Polar Decomposition Method Research Articles

Assessment of Sea-Ice Classification Capabilities during Melting Period Using Airborne Multi-Frequency PolSAR Data

Sea-ice mapping using Synthetic Aperture Radar (SAR) in the melt season poses challenges, primarily due to meltwater complicating the distinguishability of sea-ice types. In response to this issue, this study introduces a novel method for classifying sea ice during the Bohai Sea’s melting period. The method categorizes sea ice into five types: open water (OW), gray ice (Gi), melting gray ice (GiW), gray–white Ice (Gw), and melting gray–white Ice (GwW). To achieve this classification, 51 polarimetric features are extracted from L-, S-, and C-band PolSAR data using various polarization decomposition methods. This study assesses the separability of these features among different combinations of sea-ice type by calculating the Euclidean distance (ED). The Support Vector Machine (SVM) classifier, when employed with single-frequency polarimetric feature sets, achieves the highest accuracy for OW and Gi in the C-band, GiW in the S-band, and Gw and GwW in the L-band. Remarkably, the C-band features exhibit the overall highest accuracy when compared to the L-band and S-band. Furthermore, employing a multi-dimensional polarimetric feature set significantly improves classification accuracy to 94.55%, representing a substantial enhancement of 9% to 22% compared to single-frequency classification. Benefiting from the performance advantages of Random Forest (RF) classifiers in handling large datasets, RF classifiers achieve the highest classification accuracy of 95.84%. The optimal multi-dimensional feature composition includes the following: L-band: SE, SEI, α¯, Span; S-band: SEI, SE, Span, PV-Freeman, λ1, λ2; C-band: SE, SEI, Span, λ3, PV-Freeman. The results of this study provide a reliable new method for future sea-ice monitoring during the melting season.

Mueller matrix-based characterization of cervical tissue sections: a quantitative comparison of polar and differential decomposition methods.

Quantitative optical polarimetry has received considerable recent attention owing to its potential for being an efficient diagnosis and characterizing tool with potential applications in biomedical research and various other disciplines. In this regard, it is crucial to validate various Mueller matrix (MM) decomposition methods, which are utilized to extract and quantify the intrinsic individual polarization anisotropy properties of various complex optical media. To quantitatively compare the performance of both polar and differential MM decomposition methods for probing the structural and morphological changes in complex optical media through analyzing their intrinsic individual polarization parameters, which are extracted using the respective decomposition algorithms. We also intend to utilize the decomposition-derived anisotropy parameters to distinguish among the cervical tissues with different grades of cervical intraepithelial neoplasia (CIN) and to characterize the healing efficiency of an organic crystal. Polarization MM of the cervical tissues with different grades of CIN and the different stages of the self-healing crystal are recorded with a home-built MM imaging setup in the transmission detection geometry with a spatial resolution of . The measured MMs are then processed with both the polar and differential MM decomposition methods to extract the individual polarization parameters of the respective samples. The derived polarization parameters are further analyzed to validate and compare the performance of both the MM decomposition methods for probing and characterizing the structural changes in the respective investigated optical media through their decomposition-derived intrinsic individual polarization properties. Pronounced differences in the decomposed-derived polarization anisotropy parameters are observed for cervical tissue sections with different grades of CIN. While a significant increase in the depolarization parameter is obtained with the increment of CIN stages for both the polar [ for CIN grade one (CIN-I) and for CIN grade two (CIN-II))] and differential ( for CIN-I and for CIN-II) decomposition methods, a trend reversal is seen for the linear diattenuation parameter , indicating the structural distortion in the cervical morphology due to the CIN disease. More importantly, with the differential decomposition algorithm, the magnitude of the derived parameter decreases from 0.26 to 0.19 with the progression of CIN, which was not being probed by the polar decomposition method. Our results demonstrate that the differential decomposition of MM holds certain advantages over the polar decomposition method to characterize and probe the structural changes in the cervical tissues with different grades of CIN. Although the quantified individual polarization parameters obtained through both the MM decomposition methods can be used as useful metrics to characterize various optical media, in case of complex turbid media such as biological tissues, incorporation of the differential decomposition technique may yield more efficient information. Also, the study highlights the utilization of MM polarimetry with an appropriate decomposition technique as an efficient diagnostic and characterizing tool in the realm of biomedical clinical research, and various other disciplines.

Creep Monitoring of Submersible Observation Windows Using Mueller Matrix Imaging.

Safety of the observation window is one of the core concerns for manned submersibles. When subjected to underwater static pressure, extrusion and creep deformation always occur in the observation window, which can pose a threat to both safety and optical performance. To assess the deformation, real-time and non-contact monitoring methods are necessary. In this study, a conceptual setup based on the waveplate rotation and dual-DoFP (division of focal-plane polarimeter) polarization camera is built for the observation window's creep monitoring by measuring the Mueller matrix images of the samples under different pressures and durations. Then, a series of characteristic parameters, such as t1, R, r, R', are extracted from the Muller matrix images by Mueller matrix transformation (MMT), Mueller matrix polar decomposition (MMPD), correlation analysis and phase unwrapping method. The results demonstrate that these parameters can effectively describe the observation window's creep at different pressure levels which are simulated by finite element analysis. Additionally, more characterization parameters, such as ψ, A and D, are given from the Mueller matrix images and discussed to illustrate the method's potential for further applications and investigations. Ultimately, future devices based on this method could serve as a valuable tool for real-time and non-contact creep monitoring of the submersible observation windows.

Forest total and component biomass retrieval via GA-SVR algorithm and quad-polarimetric SAR data

A reliable evaluation of biomass is a vital prerequisite for realizing the international goal of “emission peak and carbon neutrality”. It is critical to estimate the components of forest biomass, for ecosystem management. Additionally, working on components we may solve the saturation problems in AGB estimation using remote sensing features. In our previous works we proposed GA-SVR (Genetic algorithms and support vector regression) algorithm with polarimetric SAR (Synthetic Aperture Rader) to retrieve total forest Above Ground Biomass (AGB) estimation in our previous works, however, the potential of GA-SVR algorithm applied in component AGB estimation especially using combination of multi-frequency polarimetric SAR features deserves further exploration. In this study, we use quad-polarimetric SAR data at C- and L- bands, extracting the backscatter coefficients and polarimetric features derived from four polarization decomposition methods (Yamaguchi 3-component decomposition, Freeman 2-component decomposition, H/A/alpha decomposition, and TSVM decomposition) as the input to the GA-SVR for forest component AGB estimation. The effectiveness of 66 polarimetric features derived from C-, L-band at each test site was evaluated for forest component AGB prediction at two test sites. The outcomes demonstrated that the GA-SVR attained high estimation accuracy according to the values of coefficient of determination R2, root mean square error, relative root mean square error, mean deviation, mean absolute deviation, mean percentage error, and mean absolute percentage error. The highest attained values of them were 0.77, 1.01 Mg/ha, 23.02%, −0.07 Mg/ha, 0.71 Mg/ha, 0.15%, and 18.42%, respectively. The study reconfirmed the robustness of GA-SVR algorithm and effectiveness of polarimetric SAR features extracted from four decomposition methods for forest total and AGB estimation. It also revealed that the capability of combining C- band L-band SAR polarimetric features for improving forest total and component AGB relies on the difference of forest structures.

Stokes–Mueller polarization-based analysis of model SARS-CoV-2 virions

Understanding the virology of the coronavirus at the structural level has gained utmost importance to overcome the constant and long-term health complications induced by them. In this work, the light scattering properties of SARS-CoV-2 of size 140 nm were simulated by using discrete dipole approximation (DDA) for two incident wavelengths 200 nm and 350 nm, respectively. Three different 3-dimensional (3D) models of SARS-CoV-2 corresponding to 15, 20, and 40 numbers of spike proteins on the viral capsid surface were constructed as target geometries for the DDA calculations. These models were assessed by employing Stokes–Mueller polarimetry to obtain individual polarization properties such as degree of polarization (DOP), degree of linear polarization (DOLP), and degree of circular polarization (DOCP). Irrespective of its spike numbers, all the coronavirus models were found to display higher DOP and DOCP values and negligibly small DOLP values for circularly polarized incident light, indicating the presence of chiral structures. On the other hand, the lack of understanding about the dependence of the Mueller matrix on its microstructural properties was overcome by transforming 16 Mueller elements into sub-matrices with specific structural and physical properties using Lu–Chipman-based Mueller matrix polar decomposition method. The obtained properties such as retardance, diattenuation, and depolarization were used for investigating the composition and microstructural information. The approach presented in this work has the potential to understand the virology of the coronavirus at the structural level and, therefore, will be beneficial in developing effective detection strategies by exploiting their characteristic electromagnetic scattering signatures.

Polarization clustering of biological structures with Mueller matrix parameters.

Mueller matrix imaging polarimetry (MMIP) is a promising technique for the characterization of biological tissues, including the classification of microstructures in pathological diagnosis. To expand the parameter space of Mueller matrix parameters, we propose new vector parameters (VPs) according to the Mueller matrix polar decomposition method. We measure invasive bladder cancer (IBC) with extensive necrosis and high-grade ductal carcinoma in situ (DCIS) with MMIP, and the regions of cancer cells and fibrotic stroma are classified with the VPs. Then the proposed and existing VPs are mapped on the Poincaré sphere with 3D visualization, and an indicator of spatial feature is defined based on the minimum enclosing sphere to evaluate the classification capability of the VPs. For both IBC and DCIS, the results show that the proposed VPs exhibit evident contrast between the regions of cancer cells and fibrotic stroma. This study broadens the fundamental Mueller matrix parameters and helps to improve the characterization ability of the MMIP technique.

Polarization Descattering Imaging of Underwater Complex Targets Based on Mueller Matrix Decomposition

The traditional polarization imaging techniques cannot obtain the polarization characteristics with global variation, and the reconstruction of the target with different optical properties concurrently is seriously distorted. In this work, we overcome the aforementioned shortcomings by using the polar decomposition method to estimate the Mueller matrix of the target in the full field of view. Simultaneously, the illumination light with globally varying polarization state is calculated to suppress the noise caused by computational imaging. The descattering imaging experiments through turbid water indicate that the images recovered by our method present the similarity to the targets without scattering, and the noise is suppressed to some extent. Further, we prove the superiority of the proposed method by comparing with other polarization underwater imaging strategies.

Linear convergence of an alternating polar decomposition method for low rank orthogonal tensor approximations

Low rank orthogonal tensor approximation (LROTA) is an important problem in tensor computations and their applications. A classical and widely used algorithm is the alternating polar decomposition method (APD). In this paper, an improved version iAPD of the classical APD is proposed. For the first time, all of the following four fundamental properties are established for iAPD: (i) the algorithm converges globally and the whole sequence converges to a KKT point without any assumption; (ii) it exhibits an overall sublinear convergence with an explicit rate which is sharper than the usual O(1/k) for first order methods in optimization; (iii) more importantly, it converges R-linearly for a generic tensor without any assumption; (iv) for almost all LROTA problems, iAPD reduces to APD after finitely many iterations if it converges to a local minimizer.

Characterization of three-dimensional fractional viscoelastic models through complex modulus analysis and polar decomposition

Soft materials such as gels, elastomers, and biological tissues have diverse applications in nature and technology due to their viscoelastic nature. These soft materials often exhibit complex rheology and display elastic and viscous characteristics when undergoing deformation. In recent years, fractional calculus has emerged as a promising tool to explain the viscoelastic behavior of soft materials. Scalar constants are primarily used to quantify viscoelastic elements such as springs and dashpots. However, in three-dimensional (3D) space, not all materials show the same elastic or viscoelastic properties in all directions, especially under elastic/viscoelastic wave propagation (or anisotropy). Though previously reported studies on viscoelastic models have explained a power-law decay of the memory functions, none of them explicitly explained the 3D complex modulus through a matrix notation. In this paper, we present a mathematical formulation that employs tensor algebra and fractional calculus to derive the 3D complex modulus of Kelvin–Voigt, Maxwell, and other arrangements of viscoelastic models. The 3D complex modulus provides information about the elastic wave propagation in a media and can be used to explain anisotropy in different viscoelastic materials. Additionally, an advanced formulation of the moduli can improve the modeling in finite element analysis of 3D viscoelastic materials where discretization is vital for studying media of asymmetric shapes. Finally, we demonstrated a polar decomposition method to visualize viscoelastic tensors using the Green–Christoffel tensor and surface plots to represent the degrees of anisotropy and viscoelasticity in the Fourier domain when the medium is probed by a time-harmonic homogeneous plane wave.

Polarization Aberrations in High-Numerical-Aperture Lens Systems and Their Effects on Vectorial-Information Sensing

The importance of polarization aberrations has been recognized and studied in numerous optical systems and related applications. It is known that polarization aberrations are particularly crucial in certain photogrammetry and microscopy techniques that are related to vectorial information—such as polarization imaging, stimulated emission depletion microscopy, and structured illumination microscopy. Hence, a reduction in polarization aberrations would be beneficial to different types of optical imaging/sensing techniques with enhanced vectorial information. In this work, we first analyzed the intrinsic polarization aberrations induced by a high-NA lens theoretically and experimentally. The aberrations of depolarization, diattenuation, and linear retardance were studied in detail using the Mueller matrix polar-decomposition method. Based on an analysis of the results, we proposed strategies to compensate the polarization aberrations induced by high-NA lenses for hardware-based solutions. The preliminary imaging results obtained using a Mueller matrix polarimeter equipped with multiple coated aspheric lenses for polarization-aberration reduction confirmed that the conclusions and strategies proposed in this study had the potential to provide more precise polarization information of the targets for applications spanning across classical optics, remote sensing, biomedical imaging, photogrammetry, and vectorial optical-information extraction.

Characterizing Ancient Channel of the Yellow River From Spaceborne SAR: Case Study of Chinese Gaofen-3 Satellite

The lower reaches of the ancient Yellow River (AYR) migrated very frequently, like a loong swinging its tail on the land of China. As the origin of Chinese civilization, AYR provided natural conditions for the people to thrive. However, the sediment carried by AYR still has a negative impact on local agricultural production. This letter, based on Gaofen-3, extracted scattering characteristics of archeological anomalies, detecting part of AYR during Song and Jin Dynasties, which was confirmed with field investigations. Then, an adaptive irregular convolution kernel U-Net (AICK-U-Net) was proposed to reconstruct the channel of AYR, based on the images obtained by the different polarization decomposition methods in October, and the precision and recall reached 96.21% and 94.45%, respectively. Finally, two decision-level methods were proposed to optimize the reconstruction results, improving the precision and recall to 96.39% and 97.36%, respectively. In summary, Spaceborne synthetic aperture radar (SAR), with the application of polarization decomposition and neural network, provides new insights for detecting archeological anomalies and reconstructing archaeolandscapes.

Multiparameter Adaptive Target Classification Using Full-Polarimetric GPR: A Novel Approach to Landmine Detection

Full-polarimetric ground penetrating radar (FP-GPR) can measure the ability of an object to change the polarization of electromagnetic waves. Compared to the traditional GPR, it has a stronger capability to identify underground objects. In recent years, a series of polarization decomposition methods have been applied to the FP-GPR data processing to obtain the polarimetric attributes and enhance the capability of targets identification. Different polarimetric attributes characterize different features of a target but there is still no effective way to integrate these attributes and take their respective advantages for target classification. In this article, we propose a particle center AdaBoost (PCAD) method and achieve the multiparameter adaptive target identification. The experimental results indicate that the PCAD method can automatically select suitable parameters during the training process for different targets. Compared to the single-parameter classification and the AdaBoost methods based on the traditional average and Bagging method, the PCAD method presents higher correct rates in classification. Finally, the proposed method is applied to landmine detection. The results demonstrate that the landmine is a composite scatterer that can generate surface scattering signals on its surface and dipole and volume scattering signals from its interior; based on the color-coded two-dimensional image by PCAD, we can distinguish landmines from other targets.

Dryland Crop Classification Combining Multitype Features and Multitemporal Quad-Polarimetric RADARSAT-2 Imagery in Hebei Plain, China.

The accuracy of dryland crop classification using satellite-based synthetic aperture radar (SAR) data is often unsatisfactory owing to the similar dielectric properties that exist between the crops and their surroundings. The main objective of this study was to improve the accuracy of dryland crop (maize and cotton) classification by combining multitype features and multitemporal polarimetric SAR (PolSAR) images in Hebei plain, China. Three quad-polarimetric RADARSAT-2 scenes were acquired between July and September 2018, from which 117 features were extracted using the Cloude–Pottier, Freeman–Durden, Yamaguchi, and multiple-component polarization decomposition methods, together with two polarization matrices (i.e., the coherency matrix and the covariance matrix). Random forest (RF) and support vector machine (SVM) algorithms were used for classification of dryland crops and other land-cover types in this study. The accuracy of dryland crop classification using various single features and their combinations was compared for different imagery acquisition dates, and the performance of the two algorithms was evaluated quantitatively. The importance of all investigated features was assessed using the RF algorithm to optimize the features used and the imagery acquisition date for dryland crop classification. Results showed that the accuracy of dryland crop classification increases with evolution of the phenological period. In comparison with SVM, the RF algorithm showed better performance for dryland crop classification when using full polarimetric RADARSAT-2 data. Dryland crop classification accuracy was not improved substantially when using only backscattering intensity features or polarization decomposition parameters extracted from a single-date image. Satisfactory classification accuracy was achieved using 11 optimized features (derived from the Cloude–Pottier decomposition and the coherency matrix) from 2 RADARSAT-2 images (acquisition dates corresponding to the middle and late stages of dryland crop growth). This study provides an important reference for timely and accurate classification of dryland crop in Hebei plain, China.

Research on an Urban Building Area Extraction Method with High-Resolution PolSAR Imaging Based on Adaptive Neighborhood Selection Neighborhoods for Preserving Embedding

Feature extraction of an urban area is one of the most important directions of polarimetric synthetic aperture radar (PolSAR) applications. A high-resolution PolSAR image has the characteristics of high dimensions and nonlinearity. Therefore, to find intrinsic features for target recognition, a building area extraction method for PolSAR images based on the Adaptive Neighborhoods selection Neighborhood Preserving Embedding (ANSNPE) algorithm is proposed. First, 52 features are extracted by using the Gray level co-occurrence matrix (GLCM) and five polarization decomposition methods. The feature set is divided into 20 dimensions, 36 dimensions, and 52 dimensions. Next, the ANSNPE algorithm is applied to the training samples, and the projection matrix is obtained for the test image to extract the new features. Lastly, the Support Vector machine (SVM) classifier and post processing are used to extract the building area, and the accuracy is evaluated. Comparative experiments are conducted using Radarsat-2, and the results show that the ANSNPE algorithm could effectively extract the building area and that it had a better generalization ability; the projection matrix is obtained using the training data and could be directly applied to the new sample, and the building area extraction accuracy is above 80%. The combination of polarization and texture features provide a wealth of information that is more conducive to the extraction of building areas.

Sources of tourism growth in Mainland China: An extended data envelopment analysis‐based decomposition analysis

AbstractUnderstanding the driving factors of tourism growth provides insights into tourism growth patterns and can inform tourism policymaking. This paper develops a novel data envelopment analysis (DEA)‐based decomposition approach, a combined use of DEA, meta‐frontier theory, and polar decomposition method, for decomposing tourism growth into seven components, that is, technological efficiency, technology gap effect, technological progress, labour input effect, capital input effect, tourism resource endowment effect, and environmental overload effect. Subsequently, an empirical study has been undertaken for Mainland China during the period of 2005–2015. The results reveal that factor inputs contribute more to China's tourism growth than total factor productivity. The gap between the contributions of factor inputs and total productivity to tourism growth has gradually been narrowing over time. Further decomposition shows that the above seven sources of tourism growth show distinct spatial characteristics. Finally, according to the estimation results, this paper formulates targeted strategies to promote sustainable tourism growth in Mainland China.

Combining of the H/A/Alpha and Freeman–Durden Polarization Decomposition Methods for Soil Moisture Retrieval from Full-Polarization Radarsat-2 Data

Soil moisture (SM) plays important roles in surface energy conversion, crop growth, environmental protection, and drought monitoring. As crops grow, the associated vegetation seriously affects the ability of satellites to retrieve SM data. Here, we collected such data at different growth stages of maize using Bragg and X-Bragg scattering models based on the Freeman–Durden polarization decomposition method. We used the H/A/Alpha polarization decomposition approach to extract accurate threshold values of decomposed scattering components. The results showed that the H and Alpha values of bare soil areas were lower and those of vegetated areas were higher. The threshold values of the three scattering components were 0.2–0.4 H and 7–24° Alpha for the surface scattering component, 0.6–0.9 H and 22–50° Alpha for the volume scattering component, and other values for the dihedral scattering component. The SM data retrieved (using the X-Bragg model) on June 27, 2014, were better than those retrieved at other maize growth stages and were thus associated with the minimum root-mean-square error value (0.028). The satellite-evaluated SM contents were in broad agreement with data measured in situ. Our algorithm thus improves the accuracy of SM data retrieval from synthetic-aperture radar (SAR) images.

Extended polar decomposition method of Mueller matrices for turbid media in reflection geometry.

The polar decomposition method for Mueller matrices proposed by Lu-Chipman has been demonstrated and validated for many applications. However, in some situations, e.g.,when analyzing the Mueller matrix of birefringent turbid media with Mie-sized scatterers acquired in reflection geometry, the method may suffer from limitations due to the assumptions required by this method. Here we extend the Lu-Chipman method and show that it can provide more reasonable results for these situations. The method has been validated experimentally with turbid phantoms. Thus, this Letter may prove useful in tissue polarimetry.

Spherical Parameterization Balancing Angle and Area Distortions.

This work presents a novel framework for spherical mesh parameterization. An efficient angle-preserving spherical parameterization algorithm is introduced, which is based on dynamic Yamabe flow and the conformal welding method with solid theoretic foundation. An area-preserving spherical parameterization is also discussed, which is based on discrete optimal mass transport theory. Furthermore, a spherical parameterization algorithm, which is based on the polar decomposition method, balancing angle distortion and area distortion is presented. The algorithms are tested on 3D geometric data and the experiments demonstrate the efficiency and efficacy of the proposed methods.

Singular observation of the polarization-conversion effect for a gammadion-shaped metasurface.

In this article, the polarization-conversion effects of a gammadion-shaped metasurface in transmission and reflection modes are discussed. In our experiment, the polarization-conversion effect of a gammadion-shaped metasurface is investigated because of the contribution of the phase and amplitude anisotropies. According to our experimental and simulated results, the polarization property of the first-order transmitted diffraction is dominated by linear anisotropy and has weak depolarization; the first-order reflected diffraction exhibits both linear and circular anisotropies and has stronger depolarization than the transmission mode. These results are different from previously published research. The Mueller matrix ellipsometer and polar decomposition method will aid in the investigation of the polarization properties of other nanostructures.

An efficient rotational matrix extraction scheme for finite element method-based deformation

With the development of computer science and mechanical engineering, advanced and stable soft tissue deformation modelling methods have been employed, such as mass-spring model, finite element method and meshless method. The co-rotational finite element method (co-rotational FEM), which was first introduced in physics-based computer animations, has shown its strengths to be a feasible approach to modelling the process of soft tissue deformation in a virtual surgery simulation system. In this study, we mainly investigated the method of extracting the rotational matrix which is used to perform stiffness warping assembly at each simulation time step. We first introduced and compared the time-consuming polar decomposition method and the efficient QR decomposition method, and then our hybrid rotational matrix extraction method is described. The final experimental results show that our efficient rotational matrix extraction method can improve the computation efficiency greatly without deformation accuracy losing.