We propose a novel regularization method for compressive imaging in the context of the CS theory with coherent and redundant dictionaries. The approach relies on the conjecture that natural images exhibit strong average sparsity over multiple coherent frames. The associated reconstruction algorithm, based on an analysis prior and a reweighted $\ell_1$ scheme, is dubbed Sparsity Averaging Reweighted Analysis (SARA). We illustrate the performance of SARA in the context of Fourier imaging, for a particular application to radio interferometric (RI) imaging. We show through realistic simulations that the proposed approach outperforms state-of-the-art imaging methods in the field, which are based on the assumption of signal sparsity in a single frame.