The correct reconstruction of radio images from visibility data is an intense field of research since the coming of new generation radio interferometers such as LOFAR (LOw Frequency Array) and SKA (Square Kilometre Array). These instruments require a correct approach taking into account Direction-(in)Dependent Effects (such as variation of the beam, polarization, ...). The mathematical framework for calibration is provided by the RIME, the **Radio Interferometer Measurement Equation**, (refer to Hamaker, Sault, Bregman series of papers and Smirnov 2011 series) enables a proper handling for data modelling and calibration.

In spite of the high angular/time/frequency resolutions and the large variety of baselines, these interferometers measure a finite number of visibilities over the course of an observation, giving an incomplete frequency sampling of the sky Fourier Transform. This incomplete knowledge of the sky FT creates distorted images when the visibility data are gridded and projected back to the image plane. These images are distorted by the instrumental Point Spread Function (PSF) which encode this lack of information. A robust imaging of radio interferometric data resides in the robustness of the deconvolution algorithm used to remove the effect of this PSF. CLEAN and its derivatives (see family of CLEAN algorithms and associated papers) have been performing this task for decades on point sources will relatively good performance and robustness.

However, Sparse data and the existence of multi-scale radio emission (mix of point source and extended emissions) are obstacles to the deconvolution. The framework of **Compressed Sensing** offer us an opportunity to redefine the deconvolution problem as an optimization problem (*inpainting problem*) targeting solutions close to the real sky brightness with the lowest reconstruction bias.

Our approach was to construct an alternative to CLEAN with the implementation of another deconvolution method based on the FISTA algorithm (Beck et Teboulle, 2009).

**SASIR **(Sparse Aperture Synthesis Image Reconstruction) is an in-painting imager which combines sparse representation with $$l_1$$-minimization.

**SASIR 2D-1D** is a spin-off of SASIR (based on Condat-Vu algorithm) applied to the reconstruction of transient sources in the image plane.

*Project contributors: Dr. Julien N. Girard, Ming Jiang, Jean-Luc Starck, Stéphane Corbel and formerly Dr. H. Garsden and Dr. A. Woiselle.*