## 1 Introduction  
Synthetic aperture radar (SAR) imagery has demonstrated its potential in the military and in civilian fields, such as ground deformation observation and computer vision systems [1; 2; 3; 4]. However, a challenge to the SAR imagery, particularly with low-frequency SAR systems, is the influence of the ionosphere. When SAR signals propagate through the ionosphere, their phase and polarization change [5; 6; 7; 8]. There are a number of studies about ionospheric influences on SAR and SAR interferometry (InSAR), such as ionosphere-induced Faraday rotation (FR) on linearly polarized polarimetric SAR data [9; 10; 11; 12; 13], ionosphere-induced interferometric phase errors and azimuth offsets on InSAR measurements [14; 15; 16], ionospheric effects on simulated P-band SAR imagery [17; 18] and comprehensive investigation of this effect on SAR and InSAR [19; 20; 21; 22; 23; 24]. Moreover, with increasing interest in the low-frequency SAR systems (e.g., L-band TerraSAR operated by German Aerospace Center (DLR), NASA-ISRO Synthetic Aperture Radar (NISAR) operated by National Aeronautics and Space Administration (NASA), and P-band Biomass monitoring mission for Carbon Assessment (BIOMASS) operated by European Space Agency (ESA), this effect has become more significant and limits the further development of advanced SAR techniques [5]. To correct ionospheric distortions on SAR and InSAR, several methods have been proposed by researchers. [PERSON] and [PERSON] [25] discussed and proposed a method to estimate and compensate of ionospheric effects by means of coherent scatterers, which had a high spectral correlation and point-like scattering behaviour. [PERSON] et al. [24] proposed an ionospheric correction method based on a multi-frequency split-spectrum processing technique. This method exploited the dispersive nature of radar signals in estimating the ionospheric contribution. When topography, ground deformation and atmospheric errors were non-dispersive, the ionospheric effect was dispersive. Thus, the ionospheric effect could be separated by observations at two different frequencies. Several researchers have proved the feasibility of this method [26; 27; 28; 29; 30]. Another method called Delta-k, which is similar to the multi-frequency split-spectrum processing technique, employs subband processing in range to separate frequency dependence of ionospheric phase delay versus the frequency proportional dependence of topographic phase delay [5; 6; 31]. [PERSON] et al. [20] successfully developed a method to map the ionospheric structures using SAR interferograms. This method exploited the differences in sign between range group and phase delays caused by the ionosphere. A recent method aimed to use the approximate linear relationship between the azimuth gradient of ionospheric phase delay and azimuth pixel shift to correct the ionospheric effect on InSAR [14; 15; 32; 33; 34; 35; 36]. Several researchers tested the feasibility of this method. As a result, it was reported that the method was able to correct the ionospheric phase error on the interferogram. As the most sensible magneto-ionic propagation effects, ionosphere-induced FR can be accurately estimated from the full-polarimetric SAR images, and consequently has been widely used to correct ionospheric effects on SAR and InSAR [9]. [PERSON] [37] outlined a step-by-step procedure to recover the true scattering matrix subject to FR. The method provided an effective method to calibrate the ionospheric distortion on full-polarimetric SAR images. From then on, intensive studies were carried out to calibrate the ionosphere-induced FR and radar system errors for L-band Advanced Land Observation Satellite (ALOS)/Phase Array L-band SAR (PALSAR) [38; 39; 40; 41; 42] and simulated P-band BIGMASS systems [43]. Due to the presence of speckle noise in single SAR images, ionospheric correction on SAR interferometry was easily contaminated by the noise when directly using FR-calibrated single SAR images.