  We discuss a novel sparsity prior for compressive imaging in the context of
the theory of compressed sensing with coherent redundant dictionaries, based on
the observation that natural images exhibit strong average sparsity over
multiple coherent frames. We test our prior and the associated algorithm, based
on an analysis reweighted $\ell_1$ formulation, through extensive numerical
simulations on natural images for spread spectrum and random Gaussian
acquisition schemes. Our results show that average sparsity outperforms
state-of-the-art priors that promote sparsity in a single orthonormal basis or
redundant frame, or that promote gradient sparsity. Code and test data are
available at https://github.com/basp-group/sopt.
