# Bias Removal for Goldstein Filtering Power Using a Second Kind Statistical Coherence Estimator

^{1}

Department of Surveying and Mapping Engineering, School of Transportation, Southeast University, Nanjing 211189, China

^{2}

State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, China

^{3}

School of Earth Science and Engineering, Hohai University, Nanjing 210098, China

^{4}

Department of Environmental, Earth and Geospatial Sciences, North Carolina Central University, Durham, NC 27707, USA

^{*}

Authors to whom correspondence should be addressed.

Received: 17 August 2018 / Revised: 21 September 2018 / Accepted: 25 September 2018 / Published: 28 September 2018

(This article belongs to the Special Issue InSAR for Earth Observation)

The adaptive Goldstein filter driven by InSAR coherence is one of the most famous frequency domain-based filters and has been widely used to improve the quality of InSAR measurement with different noise features. However, the filtering power is biased to varying degrees due to the biased coherence estimator and empirical modelling of the filtering power under a given coherence level. This leads to under- or over-estimation of phase noise over the entire dataset. Here, the authors present a method to correct filtering power on the basis of the second kind statistical coherence estimator. In contrast with regular statistics, the new estimator has smaller bias and variance values, and therefore provides more accurate coherence observations. In addition, a piece-wise function model determined from the Monte Carlo simulation is used to compensate for the nonlinear relationship between the filtering parameter and coherence. This method was tested on both synthetic and real data sets and the results were compared against those derived from other state-of-the-art filters. The better performance of the new filter for edge preservation and residue reduction demonstrates the value of this method.