Fast Phase Estimation Approach for Distributed Scatterer Based on Power Method

Distributed scatterer (DS) possesses a medium signal-to-noise ratio (SNR), and its interferometric phase is typically estimated from sample covariance matrix (SCM) using phase linking (PL) algorithm. However, the phase estimation of DS is very time consuming. The eigenvalue decomposition (EVD) methods benefit from highly optimized eigen-decomposition libraries and therefore have a higher computational efficiency. Nevertheless, EVD methods are still insufficient due to the massive data provided by modern SAR satellites with multi-polarizations and high spatio-temporal resolution. The essence of conventional EVD methods is to decompose the SCM (or modified SCM) with a series of eigenvalue-eigenvector pairs and then select only the eigenvector corresponding to the largest eigenvalue as the optimal estimate. Inspired by that, we proposed a fast phase estimation approach based on power method (PM), a straightforward algorithm that approximates the largest eigenvalue and its associated eigenvector. The convergence rate of PM depends on the ratio between the second and the first largest eigenvalue, i.e., λ<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub>/λ<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub>. We demonstrate that there is an intrinsic correlation between λ<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub>/λ<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> and the traditional quality measure (γ<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">_PTA</i>). Based on this correlation, we design two termination criteria for PM to enable fast and accurate phase estimation. Experiments with simulated and real SAR data demonstrate that PM achieves comparable phase estimation accuracy to EVD but is 3–6 times faster. Additionally, we compare the computational efficiency and accuracy of EVD, PM, and the eigendecomposition-based maximum likelihood estimator of interferometric phase (EMI), providing practical guidance for different application scenarios.