The sparsity reconstruction approach find once again a practical application in astronomy.
The CosmoStat group developped a new way (using a FISTA implementation) to solve the aperture synthesis inverse problem posed by radio interferometry imaging. In the scope of LOFAR and SKA, a study has been published demonstrating the performance of the method (in terms of photometry, fidelity, super-resolution) while being compatible with Direction-Dependent effects.
What's next? This method is currently applied for testing different array configurations of the SKA for weak lensing studies from radio imaging.