Maximum Likelihood Estimation For SAR Interferometry

Synthetic Aperture Radar (SAR) interferometry (InSAR) uses phase differences between overlapping SAR images to estimate terrain height and terrain height changes. In addition, the coherence magnitude between the images is often used as a measure of the quality of the data and the processing. By modeling the SAR image data as independent circular Gaussian random variates, we develop the maximum likelihood (ML) estimates for interferogram phase, coherence magnitude, and the variance of the underlying circular Gaussian distribution. We show that the ML estimate of interferogram phase is equivalent to the standard technique of computing the phase of averaged complex returns. The ML estimate of the coherence magnitude depends on the estimated interferogram phase. In comparison, the sample coherence magnitude estimate based on amplitudes alone is badly biased. We also derive the Cramer-Rao bound for each ML estimate. The ML estimate of interferogram phase is close to this bound for moderate to high coherence values. Similarly, the coherence magnitude is close to the bound for values of coherence greater than approximately 1/2. For coherence magnitudes less than 1/2, the ML estimate of coherence magnitude is biased for data samples sizes up to 16 samples.