A New InSAR Persistent Scatterer Selection Technique Using Top Eigenvalue of Coherence Matrix

Differential interferometric synthetic aperture radar (InSAR) time-series processing relies on identifying coherent pixels in SAR image stacks that show the persistent scatterer (PS) or distributed scatterer (DS) behavior. Accuracy of InSAR time-series estimates is dependent on the quality of selected PS/DS pixels. Current pixel selection techniques perform well when identifying highly coherent pixels but produce many false alarms in low coherence regions due to the inherent bias in residual phase estimation. Therefore, pixels with low coherence may have the appearance of noise and be rejected if the coherence threshold is too high. In contrast, lowering the threshold increases the number of false alarms introduced in processing giving noisier time-series as a result of incorrect phase unwrapping. The multidimensional SAR data acquisition can be described as a zero mean Gaussian process fully described by the covariance matrix. In this paper, we investigate the covariance matrix using a random matrix theory approach to find the statistical properties of the eigenvalues for simulated and real SAR data. The probability distribution of all the eigenvalues in this case is limited by the Marcenko-Pastur distribution. The histogram of the highest eigenvalue follows a Tracy-Widom distribution. Thus, by adopting a pixel selection strategy based on a threshold on the highest eigenvalue of the coherence matrix, we can differentiate between low coherence and noise pixels. In addition, our technique provides a methodology to detect the number of targets present in multiscatterer layover pixels and extract time-series information from double bounce response of bridges. Applying the technique for TerraSAR-X data over Berlin shows the effectiveness of the algorithm.