Multi scatterer detection within tomographic SAR using a compressive sensing approach

Synthetic Aperture Radar (SAR) tomography has seen a strong evolution in the past years as it has shown to be a worthwhile tool for analysing data obtained with high range resolution interferometric SAR sensors at pixel size. In particular by transforming them into a 3-D, 4-D, and in general Multi-Dimensional SAR image. The resolution in the higher dimensions, for instance in elevation and time, depends on the size of the elevation aperture and on the temporal separation which will be spanned by the different repeat paths. However, for more recent space-borne SAR systems which has sub-meter range resolution, like COSMO-Skymed or TerraSAR-X, the orbital tracks are tightly controlled so that they show only a small variation. According to this, the tomographic resolution in elevation is an order of magnitude lower than in range or azimuth. This is normally not a problem as only the strongest reflector is of interest. However, for urban scenes or man made objects one can expect that each azimuth-range cell consists of a few point-like scatterers in the elevation direction. To resolve these scatterers super-resolution algorithms are required to improve the performance of tomographic tools. Due to the present of only a few scatterers we can use compressive sensing (CS) techniques for reconstructing the elevation for tomographic images. This paper presents an adapted CS method for 4-D tomographic SAR and compares it with classical matched filter. Super-resolution properties of the proposed CS is proven by results obtained from simulations and from real TerraSAR-X data.