Fast Spatial Denoising of InSAR Interferograms via Empirical Statistical Modeling

SAR interferometry (InSAR) provides a framework for extracting high-resolution topographic information and detecting surface deformation. By analyzing the phase difference between radar acquisitions obtained at different times, one can characterize landscape geometry and surface changes. However, inherent phase noise often compromises the reliability of the resulting interferometric products. Consequently, there is a sustained need for spatial filtering techniques that suppress noise while preserving structural integrity and resolution. This work addresses the challenge of filtering the unwrapped phase, a process traditionally reliant on accurate coherence images to identify reliable pixels. We evaluate three statistically based spatial filters for phase noise reduction. The Enhanced Lee filter, which utilizes spatial adaptation and a physically grounded probability model, serves as the baseline for comparison. We examine the Gierull model, which improves computational efficiency by restricting the parameter space. To further reduce execution time, we propose and evaluate two empirical alternatives: the truncated wrapped normal (TcN) and the truncated wrapped Cauchy (TcC) distributions. Results indicate that these empirical models significantly reduce computational demand without degrading the quality of the filtered phase. We assess performance using a simulated dataset for objective validation alongside InSAR imagery of La Cumbre volcano, Los Alamos, and Robledo volcano. While the proposed models demonstrate significant gains in computational efficiency compared to current methods, we identify numerical integration as a primary bottleneck in the filtering process; this challenge warrants further investigation. Our results indicate that empirical statistical models provide a viable path for accelerated InSAR processing with accuracy equivalent to traditional, computationally intensive approaches.