An improved Hoerl-Kennard-based ridge estimation method for SBAS-InSAR deformation model resolution

Based on the traditional Differential Interferometric Synthetic Aperture Radar (D-InSAR) technique, the Small Baseline Subset (SBAS)-InSAR performs time-series analysis of multi-temporal Synthetic Aperture Radar (SAR) images for subsidence retrieval and has strong application potential. During processing, one SAR image may form interferograms with multiple images, inducing multicollinearity in the coefficient matrix and resulting in an ill-posed problem. To improve subsidence monitoring accuracy, an improved Hoerl – Kennard (HK) method was adopted to determine the ridge parameter for the SBAS-InSAR deformation model. By using the mean of the characteristic components instead of the maximum value, the proposed method alleviates the ill-posed problem caused by very small eigenvalues in the normal matrix. Simulated data and SAR images over the Jinan Start-up Area were used to validate the method against the L-curve and traditional HK methods. The results indicate that SBAS-InSAR deformation models constructed under different temporal and spatial baseline thresholds may exhibit severe ill-posed problems when all interferograms belong to the same small baseline subset, and all three ridge estimation methods effectively mitigate this issue. The root mean square error (RMSE) of the SBAS-InSAR deformation model decreases steadily with increasing coherence. Compared with the traditional HK method, the improved HK method improves accuracy by 9.41% while maintaining accuracy comparable to the L-curve method. Moreover, its computational efficiency is comparable to that of the traditional HK method but approximately 6.5 times higher than that of the L-curve method, demonstrating superior efficiency for large-scale SBAS-InSAR processing.