SAR tomography (TomoSAR) extends the synthetic aperture principle into the elevation direction for 3-D imaging. It uses stacks of several acquisitions from slightly different viewing angles (the elevation aperture) to reconstruct the reflectivity function along the elevation direction by means of spectral analysis for every azimuth-range pixel.
The new class of meter-resolution spaceborne SAR systems (TerraSAR-X and COSMO-Skymed) offers a tremendous improvement in tomographic reconstruction of urban areas and man-made infrastructure. The high resolution fits well to the inherent scale of buildings (floor height, distance of windows, etc.). In order to fully exploit the potential of this class of meter-resolution data there is demand for new and improved TomoSAR inversion algorithms.
Compressive sensing (CS) is a new and attractive technique for TomoSAR. It aims at minimizing the number of measurements to be taken from signals while still retaining the information necessary to approximate them well. It provides a good compromise between classical parametric and non-parametric spectral analysis methods for TomoSAR. Compared to parametric spectral analysis, CS is more robust to phase noise, has lower computational effort, and does not require model selection to provide the prior knowledge about the number of scatterers in a resolution cell. Compared to non-parametric spectral estimation CS overcomes the limitation of elevation resolution caused by the length of elevation aperture, i.e. CS has super-resolution properties.
In this paper the CS approach to TomoSAR is outlined. Its extension to differential (4-D) TomoSAR is introduced. Numerical simulations for realistic acquisition and noise scenarios will be presented to evaluate the potential and limits of the new technique. The first CS TomoSAR results with TerraSAR-X spotlight data (1 m resolution) over urban areas will be presented.
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