  We propose a novel algorithm for image reconstruction in radio
interferometry. The ill-posed inverse problem associated with the incomplete
Fourier sampling identified by the visibility measurements is regularized by
the assumption of average signal sparsity over representations in multiple
wavelet bases. The algorithm, defined in the versatile framework of convex
optimization, is dubbed Sparsity Averaging Reweighted Analysis (SARA). We show
through 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 basis only.
