Spectral Estimation for Synthetic Aperture Radar Tomography

Kurzfassung

Synthetic Aperture Radar (SAR) Tomography, a new and advanced technique in the field of SAR processing, is aimed at determining the 3-D reflectivity function from measured multi-pass SAR data. It is essentially a spectrum estimation problem as for a specific resolution cell the complex valued SAR measurements of a SAR image stack are actually the irregularly sampled Fourier transform of the reflectivity function in the elevation direction. The successful launch of the German high resolution SAR mission TerraSAR-X provides a new possibility to investigate this topic with high quality spaceborne data. Within the framework of this master thesis, the spectrum estimation problem is formulated from a mathematical point of view. Different spectrum estimation strategies such as the Singular Value Decomposition (SVD) and Nonlinear Least Squares estimation (NLS) are evaluated and compared using both simulated data and TerraSAR-X data from the testsite Las Vegas with special consideration of the difficulties caused by sparse and irregularly spaced sampling. The problem of ill-conditioning when using the Singular Value Decomposition is investigated and regularization tools (such as singular value truncation and Wiener filtering) are utilized to overcome this problem. For the sake of validation, the spectrum estimation results with TerraSAR-X data are compared to the probable ground truth. Penalized model selection criteria such as the Bayesian Information Criterion (BIC), Akaike information criterion (AIC) and Minimum Description Length criterion (MDL) are implemented on the spectral estimates to determine the number of scatterers inside one resolution cell - which is necessary a prior knowledge for precise PSI displacement estimation. The probability of correctly detecting the number of scatterers and the accuracy of the corresponding elevation estimates are evaluated from simulated data. Finally, the model selection results with PS points of TerraSAR-X data are visualized in Google-Earth and the nature of PS pixel with multi-scatterers are discussed.