  In recent works, sparse models and convex optimization techniques have been
applied to radio-interferometric (RI) imaging showing the potential to
outperform state-of-the-art imaging algorithms in the field. In this talk, I
will review our latest contributions in RI imaging, which leverage the
versatility of convex optimization to both handle realistic continuous
visibilities and offer a highly parallelizable structure paving the way to
high-dimensional data scalability. Firstly, I will review our recently proposed
average sparsity approach, SARA, which relies on the observation that natural
images exhibit strong average sparsity over multiple coherent bases. Secondly,
I will discuss efficient implementations of SARA, and sparse regularization
problems in general, for large-scale imaging problems in a new toolbox dubbed
