Reflection of and vision for the decomposition algorithm development and application in earth observation studies using PolSAR technique and data
Introduction
The mono-state polarimetric synthetic aperture radar (PolSAR) characterizes a ground target by measuring the amplitude and phase from the incident radar wave's backscattering. Usually, the wave is linearly polarized horizontally (h) and vertically (v). Measured h and v elements are typically expressed in a scattering, covariance, or coherency matrix. Nevertheless, the interpretation of the matrices in Earth observation (EO) studies is not straightforward. As the understanding and use of the PolSAR technique, scattering mechanism, and data in forests are demanded, one develops complicated radar backscatter models. They include the MIMICS (McDonald and Ulaby, 1993; Ulaby et al., 1990), Santa Barbara microwave backscattering models (Sun et al., 1991; Wang et al., 1993; Wang et al., 1995; Wang et al., 1998), 3-D models (Liu et al., 2010; Sun and Ranson, 1995), models for pine forest (Lang et al., 1994), coherent scattering model for tree canopies based on the Monte Carlo simulation of scattering from fractal-generated trees (Lin and Sarabandi, 1999; Sarabandi and Lin, 2000), and multilayer-multispecies vegetation model (Burgin et al., 2011). Primary burdens in these forward modeling studies include the model parameterization and demand of in situ data.
Meanwhile, with the eigenvalue/eigenvector analysis, the PolSAR data were decomposed in forests to understand scattering mechanisms and applications in forested environments (van Zyl, 1993; Wang and Davis, 1997). Cloude and Pottier (1996) reviewed and unified three types of decomposition algorithms. Freeman and Durden (1998) developed a three-component decomposition algorithm for forests. These developments are valued as viable alternatives to the forward modeling approaches in understanding radar backscatter in forests because of their simplicity in the formulation and no demand for the in situ data. When the decomposition algorithms primarily developed for forests are extended to other land cover types such as an urban area, their deficiency is found. Due to strong volume scattering from urban targets such as buildings with large azimuth-orientation angles, the algorithms cannot separate the volume scattering from tree canopies or urban targets. The phase information of co- and cross-pol cross-products was studied for the separation (Atwood and Thirion-Lefevre, 2018; Gan et al., 2019). With the subaperture approach (Ling et al., 2021) and the correlation analysis of cross-product of two cross-pol datasets (Zhang et al., 2021), the delineation of a stationarity target (e.g., a building) and a non-stationarity target (e.g., a tree canopy) were investigated.
The inseparability is also one fundamental impetus to further the decomposition algorithm development by adding new components or revising existing ones. Yamaguchi et al. (2005) added the helix to the Freeman-Durden algorithm (Freeman and Durden, 1998), and Xiang et al. (2015) proposed a five-component algorithm. Singh and Yamaguchi (2018) and Singh et al. (2019) included additional ones. Moreover, the azimuth-angle deorientation (e.g., Lee and Ainsworth, 2011) was included to reduce the volume scattering from urban targets with large azimuth orientation angles (Susaki et al., 2014; Yamaguchi et al., 2011). Numerous revisions of existing algorithm components were done and summarized (e.g., Chen et al., 2014; Duan and Wang, 2017; Li and Zhang, 2018). Furthermore, Du and Wang (2016) employed interferometric coherence to separate vegetation from an urban area. The smallest eigenvalue of the three eigenvalues representing single, double, and volume scattering components was used to identify the decomposed volume scattering (An and Lin, 2019). Although the current improved and revised algorithms are more powerful now in EO studies, urban targets with large azimuth orientation angles still cannot be correctly identified. Moreover, the revision of existing components and the addition of new ones make the component formulations and decomposition algorithms more complex procedurally.
In light of the increased decomposition algorithms' complicity, a reconsideration was argued (Wang et al., 2019). Dey et al. (2020) recharacterized three scattering components using the roll-invariant scattering-type parameters, and Ratha et al. (2020) explored the factorization of scattering power and unsupervised classification scheme. A search with “decomposition” as a keyword at the 2020 IEEE International GeoScience and Remote Sensing Symposium (https://igarss2020.org/technical_program.php), virtually held between September 26 and October 2, 2020, thirteen PolSAR decomposition studies are shown. Additionally, multiple civilian and operational airborne and spaceborne PolSARs exist worldwide (https://eoportal.org/web/eoportal/). No doubt, studying PolSAR decomposition algorithms will continue. Thus, it is time to reflect on how the EO research and application's advancement using the PolSAR technique and decomposition algorithm has been accomplished. What are the critical issues currently? Is it possible to propose a vision for future algorithm development to preserve the simplicity in the algorithm's formulation and procedure and the straightforward interpretation of the algorithm's components and outcomes? Thus, our study is framed with a reflection on the past and a vision for the future. The objective is to have an algorithm with well-balanced usability and complexity in formulation and procedure.
Section snippets
A covariance matrix and decomposition of PolSAR data
A mono-state PolSAR measures backscattering components Spq (p, q = h, v) at pq polarizations from a target. Spq is a complex value. Within each SAR resolution cell, multiple radar targets can exist, scattering the incoming EM wave energy. Thus, the backscatter is an ensemble average, 〈⋯〉. One writes the components in a matrix form as
For the sake of simplification, 〈⋯〉 is ignored in equations onward. When the reciprocal rule is used, Shv = Svh. (1) can be expressed as a 3 × 3
A vision for the PolSAR decomposition algorithm development and assessment
As discussed so far, three primary issues exist in the existing decomposition algorithms (e.g., Freeman and Durden, 1998; Singh and Yamaguchi, 2018; Wang and Davis, 1997; Yamaguchi et al., 2005). First, C12 and C32 are essential in the decomposition study and cannot be ignored. Second, after years of development, the existing algorithms are now more powerful and applicable to various EO studies. However, they still cannot differentiate urban targets with large azimuth-orientation angles from
Validation of the Sf's ability to delineate other types of azimuthally symmetric targets
One Gaofen-3 C-band dataset was acquired on 15 September 2017 (Table A1). After the multilook operation (Table A2), an ocean surface area off San Francisco, CA, was extracted. Fig. 5(a) shows the area as a PauliRGB (½·|Shh – Svv|2 as red, 2·|Shv|2 as green, ½·|Shh + Svv|2 as blue) image. The water surface is blue. Sample pixels within a 20 × 20 red box were extracted, and the mean and standard deviation of Sf computed. The results are shown in Table 3. The mean and standard deviation are near
Decomposition analysis of UAVSAR San Francisco data
Radarsat-2 and PALSAR-2 fly along sun-synchronous orbits and incline 98.6° and 97.9° (measured from east and counter-clockwise). Since both spaceborne datasets were acquired along ascending orbits, the azimuth angle was 351.4° for Radarsat-2 data and 352.1° for PALSAR-2 data. A 2018 UAVSAR San Francisco dataset has an azimuth angle of 235° (Table A1). The look directions of the spaceborne SARs differ ~118° from that of the UAVSAR. Because azimuth-orientation angles are between 0° and 45°, the
Conclusions
After reflecting on the existing PolSAR decomposition studies so far, we have identified three primary issues. Covariance matrix components C12 and C32 are critical in the decomposition and cannot be ignored. The existing decomposition algorithms still cannot differentiate urban targets with large azimuth-orientation angles from forests well. The algorithms are significantly complex procedurally and in formulation, contradicting the initial and fundamental motivation (to develop the
Credit author statement
Wang and Duan conceived the study. Duan designed the experiment and analyzed PolSAR data in consultation with Wang. Duan and Wang wrote the paper.
Declaration of Competing Interest
The authors have no known competing financial interests or personal relationships that could have influenced the study.
Acknowledgments
This study was supported by the National Natural Science Foundation of China under grant 41771401 to the University of Electronic Science and Technology of China. Gaofen-3 and PALSAR-2 datasets, and Radarsat-2 San Francisco data were downloaded from https://www.ietr.fr/polsarpro-bio/. Radarsat-2 Vancouver data were obtained at https://www.mdacorporation.com/geospatial/international/satellites/RADARSAT-2/sample-data/. Goldstone data were from NASA/JPL. PALSAR and UAVSAR datasets were downloaded
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