Offset-compensated nonlocal filtering of interferometric phase

The nonlocal approach, proposed originally for additive white Gaussian noise image filtering, has rapidly gained popularity in many applicative fields and for a large variety of tasks. It has proven especially successful for the restoration of Synthetic Aperture Radar (SAR) images: single-look and multi-look amplitude images, multi-temporal stacks, polarimetric data. Recently, powerful nonlocal filters have been proposed also for Interferometric SAR (InSAR) data, with excellent results. Nonetheless, a severe decay of performance has been observed in regions characterized by a uniform phase gradient, which are relatively common in InSAR images, as they correspond to constant slope terrains. This inconvenience is ultimately due to the rare patch effect, the lack of suitable predictors for the target patch. In this paper, to address this problem, we propose the use of offset-compensated similarity measures in nonlocal filtering. With this approach, the set of candidate predictors is augmented by including patches that differ from the target only for a constant phase offset, which is automatically estimated and compensated. We develop offset-compensated versions of both basic nonlocal means and InSAR-Block-Matching 3D (BM3D), a state-of-the-art InSAR phase filter. Experiments on simulated images and real-world TanDEM-X SAR interferometric pairs prove the effectiveness of the proposed method.