Conference Agenda

Soil moisture (SM) plays a critical role in hydrological phenomena, impacting life, groundwater availability, and agricultural activities. SM controls water infiltration and runoff after precipitation, determining water availability to surface vegetation and also affecting erosion and flood event occurrence and strength. Satellite remote sensing can provide synoptic and cost-effective SM monitoring capabilities, enhancing our understanding of environmental and societal challenges, such as agriculture to water resources management. In this framework, microwave remote sensing, and particularly Synthetic Aperture Radar (SAR), plays a key role thanks to its fine spatial resolution, which enables SM estimation at the scale of probing wavelength.

SAR SM estimation can be challenging due to the presence of speckle noise. In addition, the inherently ill-posed nature of the retrieval problem adds more complexity, as SAR measurements are jointly affected by SM and nuisance parameters, both coming from the radar system and from the probed scene (e.g., soil roughness, vegetation, thermal noise). This demands for tailored and robust decoupling methods, whose design is crucial for an accurate estimation of the SM from SAR imagery.

This study investigates the performance of soil moisture estimation over bare soils under a multistatic radar geometry leveraging two data augmentation strategies: polarimetric diversity, which consists of processing both co- and cross-polarized measurements at L-band; frequency diversity, which exploits L- and C-band co-polarized measurements. A novel approach is proposed, it consists in two parts: i) numerical prediction of

the normalized radar cross-section using first- and second-order small-slope approximation solutions of the scattering, adopting an anisotropic description of the soil surface; 2) Cramer-Rao lower bound (CRLB) to evaluate, from a statistical viewpoint,

the sensitivity of the normalized radar cross-section – predicted according to the above-mentioned data generation strategies – to the soil moisture under the presence of nuisance parameters, e.g., soil row orientations and small scale soil roughness. The

investigation demonstrates that both strategies offer low values of the CRLB, smaller than 5%, with optimal positions of the receivers identified across multiple regions, particularly along the track with respect to the master radar.

Polarimetric Synthetic Aperture Radar (PolSAR) is highly effective for characterizing scattering targets, offering rich information about their physical and structural properties. Over the years, numerous decomposition techniques—both data-driven and model-based—have been developed to interpret PolSAR measurements and separate the contributions of different scattering mechanisms. Examples include model-based approaches such as Freeman–Durden and Yamaguchi decompositions.

However, a key limitation of most model based approaches lies in how the scattering components are extracted. The mathematical operations involved often fail to preserve the positive semi-definite (PSD) nature of the resulting covariance or coherency matrices. Since physical scattering matrices must remain PSD to ensure valid power, this issue can lead to non-physical or unstable results. To address this, various correction techniques could be applied as in Arii ANNED. Nevertheless, in some instances such adjustments may distort the original data or reduce interpretability, highlighting the need for decomposition strategies that naturally maintain the physical and statistical integrity of the polarimetric information.

In this study, we investigate and compare different strategies for decomposing a partial target into two distinct components: a primary (focus) partial target and a residual, physically feasible partial target. We call this 1F+R. Please note the Focus target we extract is partial and can have any entropy. Its covariance matrix is not forced to have rank 1. Specifically, we compared different extraction methods based on simple subtraction, inner product, Rayleigh quotient optimisations (RQO), vectorisation of the covariance matrix and notch filtering, and tensor fields decompositions. We checked these extraction methods evaluating which one preserves the total power and maintains the PSD property across both the Focus and Residual partial targets. Preserving these characteristics is crucial for ensuring that the decomposition remains meaningful and that each component accurately represents its corresponding scattering mechanism without introducing artifacts.

To test the mentioned methodologies, we performed extensive Monte Carlo simulations to test its accuracy under controlled conditions. Furthermore, we applied the same analysis to real quad-polarimetric datasets acquired from ALOS-2 and (soon to) BIOMASS missions. These experiments allow us to assess the algorithm’s performance on real-world data characterized by different target types and scattering conditions. The results confirm that not all extractions techniques preserve PSD and polarimetric characteristics and we come with final suggested procedures including stages like RQO or tensor field analysis to be considered.

Quad-pol (QP) SAR systems acquire comprehensive polarimetric information by transmitting two and receiving four polarizations. However, they require higher pulse repetition rates (PRF) and more complex hardware, resulting in reduced swath width. Compact-pol (CP) systems, a specialized dual-pol mode, offer wider coverage with lower PRF requirements and have proven effective for land cover mapping, crop classification, soil moisture estimation, vegetation characterization, and ship detection.

Two main approaches exist for utilizing CP SAR data: extracting polarimetric features through decompositions, and reconstructing the 3×3 QP covariance matrix from the 2×2 CP covariance matrix. This work focuses on the latter approach, enabling application of QP processing techniques to reconstructed data.

Most reconstruction methods rely on Souyris' reflection symmetry assumption to relate CP and QP matrix elements, iteratively determining cross-polarization intensity. However, this assumption is valid primarily for volume-dominated scatterers and often fails for other scattering mechanisms.

We propose a deep learning method that reconstructs QP data from CP data without assuming reflection symmetry. The network uses real and imaginary components of the complex covariance matrix to directly map CP to QP data. The model was trained and evaluated on multiple PolSAR datasets to demonstrate performance across diverse scenarios.

Performance was assessed using Hotelling Lawley Trace (HLT), Determinant Ratio Test (DRT), and Wishart Distance for qualitative evaluation, alongside Mean Square Error (MSE), Mean Absolute Error (MAE), and Coherence Index (COI) for quantitative analysis. Results were compared against Souyris' and Nord's classical reconstruction methods.

The use of polarimetric Synthetic Aperture Radar (PolSAR) has the capability to improve detection and bio-physical parameters extraction in many remote sensing applications compared to the use of a single polarisation channel. The scattering matrix or the scattering vector allow to analyse the polarimetric information of targets. Unfortunately, when dealing with distributed targets, speckle introduces a statistical variation on the observed polarimetric behaviour and we need to use statistical tools. A typical solution is to extract the second order statistics building a covariance matrix [1].

The covariance matrix is formed by performing an averaged outer product of the scattering vector with itself which imposes constraints on the power distribution in the polarimetric space (i.e. the shape of the surface drawn by varying the projection vector in the matrix quadratic form). The surface is forced to be an ellipsoid with 3 main axes (in quad-pol after reciprocity and monostatic sensor assumptions).

In the past we showed how indiscriminate averaging can produce a loss of information when we are in a situation of not fully developed speckle (e.g. the distribution of the covariance matrix is not Wishart). We proposed an alternative way to decompose the partial target into a sum of low entropy components which does not require indiscriminate pre-averaging. This allows us to extract more than 3 scattering mechanisms and it does not force orthogonality among them. This is performed doing a search in the tensor field based on angular distances. We also demonstrated its usefulness by using both Monte Carlo simulations and real quad-pol ALOS-2 and RADARSAT-2 data. The simulations also show that the new methodology is able to identify the low entropy components even if the composing scattering mechanisms are not orthogonal to each other.

In this study, we introduce two main innovations. First, we extend the extraction methodology by using a modified K-means clustering algorithm that operates using angular distances rather than traditional Euclidean metrics. This adaptation allows for a faster convergence and more accurate grouping of scattering mechanisms within the polarimetric space. Second, we will apply and evaluate this improved approach using BIOMASS mission data. The BIOMASS dataset provides a valuable test case due to its high sensitivity to vegetation and structural parameters, offering an ideal context to assess the method’s effectiveness in real-world scenarios. For instance, through this application, we aim to determine whether the proposed technique can successfully isolate and separate the surface scattering contribution from other dominant mechanisms present in the data.

[1] Polarisation: Applications in Remote Sensing, Cloude, S. R., Oxford University Press, Oxford, UK, 2009 "

Unlike surface, double-bounce, or volume scattering, helical scattering conveys the target's structural chirality and phase asymmetry, which can only be captured through full-polarimetric SAR systems. The study investigates helical scattering using full polarimetric C-band data from ISRO's EOS-04 satellite over general land cover types over Shadnagar, Telangana state, India to understand spatial distribution of different scattering mechanisms. ISRO’s Earth Observing Satellite (EOS-04) launched in 2022 is a follow-on Radar Imaging Satellite (RISAT-1) intended to serve operational users with an objective to provide high-quality quantitative data with extended swath coverage and spatial resolutions. EOS-04 is equipped with on-board Hybrid polarimetric architecture and Full polarimetry apart from conventional single/dual polarization to support land and ocean applications.

Methodology: The primary objective was to examine the traceability of the helical component within full-pol data, specifically to identified helical scattering directly from the covariance (COV) matrix instead of performing conventional polarimetric decompositions. The scattering mechanism viz surface (POdd), double-bounce (PEven), volume (PVol), and helical (PHelix) scattering powers within predefined Areas of Interest to identify regions with potential structural complexity and asymmetric features from Yamaguchi four-component decomposed images. The same AOIs were also applied to the corresponding Level-1C covariance product to ensure spatial consistency and direct comparison between decomposition-derived helical power (PHelix) and covariance-derived cross-polar terms. By mapping PHelix values from decomposed products against HHHV values from covariance products using the same AOIs, can establish direct spatial and numerical correspondence.

Results and Discussion: Statistical Correlation analysis revealed strong positive correlations between PHelix and specific covariance elements. This consistent pattern across all AOIs confirms that the HHHV element is the strongest statistical indicator of asymmetric scattering in the raw COV input. The covariance matrix structure for helical scattering exhibits specific properties: C₁₁ = C₃₃ (co-polarized symmetry), C₂₂ = 2(C₁₁+C₃₃) (cross-polarized dominance exceeding that of volume scattering), and purely imaginary off-diagonal elements C₁₂ and C₂₃ representing ±j phase relationships. The high correlation coefficients confirm that helical scattering power originates directly from the imaginary cross-polarized covariance terms (r approximately +0.79 to +0.82) that capture depolarization and phase quadrature relationships and negative correlations between PHelix and co-polarized intensity channels (HHHH)mean [r ≈ -0.32] and (VVVV)mean[r ≈ -0.29] confirms poor correlation. The imaginary components Im(C₁₂) and Im(C₂₃), which represent 90° phase shifts characteristic of circular polarization, serve as the mathematical precursors to helical scattering. Moreover, the calculated helical fraction (fc) also quantified the relative contribution of asymmetric scattering across different land covers supporting multiple physical mechanisms generating helical scattering at C-band frequencies. The core finding of this preliminary research is the definitive proof that PHelix is traceable from the covariance matrix.