Evaluating and comparing the dual polarized Sentinel-1A and TerraSAR-X data in in the optimization of the amplitude dispersion index to improve the PSInSAR algorithm

Persistent Scatterer Interferometry (PSI) is a technique for detection and analysis of a network of coherent pixels referred to as the Permanent/Persistent scatterer (PS) which have high phase strength over long time periods. This technique has been widely used by the scientific community to measure the displacement related to thesubsidence/uplift, landslide, tectonic, and volcanoes. As the density and quality of PS pixels are important factors in PSI algorithms, the concept of polarimetric optimization in the PSI algorithms was proposed to improve the number of PS pixels. The recent launch of radar sensors operating with a polarimetric configuration can help improvingthePS-InSAR analysisby increasing the PS density. Therefore, the combination of thepolarimetric and interferometric techniques helpsimprove the PSI techniques, especially in non-urban areas which suffer from lack of the PS density. In this study, we investigated how the contribution of the S1A and TSX data in the PSI analysis could lead to the improvement of the results of the PSInSAR algorithm. Indeed, the main objective of this paper is to illustrate the capability of each dataset for improving the polarimetric optimization results.
 

2.1  The proposed method was tested using a dataset of 40 dual-pol SAR data (VV/VH) acquired by Sentinel1-A between February 2017 and May 2018 and 20 dual-pol SAR data (HH/VV) acquired by TerraSAR-X betweenJuly 2013 and April 2014.
 
 2.2 Polarimetric SAR Interferometry
 
The general principle of polarimetric SAR interferometry was proposed by (Cloude & Papathanassiou, 1997) for the first time. The scattering matrix S represents the polarimetric information associated with each pixel of the image.  Considering the monostatic configuration, the scattering matrix S is defined as follows:
(1)
Where and are co-polar channels, is the cross polar channel. This matrix can be represented with the target scattering vector  as:
(2)
Where, is the transposed operator. The Pauli vector for the dual-pol data (HH/VV) of the TerraSAR-X sensor, is written as :
(3)
Similarly,the Pauli vectorfor the dual-pol data (VV/VH) of theSentinel1-A sensorcan be expressed as:
(4)
In order to generate scattering coefficient μ, projecting the scatteringvector  on the projection vectorwould be sufficient:
(5)
Where is thelinear combination of the elements of matrix S, i is the correspondent of the 2 images, and * represents the conjugate operator. The projection vectorfor the dual-pol data isdefined as:
(6)
Where, and are two real parameters whose ranges are finite and known and are related to the geometrical and electromagnetic properties of the targets. In our research, the main purpose of the polarimetric optimization is to find theoptimum projection vector, in a 2-dimensional search space,  and
 
2.3 Amplitude Dispersion Index Optimization
 
Substituting (5) into (7), the ADIfor the polarimetric case () can be expressed as follows: 
(7)
(8)
According to (6), the polarimetric optimization problem isreduced to finding a suitable  and  in a finite and known range,so that (8) is minimized.

The results showed that the proposed method improved the performance of the PSInSAR algorithm in two terms of phase quality and density of  the PS pixels. Compared with the VV channel, , the number of PSC and PS pixels increased about 2 and 1.7 times In S1A data, using the ESPO method while, compared with the normal channels like HH and VV, the number of PSC and PS pixels in ESPO method increased about 3.5 and 3 times in TSX data.Based on  these results, the optimization methods are more effective in improving the quality of the PSC densitythan in increasing the number of PS pixels. This is mainly because the employed optimization is based on minimizing ADI criterion which is used in the PSC selection. Moreover, ESPO method has been more successful for TSX data compared to the S1A data. This result is due to the higher capability of the TSX data in creating more diverse scattering mechanisms and hence identifying more optimum scattering mechanism compared to S1A data. We also investigated the effect of polarimetric optimization in increasing the PS density in urban and non-urban areas. The experimental results showed that the method succeeded to significantly increase the final set of PS pixels in both urban and nonurban areas.
    

The results show that the optimization methods have been more successful in the improvement of PS density for  the TSX data compared to the S1A data. This result is due to the higher capability of the TSX data in creating more diverse scattering mechanisms compared to the S1A data. In summary, thanks to the polarimetric data, it is possible to exploit a larger number of pixels compared with the single polarization case.