
when combined with appropriate regularizers, have been shown to be efficient at
performing this task. Sparse models with the 1-norm or low rank models with the
nuclear norm are examples of such successful combinations. Stable recovery
guarantees in these settings have been established using a common tool adapted
to each case: the notion of restricted isometry property (RIP). In this paper,
we establish generic RIP-based guarantees for the stable recovery of cones
(positively homogeneous model sets) with arbitrary regularizers. These
guarantees are illustrated on selected examples. For block structured sparsity
in the infinite dimensional setting, we use the guarantees for a family of
regularizers which efficiency in terms of RIP constant can be controlled,
leading to stronger and sharper guarantees than the state of the art.
