In the last four years, a few research groups worked on the feasibility of compressive sampling (CS) in ultrasound medical imaging and several attempts of applying the CS theory may be found in the recent literature. In particular, it was shown that using iotap-norm minimization with p different from 1 provides interesting RF signal reconstruction results. In this paper, we propose to further improve this technique by processing the reconstruction in the Fourier domain. In addition, alpha -stable distributions are used to model the Fourier transforms of the RF lines. The parameter p used in the optimization process is related to the parameter alpha obtained by modelling the data (in the Fourier domain) as an alpha -stable distribution. The results obtained on experimental US images show significant reconstruction improvement compared to the previously published approach where the reconstruction was performed in the spatial domain.