Search Results (632)

In this contribution, we introduce the concept of Fourier ambiguity resolution. We show how it is rooted in the principle of integer equivariant (IE) estimation and in its periodic representation. As a result, we present a general Fourier representation of IE-estimators. As the IE-class is the largest class of estimators used in GNSS ambiguity resolution, the periodic representation opens up a broad spectrum of new applications, both in the field of parameter estimation and in that of statistical testing. The representation also applies to the integer class, with its popular estimators of integer-rounding, integer-bootstrapping, and integer least-squares, as well as to their integer-aperture variants. In this contribution, we consider the periodic representation of the best integer equivariant (BIE) estimator. It is shown how this minimum mean squared error IE-estimator can be represented in both the spatial and frequency domains and how preference for one of the two representations should be based on the GNSS carrier-phase ambiguity precision. We also present a hybrid form of the BIE-estimator and show how the spatial and frequency representations can be mixed so as to do justice to the practical situation when carrier-phase ambiguity vectors consist of ambiguities having a wide range of varying precision. Full article

The performance of remote sensing-based mineral alteration extraction is significantly restricted in the vegetation area. Spectral unmixing is one of the effective methods to address the vegetation problem during mineral alteration extraction. However, the spectral curves of different tree species vary a lot; if multiple tree species are regarded as a whole during the spectral unmixing stage, the proportions of vegetation would be estimated with more errors. The purpose of this study was to verify the effects of dominant tree species classification on spectral unmixing and reconstruction, and to apply the proposed method to the mineral alteration extraction practice. To accomplish this, the Shabaosi gold deposit region in Mohe City, China, with an area of 650 km², was selected as the study area. Firstly, reference spectral curves, GaoFen-1/6 (GF-1/6) satellite imageries, ZiYuan-1F (ZY-1F) satellite imageries, Sentinel-1B satellite synthetic aperture radar (SAR) data, the ALOS digital elevation model (DEM), and sub-compartment dominant tree species data were collected; subsequently, simulated mixed-pixel reflectance images of ZY-1F, reflectance images of GF-1/6, ZY-1F, backscattering data of Sentinel-1B, slope, aspect, and 5484 tree species samples were derived from the collected data. Secondly, to verify the effect of dominant tree species classification on mineral alteration extraction, the reference spectra of pine, oak, goethite, and kaolinite were used to construct a simulated ZY-1F mixed-pixel image, and spectral unmixing and reconstruction experiments were conducted. Thirdly, fourteen independent variables were selected from the derived data, five dominant tree species classification models were trained and tested using tree species samples via the ResNet50 algorithm, and the pine- and birch-dominated parts were segmented from the ZY-1F images. Fourthly, minimum noise fraction (MNF), pixel purity index (PPI), n-dimensional visualizer auto-clustering, and spectral angle mapper (SAM) methods were separately applied to the pine- and birch-dominated parts of ZY-1F images to extract and identify endmembers; subsequently, the fully constrained least squares (FCLS) and linear spectral unmixing (LSU) methods were separately applied to the pine- and birch-dominated parts to estimate endmember proportions and generate spectrally reconstructed ZY-1F images. Fifthly, the pine- and birch-dominated parts of spectrally reconstructed ZY-1F images were mosaiced, and the SAM was utilized to extract mineral alteration in the study area. The result showed that in the spectral unmixing and reconstruction experiment, the spectral reconstruction error declined from 0.0594 (simulated ZY-1F image without segmentation) to 0.0292 and 0.0388 (simulated ZY-1F image that was segmented by pine- and oak-dominated parts), suggesting that dominant tree species classification could improve the accuracy of spectral unmixing and reconstruction and help obtain a more reliable mineral alteration extraction result. In the study area, the tested overall accuracies (OA) and Kappa coefficients of the five dominant tree species classification models were 0.75 ± 0.03 and 0.50 ± 0.05, respectively, suggesting that conducting dominant tree species classification was feasible in dense vegetation areas and could facilitate mineral alteration extraction. After segmenting the ZY-1F image by pine- and birch-dominated parts and spectral reconstruction, eight main types of alteration, including kaolinite, vesuvianite, montmorillonite, rutile, limonite, mica, sphalerite, and quartz, were identified, and nine mineral alteration areas (MA) were delineated accordingly. Full article

Precise control of optical intensity distributions is important for beam shaping, optical trapping, and optical potential engineering. We implement a digital micromirror device (DMD)-based programmable beam-shaping platform for generating high-fidelity optical intensity distributions with user-defined geometries. The approach combines precise system calibration, Fourier-plane spatial filtering via an optimized pinhole, and an iterative intensity feedback algorithm to transform imperfect Gaussian input beams into flat-top, lattice, and composite intensity distributions. The feedback loop typically converges within seven iterations, producing highly uniform flat-top profiles with 98.7% uniformity (corresponding to a root-mean-square error (RMSE) of 1.3%). Systematic studies identify the optimal Fourier-plane aperture that balances diffraction suppression with optical throughput. These results demonstrate a practical route to programmable beam shaping and optical intensity control. Full article

Ground-Based Interferometric Synthetic Aperture Radar (GB-InSAR) is widely used for geohazard and infrastructure health assessment because it enables high-precision deformation monitoring. However, long-term time series observations often contain phase discontinuities caused by localized deformation with large spatial gradients, which can severely compromise phase unwrapping reliability. To address this limitation, we propose an Adaptive Shortest-Path Network (ASPN) method for GB-InSAR phase unwrapping. A temporal sliding window strategy is used to partition the acquisition stream into processing units. Within each unit, arc quality is quantified by least squares inversion using the mean square error (MSE) and temporal coherence. The unreliable arcs are removed, and the network is then reconnected using Dijkstra’s shortest-path algorithm to improve unwrapping stability and accuracy. The method is evaluated on a corner reflector-controlled deformation dataset and a stope slope dataset. In the controlled experiment, ASPN reduces the root mean square error (RMSE) of cumulative deformation from 1.684 mm to 0.037 mm, representing a 97.8% reduction, while in the stope slope experiment, it reduces the mean phase residual by 30.3% relative to the Delaunay network and by 11.6% relative to APSP. Overall, ASPN provides an efficient dynamic update mechanism and a robust, high-accuracy solution for long-term GB-InSAR time series deformation monitoring. Full article

Freeform Fresnel lenses combine the powerful beam-shaping capability of freeform optics with the lightweight and compact characteristics of conventional Fresnel structures, leading to their increasing adoption across diverse applications. This paper proposes and experimentally validates a method for generating rectangular dark hollow beams using a freeform Fresnel lens. The lens is divided into multiple fan-shaped sectors centered on the optical axis, with each sector generating a defocused spot at a distinct spatial location. Based on geometrical optics, a freeform Fresnel lens with a 25 mm aperture is designed to produce a square hollow beam with a side length of 10 mm. A lens with a division angle of 5° was fabricated using ultra-precision diamond turning. The angular form error was measured to be below 0.1°, and the surface roughness was found to be below 10 nm. An optical testing system was established to characterize the generated beam profile. The experimental results successfully demonstrate the formation of the desired rectangular dark hollow beam. The measured results agree well with the simulations, confirming the feasibility and practical potential of the proposed method. Full article

The sixth generation (6G) of wireless networks demands extreme energy efficiency and massive connectivity, positioning large intelligent surfaces (LIS) as a pivotal technology. However, the practical deployment of LIS is constrained by the overwhelming computational complexity and power consumption required to process thousands of antenna elements. To address these challenges, this article proposes a deep learning-based receiver architecture that integrates the spatial efficiency of Partial LIS with advanced non-linear detection. By activating only a subset of antenna panels closest to the user terminal (Partial LIS), the system significantly reduces hardware overhead and Radio Frequency (RF) power consumption. To compensate for the performance loss, the multi-user interference (MUI) generated by the linear combining stage, and the increased MUI inherent in a reduced-aperture environment, a specialized Multilayer Perceptron (MLP) network is implemented. Unlike traditional Zero-Forcing (ZF) or Minimum Mean Squared Error (MMSE) receivers, which require energy-intensive matrix inversions for each frequency component, the proposed neural-network-enabled receiver achieves near-optimal performance using low-complexity combining followed by intelligent learning-based interference suppression. Simulation results demonstrate that the proposed hybrid architecture provides a scalable, “green” solution for 6G uplink scenarios. Notably, the deep learning approach is shown to effectively suppress the performance loss of reduced apertures, achieving a BER comparable to traditional linear benchmarks even with a reduced physical aperture, maintaining good Bit Error Rate (BER) performance while dramatically reducing the computational and hardware footprint. Full article

In emergency decision-making for carbon capture, utilization, and storage (CCUS) CO₂ pipeline leakage, risk levels and warning distances/impact ranges are often derived from different methodological systems—risk-matrix scoring versus mechanistic consequence modeling. Differences in threshold definitions and modeling assumptions make it difficult to align level assignment with distance boundaries for the same scenario, which in turn reduces the comparability and traceability of multi-scenario batch screening. To address this, this study proposes an integrated framework based on “threshold impact-distance calculation–risk-matrix mapping,” with physical consequence quantification as the main thread. A scenario library (N = 4320) covering phase state, leak aperture, operating conditions, and meteorological fields is constructed; impact distances corresponding to CO₂ volume-fraction thresholds of 1%/4%/10% (R_1%, R_4%, R_10%) are computed and then mapped to five RiskLevel classes under a unified rule set, enabling standardized synchronous outputs. The modeling tasks are formulated as RiskLevel classification and threshold-distance regression. Using a stratified 70%/30% train–test split, Extreme Gradient Boosting (XGBoost) is adopted as the primary model and compared with logistic regression (LR), support vector classification (SVC), ordinary least squares regression (OLS), and support vector regression (SVR). Results show that XGBoost achieves an accuracy of 0.806 and a macro-F1 of 0.825 for RiskLevel classification, with a recall of 0.631 for the high-risk classes (RiskLevel 4–5), and yields mean absolute errors (MAEs) of 95/62/41 m for R_1%/R_4%/R_10% regression with coefficient of determination (R²) values of 0.795–0.814. Distributional analysis further indicates that threshold impact distances increase overall with higher RiskLevel, while dispersion becomes larger at higher levels. Accordingly, a parallel representation of “RiskLevel + multi-threshold rings” is recommended to support coordinated graded control and zoned warning delineation. Full article

Retrieving farmland soil water content with both high accuracy and physical interpretability remains a significant challenge, particularly for winter wheat. To bridge the gap between purely empirical data-driven approaches and mechanistic scattering models, this study proposed a novel hybrid framework that integrates an improved water cloud model (IWCM) with machine learning algorithms. Multi-modal unmanned aerial vehicle (UAV) experiments were conducted during the heading stage of winter wheat over two consecutive years (2024–2025) using a synchronized system equipped with a miniature synthetic aperture radar (MiniSAR) and a multi-spectral sensor. The core innovation of the proposed framework lies in the IWCM, which explicitly decouples vegetation and soil scattering contributions by incorporating fractional vegetation cover, thereby deriving physically meaningful soil backscatter coefficients from complex microwave signals. Unlike traditional methods that treat remote sensing variables as black box inputs, our approach employed these physics-derived features to guide data-driven modeling. Four feature input schemes including spectral reflectance, vegetation indices, MiniSAR polarimetric parameters, and their multi-source fusion were systematically evaluated using back propagation neural network (BPNN) and random forest (RF) regressors. The results demonstrated that the proposed framework significantly enhances retrieval performance. Notably, the RF model driven by spectral band reflectance within this physically constrained architecture achieved optimal accuracy, with a coefficient of determination (R²) of 0.865, a mean absolute error (MAE) of 0.0152, and a root mean square error (RMSE) of 0.0197. Compared to purely empirical approaches, the IWCM significantly improved the physical interpretability of microwave polarimetric characteristics, enabling the multi-source data fusion to better represent the interactions among vegetation, soil, and microwave scattering. This study demonstrated that integrating mechanistic models with multi-source UAV remote sensing data not only improves soil water content retrieval accuracy in winter wheat fields but also provides a valuable reference for developing operationally applicable and physically interpretable farmland soil water content monitoring systems. Full article

Building height is a key indicator of vertical urbanization and urban morphological complexity, yet accurately mapping building height at fine spatial resolution and large spatial scales remains challenging. This study proposes an attention-based deep learning framework (ABHNet) for building height estimation at a 10 m spatial resolution by integrating multi-source remote sensing data and socioeconomic information. The model jointly exploits Sentinel-1 synthetic aperture radar data, Sentinel-2 multispectral imagery, and point of interest (POI) data. The proposed framework is evaluated in Shanghai, a megacity with dense and vertically complex urban structures, using Baidu Maps-derived building height data as reference information. The results demonstrate that the proposed method achieves accurate building height estimation, with a root mean squared error (RMSE) of 3.81 m and a mean absolute error (MAE) of 0.96 m for 2023, and an RMSE of 3.30 m and an MAE of 0.78 m for 2019, indicating robust performance across different time periods. Also, this model is applied in two other cities (Changzhou and Guiyang) and the results indicate good performance. In addition, the expandability of the framework is examined by incorporating higher-resolution ZY-3 imagery, for which the spatial resolution was increased to 2.5 m, highlighting the potential extension of the model to heterogeneous data sources. Overall, this study demonstrates the effectiveness of attention-based deep learning and multimodal data fusion for large-scale and fine-resolution building height estimation using open-source data. Full article

Systematically characterizing the time series deformation evolution of open-pit mine slopes is key to revealing their potential instability development and supporting subsequent deformation-level classification. Interferometric Synthetic Aperture Radar (InSAR), by enabling measurement of ground deformation at a global scale approximately every ten days, may hold the key to those interactions. However, atmospheric propagation delays still have a significant impact on deformation calculations, and open-pit mine slopes monitored by InSAR often suffer from low coherence. This noise can obscure nonlinear and transient precursory signatures in deformation time series, reducing the identifiability of key temporal patterns required for automated interpretation. Here, we present a Coherence-conditioned Encoder–Decoder Long Short-Term Memory (CED-LSTM) denoising network for deformation time series. We generate a physics-aware synthetic dataset by modeling coherence-dependent measurement noise and temporally correlated atmospheric delays. The network jointly models deformation time series and coherence, using residual learning and adaptive gated composite loss to preserve deformation trends. It is designed to autonomously extract ground deformation signals from noise in InSAR time series without prior knowledge of where deformation occurs or how it evolves. On the synthetic validation set, the network achieved a root mean square error (RMSE) of 2.2 mm across the validation sequences. Applied to three InSAR datasets over an open-pit mine from March 2019 to March 2022, denoising suppresses noise and stabilizes deformation boundaries, enabling extraction of trend and transient indicators and a data-driven deformation-level score. Using quantile-based thresholds, these scores are then used to produce multi-year deformation-level classification maps. Full article

Forest height is a key structural parameter for characterizing forest architecture and estimating carbon storage. However, under complex terrain and heterogeneous forest conditions, Polarimetric synthetic aperture radar (PolSAR)-based forest height inversion using multi-category features still faces several challenges, including feature redundancy, insufficient characterization of the nonlinear couplings among high-dimensional features by deep learning models, and the difficulty of jointly achieving model stability and interpretability. In this paper, to address these issues, we propose a method for SHapley Additive exPlanations (SHAP) interpretability-driven PolSAR forest height inversion based on deep learning and multi-category feature fusion. Firstly, a deep neural network (DNN) is constructed, and SHAP is introduced to interpret the model decision process, enabling the identification of key feature interactions with clear physical significance and guiding the iterative model optimization in an explainability-driven manner. Furthermore, a SHAP-guided feature attention DNN is developed, in which the feature contribution scores are incorporated as prior knowledge for attention weight initialization, thereby establishing a closed-loop modeling framework from “interpretation” to “optimization”. Experiments were conducted at the site of the Huangfengqiao forest farm, Youxian County, Hunan province, China, using ALOS-2 L-band fully polarimetric SAR imagery. The experimental results demonstrated that the proposed method can significantly outperform the conventional machine learning approaches and various deep learning architectures for forest height inversion. The final model achieved a coefficient of determination (R²) score of 0.75 and a root-mean-square error (RMSE) of 1.35 m on the test dataset. These findings indicate that the combination of SHAP-driven multi-category feature fusion and deep learning can effectively enhance both the inversion accuracy and physical interpretability, providing a reliable solution for PolSAR-based forest structural parameter retrieval at the Huangfengqiao study site, with potential applicability to complex terrain conditions. Full article

To address the limitations of traditional forest above-ground biomass (AGB) retrieval methods—namely, the restricted accuracy of physical models and the limited generalization ability of purely data-driven models—this study proposes a differentiable physical modeling (DPM) approach for forest AGB estimation. The method adopts the water cloud model (WCM) as a physics-based framework, grounded in radiative transfer theory, and integrates C-band synthetic aperture radar (SAR) data with multispectral imagery. Within the PyTorch tensor computation framework, automatic differentiation (AD) is employed to seamlessly couple the WCM with the deep fully connected neural network (DFCNN), enabling a differentiable implementation of the WCM. Using mean squared error (MSE) as the loss function, the neural network parameters are optimized through backpropagation and gradient descent, thereby constructing an end-to-end trainable DPM model that effectively retrieves forest AGB while preserving physical interpretability and generalization capability. To validate the proposed method, two representative test sites were selected: Simao in Pu’er, Yunnan Province, and Genhe in Inner Mongolia. GF-3 PolSAR and RADARSAT-2 data were used to extract backscattering coefficients and compute the radar vegetation index (RVI), while Landsat 8 OLI imagery was employed to calculate the normalized difference vegetation index (NDVI), difference vegetation index (DVI), and soil-adjusted vegetation index (SAVI). These datasets, together with ASTER GDEM, field-measured biomass, and other relevant datasets, were integrated to construct a multisource dataset combining remote sensing and ground observations. The performance of the DPM model was then compared with the traditional WCM and several data-driven models, including the fully connected neural network (FNN), generalized regression neural network (GRNN), RF, and Adaptive Boosting (AdaBoost). The results indicate that the DPM model achieved R² = 0.60, RMSE = 24.23 Mg/ha, Bias = 0.4 Mg/ha, and ubRMSE = 22.43 Mg/ha in Simao, and R² = 0.48, RMSE = 33.29 Mg/ha, Bias = 0.87 Mg/ha, and ubRMSE = 33.28 Mg/ha in Genhe, demonstrating consistently better performance than both the WCM and all tested data-driven models. The DPM model demonstrated consistent performance across ecologically contrasting forest regions. It alleviated the systematic overestimation bias of purely data-driven models and overcame the limitations in predictive accuracy resulting from the simplified structure of the WCM. The differentiability of the WCM enables the loss function errors to be backpropagated through the neural network, thereby allowing the optimization of the physical model parameters. Overall, the DPM framework integrates the advantages of both physical models and data-driven approaches, providing an estimation method with acceptable accuracy for forest AGB retrieval. It also offers theoretical and practical insights for the integration of deep learning and physical knowledge in other research fields. Full article

Forest height is a key parameter for quantifying forest biomass and carbon stocks and serves as an important indicator of forest ecosystem health. The successful launch of the European Space Agency’s P-band Biomass satellite, which provides Polarimetric Interferometric Synthetic Aperture Radar (PolInSAR) data for global high-precision forest height mapping, heralds a new era in global forest carbon monitoring. However, the accuracy of forest height inversion is significantly influenced by scattering mechanisms. This study investigates the impact of dominant scattering mechanisms on forest height inversion accuracy. Four classical algorithms were selected: the polarimetric phase center height estimation method (PPC), the complex coherence phase center differencing algorithm (CCPCD), the coherence amplitude inversion method (CAI), and the hybrid inversion method using both phase and coherence information. The Freeman–Durden three-component decomposition was employed to identify the dominant scattering mechanisms. The results show that (1) at P-band, inversion model performance exhibits strong coupling with scattering mechanisms, and no single algorithm achieves global robustness; (2) the hybrid inversion method using both phase and coherence information performs better in regions dominated by surface and double-bounce scattering, whereas the coherence amplitude inversion method (CAI) yields higher accuracy in volume-scattering-dominated regions; and (3) the adaptive joint inversion strategy based on scattering mechanisms achieved a root mean square error ($\mathrm{RMSE}$) of 4.62 m and a coefficient of determination ($R^2$) of 0.76 at P-band, representing an improvement of approximately 30% over the best single-model performance ($\mathrm{RMSE}$ = 6.51 m). This approach overcomes the accuracy limitations of single models in complex global forest scenarios and provides a valuable reference for scientific forest height inversion. Full article

In microwave imaging with finite antenna arrays, the limited number of array elements constrains spatial sampling and degrades reconstruction quality. To enlarge the aperture effectively, virtual antennas are usually adopted. However, it may lead virtual data to dominate the reconstruction process, thereby amplifying artifacts. This work proposes an interpolation-weighted truncated singular value decomposition (IW-TSVD) framework that expands multistatic scattering matrix by using an integer interpolation factor. The proposed method preserves all physically measured antenna data and applies explicit weighting to virtual channels to suppress their influence. Simulations and hardware experiments show that IW-TSVD improves structural similarity index (SSIM), reduces the mean squared error (MSE), and suppresses artifacts compared with conventional TSVD and zero-padding-based interpolated TSVD, without increasing hardware complexity. Full article

Polarimetric information is essential for scattering interpretation and target characterization in synthetic aperture radar (SAR) remote sensing, yet many resource-constrained platforms (e.g., small satellites and unmanned aerial vehicles (UAVs)) operate with limited polarization modes or even a single radio frequency (RF) chain, which limits full polarimetric scattering acquisition. To address this limitation, this paper proposes a single-channel framework for estimating the full polarization scattering matrix (PSM) enabled by time-varying polarization modulation. The transmit/receive polarization states are steered along predefined trajectories on the Poincaré sphere to generate time-varying polarization tags that are encoded into the received echoes through the target’s polarization-varying response. A compact observation model is then derived to relate the single-channel echoes, the known polarization tags, and the unknown PSM; based on this, the PSM is then estimated via a least squares formulation with a low-rank approximation. Simulation results demonstrate the robust reconstruction of the full polarimetric scattering matrix under diverse modulation trajectories. For arbitrarily chosen random point targets, when the signal-to-noise ratio (SNR) exceeds −20 dB, the polarimetric similarity coefficient approaches 1, and the estimation errors of Pauli power components converge toward zero. Furthermore, the method’s reliability is validated on distributed vegetation clutter. Quantitative metrics demonstrate near-perfect statistical consistency, with polarimetric entropy and alpha angle errors within 0.14%. Overall, the proposed approach provides a practical pathway to enhance the availability of full polarimetric scattering information under limited-observation conditions, confirming its feasibility for downstream analysis in complex natural scenes while maintaining a single radio frequency (RF) chain architecture augmented by a polarization modulator. Full article