The next generation of giant and sensitive radio telescopes such as LOFAR and MeerKAT/SKA, give access to a new window of high-time, angular, spectral resolutions and high instantaneous sensitivity. On one hand, one has to face this new deluge of data, on the other hand, improved sensitivity brings new instrumental challenges that need to be solved for to create high dynamic range images (HDR – contrast > 1:10^6). For this, we use sparse representations, convex optimization and the general « compressed sensing » framework that has recently demonstrated its robustness in solving a variety of inverse problems. After introducing sparsity and compressed sensing, I will present two applications for radio interferometry:
1) the signal reconstruction/deconvolution of multi-spectral/multi-temporal radio images of resolved radio sources, blind source separation (Jiang et al., PhD, 2017), transient source detection (Girard et al. in prep.)
2) the sparse modelling of radio antennas to improve the quality wide-field imaging and calibration in radio (Girard et al. in rev.).
Beyond these applications, I will try to show in the course of the presentation, that such methods can also be useful for tackling similar inverse problems in other fields.