## 1 Introduction  
Driven by the development of geophysical applications, investments in the construction and launch of satellites equipped with high-resolution imaging radars, specifically Synthetic Aperture Radars (SAR), have been multiplied in recent years. In addition to operating at different frequencies, SAR sensors are characterized by the availability of different operating, modes thus giving the possibility to trade-off the resolution and coverage. On one hand, very high-resolution--up to a sub-metric level at X-Band (e.g., COSMO/Skymed and TerraSAR-X/Tandem-X)--data are available with a limited coverage of a few tens of kilometers. On the other hand, by exploiting scanning beams with electronic steering of the antenna, high-resolution modes with decametric resolution at C-Band allow to achieve coverage approaching (ERS and ENVISAT) and even far exceeding (Sentinel-1) hundreds of kilometers. Above all, the increase in the number of available SAR sensors is significantly reducing the access area and the revisiting time, thus expanding the SAR data archives that frequently can go back up to 20 years for many regions of the Earth's globe [1; 2; 3]. Sea surface scattering shows large variation over repeated orbits, depending on the sea state conditions. When compared to the return from terrestrial regions, the signal scattered back from the sea shows a larger (relative) dynamic, thus providing a potentially valuable source of information for understanding several geophysical processes. However, the observed scenario is, in this case, rapidly changing and influenced, much more than on the land, by the presence of processes occurring in the atmosphere, thus making the interpretation of the signal more complex. SAR image formation mainly depends on the small gravity waves, also referred to as ripples: the occurrence of Bragg conditions coupled with the wavelength of the illuminating (microwave) radiation offers favorable conditions for an increase of backscattering. Ripples are generated by the wind and are modulated by longer waves thus providing the possibility to analyze the images to derive information on both the wind and the sea surface waves. [4]. The large sensitivity of the sea scattering makes it possible for SAR images to distinguish oceanographic features related to wind waves and swell as well as ocean internal waves and sea currents [5; 6; 7; 8; 9]. These phenomena have different spatial scales and spatial layouts and often, are present together in a single SAR image covering swaths of several tens of kilometers. Modulation of the radar backscatter due to the wind reflects the spatial properties of the wind itself, which depends on factors such as wind speed, air stability conditions, and interaction with orography in coastal regions. The extraction of the spatial properties of the wind from SAR images has been extensively studied [10; 11] and well demonstrated. Another \"hot-point\" in the area of extraction of information from sea SAR images, which is the main interest of this work, is related to sea currents [12; 13]. The process of hydrodynamic modulation of the sea-surface roughness allows, for example, sea surface currents signatures to be observable in SAR images, as well established in the literature, see, for instance [4; 12; 13; 14]. The extraction of quantitative parameters on currents from the amplitude image alone is, however, a rather complex issue. Many variables are involved for the backscattering determination, such as wind vector, bathymetry, etc. [15]. For this reason, similarly to other SAR applications, the phase information may provide valuable information [4; 12]. The possibility to observe the surface ocean currents by SAR images dates back to the eighties, when scientists associated some of the large scale features imaged by SAR with mesoscale oceanic eddies [16] and ocean current fronts [17]. Since then, a quantitative measurement of the radial component of the sea surface currents can be achieved from a single SAR image using spectral analysis.