We consider two imaging applications of compressed sensing where the acquired data corresponds to samples
in the Fourier domain (aka k- space). The rst one is magnetic resonance imaging (MRI), which has been
one of the standard examples in the compressed sensing literature. The second one is synthetic aperture radar
(SAR). We consider the practical issues of applying compressed sensing ideas in these two applications noting
that the physical prossesses involved in these two sensing modalities are very different. We consider the issues
of: appropriate image models and sampling strategies, dealing with noise, and the need for calibration.