In this paper we investigate SAR image compression based on sparse representation. Two approaches are considered: the first one is based on the use of an Overcomplete ICA transform coding method, the second one is based on Compressive Sensing (CS). In both cases an Overcomplete ICA representation is used as sparse representation, but while in the first case the significant overcomplete ICA coefficients are coded using an optimal entropy constrained threshold quantizer, in the latter case a reduced number of measurements obtained combining the SAR image pixels through a random measurement matrix are directly coded. Numerical results on TerraSAR-X images are presented.