This paper utilizes the algebraic property of the Gershgorin circle theorem to explore the association between the orthogonal odd- and even-bounce scattering mechanisms. First, we use two unitary transformations to decouple this association, thereby reducing the ambiguity in the underlying scattering mechanisms. We then derive a descriptor utilizing the properties of circles in the Gershgorin theorem to gauge the mixture property of coherent type scattering in a pixel. We explain and validate the proposed findings with suitable experiments and examples from the full polarimetric L-band PiSAR Tomakomai dataset. The results demonstrate the effectiveness of the proposed approach in characterizing deterministic scattering mixtures.

In this paper, we propose a new hybrid methodology to decompose the polarimetric synthetic aperture radar (PolSAR) coherency matrix into sum of three basic scattering mechanisms. The proposed methodology first utilizes a physical scattering model to compute the volume scattering contribution using generalized eigen-decomposition approach. Later, the surface and dihedral scattering powers are computed simultaneously utilizing eigenvalues and dominant eigenvector (α1) of the remainder coherency matrix. We further enhance the performance of the proposed approach by two special unitary transformations which optimize α1parameter by increasing its dominancy towards a single scattering-type phenomenon. We demonstrated the superiority of the proposed two approaches by comparing the experimetal results on a fully polarimetric SAR dataset with recent state-of-the-art techniques.

This work proposes a methodology that begins by extracting a rank-deficient residue matrix by suitably subtracting a volume scattering model from the measured full-rank coherency matrix. Then, two unitary rotation matrices transform the residue matrix aiming to decorrelate single and double-bounce scattering mechanisms. The rotated residue matrix is eigen-decomposed as the sum of two rank-1 matrices. A normalized target symmetry-asymmetry difference index is proposed that is computed from the dominant rank-1 coherency matrix elements. This index relates the two Huynen parameters: the generator of target symmetry (A0) and the generator of target structure (B0). The dominant scattering power components are computed using this proposed normalized difference index. The performance of the proposed approach is evaluated using two polarimetric Synthetic Aperture Radar (PolSAR) datasets. Analysis shows that the obtained results outperform the state-of-the-art techniques.

This letter presents a new decomposition approach with independent physical scattering models for odd- and even-bounce mechanisms. The rationale behind the method is to provide orthogonality between the odd- and even-bounce scattering components by removing their correlation from a rank-deficient residue coherency matrix by two successive unitary rotations. The rotated residue coherency matrix is then decomposed into the sum of two rank-1 orthogonal Hermitian positive semi-definite matrices. We show that these two orthogonal matrices consistently depict a single-type scattering phenomenon. Therefore, without branching criteria, one can independently compute the nonnegative odd- and even-bounce scattering powers. We used two full polarimetric SAR data to validate the effectiveness of the proposed method. We first affirm the orthogonality of the proposed scattering models. Then, we perform decomposition to derive the scattering power components and compare them with conventional and state-of-the-art methods. The quantitative analysis supports the merit of the proposed method.

For more than four decades, it has been known that the dielectric constant of the lunar surface can be retrieved from the Fresnel reflection coefficients. However, theoretical models have met with limited success in validating laboratory test results from the Apollo missions to date. This paper is the first study to focus on the use of high-resolution full-polarimetric synthetic aperture radar datasets for the retrieval of the dielectric constant of the lunar surface from the Fresnel reflection coefficients. We initially show that it is possible to retrieve the lunar dielectric constant via the classical Freeman-Durden Decomposition (FDD). The performance of the FDD algorithm is found to be unacceptable over regions with surface slopes and craters, and for sub-surface soil samples. Accurate estimation is not possible by simply replacing the volume scattering model in the FDD with popular and widely used volume scattering models. Therefore, a model-based three-component decomposition (TCD) algorithm for a robust retrieval of the lunar dielectric constant is proposed. The proposed TCD algorithm implements an efficient branching condition combined with double unitary matrix rotations and provides exceptionally accurate dielectric constant estimation. The proposed TCD algorithm is validated by using L band full-polarimetric datasets acquired by the Chandrayaan-2 mission over Apollo 12, Apollo 15, and Apollo 17 landing sites. Comparisons are also made with other three-component decomposition algorithms. Excellent agreement between the estimated values by the proposed TCD algorithm and the reference values for the dielectric constant, available from the literature, has been observed.

Rapid advancements have been made in model-based decomposition techniques for polarimetric Synthetic Aperture Radar (PolSAR) data. Improvements have been primarily driven by including additional scattering models to the three-component model-based method first introduced by Freeman and Durden. Nevertheless, the three-component method is still extensively used due to its simplicity and ease of interpretability. Recently, the paradigm of the decomposition strategy has been changed to non-model types with notable success. Thus utilizing this new approach, we propose a hybrid (i.e., combining non-model and model-based) three-component methodology in this work. The proposed method primarily involves three steps: (i) the generalized eigendecomposition technique is first used to determine the optimum volume scattering power, (ii) the residual rank-2 coherency matrix (i.e., volume scattering model deducted) is appropriately transformed using two unitary transformations to decorrelate the odd and even bounce scattering components, and (iii) compute the odd and even bounce scattering power contributions using the newly developed scattering-type parameter obtained from the rank-2 matrix. Each step carries relevant physical significance that is appropriately addressed in this work. The proposed methodology is first demonstrated using some specific coherency matrices from canonical targets and a few matrices extracted from different landcover types from full-polarimetric SAR images. We then apply the proposed method over diverse landcover types using two full-polarimetric SAR images. We compare the results with the state-of-the-art three-component model-based decomposition techniques to validate the effectiveness of the proposed method that deals with the existing challenges of model-based decomposition methods.

We present an unsupervised learning method for dense crowd count estimation. Marred by large variability in appearance of people and extreme overlap in crowds, enumerating people proves to be a difficult task even for humans. This implies creating large-scale annotated crowd data is expensive and directly takes a toll on the performance of existing CNN based counting models on account of small datasets. Motivated by these challenges, we develop Grid Winner-Take-All (GWTA) autoencoder to learn several layers of useful filters from unlabeled crowd images. Our GWTA approach divides a convolution layer spatially into a grid of cells. Within each cell, only the maximally activated neuron is allowed to update the filter. Almost 99.9% of the parameters of the proposed model are trained without any labeled data while the rest 0.1% are tuned with supervision. The model achieves superior results compared to other unsupervised methods and stays reasonably close to the accuracy of supervised baseline. Furthermore, we present comparisons and analyses regarding the quality of learned features across various models.

In this letter, a special unitary SU(3) matrix group is exploited for coherency matrix transformations to decouple the energy between orthogonal states of polarization. This decoupling results in the minimization of the cross-polarization power along with the removal of some off-diagonal terms of coherency matrix. The proposed unitary transformations are utilized on the basis of the underlying dominant scattering mechanism. By doing so, the reduced power from the cross-polarization channel is always concentrated on the underlying dominant co-polar scattering component. This makes it unique in comparison to state-of-the-art techniques. The proposed methodology can be adopted to optimize the coherency matrix to be used for the model-based decomposition methods. To verify this, pioneer three-component decomposition model is implemented using the proposed optimized coherency matrix of two different test sites. The comparative studies are analyzed to show the improvements over state-of-the-art techniques.

In this letter, we investigate the existing branching conditions used to solve the unknown model-coefficients of modelbased decomposition methods and show that they are less efficient in discriminating between dominant surface and dihedral scattering mechanisms. The discrimination ability of the branching conditions further deteriorates when the target has some random slope and orientation. This greatly suppressed the performance of the model-based decomposition methods. To overcome this problem, we propose an efficient alternate to existing branching conditions of model-based methods. The proposed branching condition is based on the value of the alpha (α) angle derived from the eigenvector analysis of the measured coherency matrix. The roll-invariance property of α angle makes it work efficiently even in the sloped and oriented areas. The proposed concept is experimentally validated over three different polarimetric synthetic aperture radar (PolSAR) data sets. The effectiveness of the α angle is analyzed and compared with the other branching conditions in terms of ability to discriminate between dominant surface and dihedral scattering mechanisms. The experimental results on different PolSAR data sets clearly demonstrate that by replacing the existing branching conditions with the α angle, the performances of the model-based decomposition methods are significantly improved.