# SAR Interferogram Filtering of Shearlet Domain Based on Interferometric Phase Statistics
## 1 Introduction  
Interferometric Synthetic Aperture Radar (InSAR) has proven to be an effective technology for creating a digital elevation model (DEM) and detecting ground deformation [1], so it has been widely applied in the study of seismic deformation, volcanic activity, glacial drift, urban subsidence and landslides [2; 3]. However, the accuracy and reliability of InSAR measurements are highly dependent on the quality of interferometric phase. The interferogram phase is often contaminated by noises caused by the SAR imaging process and data processing, as well as temporal and baseline decorrelation effects [4] that impact the unwrapping process and decrease DEM accuracy [5]. Several techniques proposed to reduce the interferometric phase noises can be divided into two categories: spatial filtering and the frequency domain filtering. Spatial filtering, such as the multi-looking procedure, reduces noises at the expense of spatial resolution [5]. To maintain the resolution, [PERSON] et al. [6] proposed a self-adaptive filter based on local gradient slope estimation, which can obtain satisfactory results by taking the images' directional characteristics into consideration. [PERSON] et al. [7] presented an improved method by excluding singular pixels within a selected direction via the minimum mean squared error estimator. [PERSON] et al. [8] presented a directionally adaptive filter (DAF) with a filter window and its direction is able to vary continuously with the fringe direction. [PERSON] et al. [9] proposed a maximum posterior estimator that makes use of the Gaussian Markov Random Fields (MRF). [PERSON] and [PERSON] [10] suggested suppressing noise by incorporating InSAR magnitude information with a fractal surface scattering model. Because the signal and noise could be separated in the frequency domain, the method is performed by suppressing the transformed coefficients. Furthermore, the most widely used frequency domain filtering method is the Goldsteinfilter, in which the filter factor, varying between zero and one, has a great impact on the filter performance [11]. [PERSON] et al. [12] improved the Goldstein filter by adjusting the filtering factor with coherence. By this method, the quality of the filtered interferogram can be highly improved with less resolution loss. However, the filter factor is only related to coherence, but not directly related to the parameters that can reflect the interferogram noise level. Based on this, [PERSON] et al. [13] improved filtering parameters, and the parameters depend on interferometric coherence and number of looks of the interferogram. [PERSON] et al. [14] presented an efficient denoising approach based on the assumption that the true phase is composed of principal phase components and residual phase components, and the filter equals to three common filters by varying the bound parameter to three different values. Recently, some papers about the adaptive filtering of interferometric stacks have been published. [PERSON] et al. [15] proposed the Despec KS algorithm, a space adaptive filtering procedure which identifies statistically homogeneous areas. [PERSON] et al. [16] presented different methods to select similar pixels based on their amplitude distribution for the purpose of adaptive multi-looking and practical results. [PERSON] et al. [17] proposed a temporal filtering, which uses the Phase Linking (PL) algorithm to estimate a set of N acquisition phases that satisfies the property of phase triangularity. [PERSON] et al. [18] proposed an effective noise filtering approach to improve the performance of classical extended minimum cost flow-small baseline subset (EMCF-SBAS) inversion technique. The filtering process is a nonlinear minimization process and needs no priori information on the statistics of the complex-valued SAR images. The wavelet filtering method, a signal analysis tool, can combine the spatial domain and frequency domain, meaning it has time-frequency analysis capability [19]; it can also separate the phase information and noise more easily.