  Compressive sampling (CoSa) is a new methodology which demonstrates that
sparse signals can be recovered from a small number of linear measurements.
Greedy algorithms like CoSaMP have been designed for this recovery, and
variants of these methods have been adapted to the case where sparsity is with
respect to some arbitrary dictionary rather than an orthonormal basis. In this
work we present an analysis of the so-called Signal Space CoSaMP method when
the measurements are corrupted with mean-zero white Gaussian noise. We
establish near-oracle performance for recovery of signals sparse in some
arbitrary dictionary. In addition, we analyze the block variant of the method
for signals whose supports obey a block structure, extending the method into
the model-based compressed sensing framework. Numerical experiments confirm
that the block method significantly outperforms the standard method in these
settings.
