Improvement of PolSAR Decomposition Scattering Powers Using a Relative Decorrelation Measure

In this letter, a methodology is proposed to improve the scattering powers obtained from model-based decomposition using Polarimetric Synthetic Aperture Radar (PolSAR) data. The novelty of this approach lies in utilizing the intrinsic information in the off-diagonal elements of the 3$\times$3 coherency matrix $\mathbf{T}$ represented in the form of complex correlation coefficients. Two complex correlation coefficients are computed between co-polarization and cross-polarization components of the Pauli scattering vector. The difference between modulus of complex correlation coefficients corresponding to $\mathbf{T}^{\mathrm{opt}}$ (i.e. the degree of polarization (DOP) optimized coherency matrix), and $\mathbf{T}$ (original) matrices is obtained. Then a suitable scaling is performed using fractions \emph{i.e.,} $(T_{ii}^{\mathrm{opt}}/\sum\limits_{i=1}^{3}T_{ii}^{\mathrm{opt}})$ obtained from the diagonal elements of the $\mathbf{T}^{\mathrm{opt}}$ matrix. Thereafter, these new quantities are used in modifying the Yamaguchi 4-component scattering powers obtained from $\mathbf{T}^{\mathrm{opt}}$. To corroborate the fact that these quantities have physical relevance, a quantitative analysis of these for the L-band AIRSAR San Francisco and the L-band Kyoto images is illustrated. Finally, the scattering powers obtained from the proposed methodology are compared with the corresponding powers obtained from the Yamaguchi \emph{et. al.,} 4-component (Y4O) decomposition and the Yamaguchi \emph{et. al.,} 4-component Rotated (Y4R) decomposition for the same data sets. The proportion of negative power pixels is also computed. The results show an improvement on all these attributes by using the proposed methodology.Comment: Accepted for publication in Remote Sensing Letter

Scattering systems with several evolutions and formal reproducing kernel Hilbert spaces

A Schur-class function in $d$ variables is defined to be an analytic contractive-operator valued function on the unit polydisk. Such a function is said to be in the Schur--Agler class if it is contractive when evaluated on any commutative $d$-tuple of strict contractions on a Hilbert space. It is known that the Schur--Agler class is a strictly proper subclass of the Schur class if the number of variables $d$ is more than two. The Schur--Agler class is also characterized as those functions arising as the transfer function of a certain type (Givone--Roesser) of conservative multidimensional linear system. Previous work of the authors identified the Schur--Agler class as those Schur-class functions which arise as the scattering matrix for a certain type of (not necessarily minimal) Lax--Phillips multievolution scattering system having some additional geometric structure. The present paper links this additional geometric scattering structure directly with a known reproducing-kernel characterization of the Schur--Agler class. We use extensively the technique of formal reproducing kernel Hilbert spaces that was previously introduced by the authors and that allows us to manipulate formal power series in several commuting variables and their inverses (e.g., Fourier series of elements of $L^2$ on a torus) in the same way as one manipulates analytic functions in the usual setting of reproducing kernel Hilbert spaces

Modifying the Yamaguchi Four-Component Decomposition Scattering Powers Using a Stochastic Distance

Model-based decompositions have gained considerable attention after the initial work of Freeman and Durden. This decomposition which assumes the target to be reflection symmetric was later relaxed in the Yamaguchi et al. decomposition with the addition of the helix parameter. Since then many decomposition have been proposed where either the scattering model was modified to fit the data or the coherency matrix representing the second order statistics of the full polarimetric data is rotated to fit the scattering model. In this paper we propose to modify the Yamaguchi four-component decomposition (Y4O) scattering powers using the concept of statistical information theory for matrices. In order to achieve this modification we propose a method to estimate the polarization orientation angle (OA) from full-polarimetric SAR images using the Hellinger distance. In this method, the OA is estimated by maximizing the Hellinger distance between the un-rotated and the rotated $T_{33}$ and the $T_{22}$ components of the coherency matrix $\mathbf{[T]}$. Then, the powers of the Yamaguchi four-component model-based decomposition (Y4O) are modified using the maximum relative stochastic distance between the $T_{33}$ and the $T_{22}$ components of the coherency matrix at the estimated OA. The results show that the overall double-bounce powers over rotated urban areas have significantly improved with the reduction of volume powers. The percentage of pixels with negative powers have also decreased from the Y4O decomposition. The proposed method is both qualitatively and quantitatively compared with the results obtained from the Y4O and the Y4R decompositions for a Radarsat-2 C-band San-Francisco dataset and an UAVSAR L-band Hayward dataset.Comment: Accepted for publication in IEEE J-STARS (IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing

Geometric Scattering in Robotic Telemanipulation

In this paper, we study the interconnection of two robots, which are modeled as port-controlled Hamiltonian systems through a transmission line with time delay. There will be no analysis of the time delay, but its presence justifies the use of scattering variables to preserve passivity. The contributions of the paper are twofold: first, a geometrical, multidimensional, power-consistent exposition of telemanipulation of intrinsically passive controlled physical systems, with a clarification on impedance matching, and second, a system theoretic condition for the adaptation of a general port-controlled Hamiltonian system with dissipation (port-Hamiltonian system) to a transmission line

Scattering in Multilayered Structures: Diffraction from a Nanohole

The spectral expansion of the Green's tensor for a planar multilayered structure allows us to semi analytically obtain the angular spectrum representation of the field scattered by an arbitrary dielectric perturbation present in the structure. In this paper we present a method to find the expansion coefficients of the scattered field, given that the electric field inside the perturbation is available. The method uses a complete set of orthogonal vector wave functions to solve the structure's vector wave equation. In the two semi-infinite bottom and top media, those vector wave functions coincide with the plane-wave basis vectors, including both propagating and evanescent components. The technique is used to obtain the complete angular spectrum of the field scattered by a nanohole in a metallic film under Gaussian illumination. We also show how the obtained formalism can easily be extended to spherically and cylindrically multilayered media. In those cases, the expansion coefficients would multiply the spherical and cylindrical vector wave functions.Comment: 9 pages, 5 figure

5G Positioning and Mapping with Diffuse Multipath

5G mmWave communication is useful for positioning due to the geometric connection between the propagation channel and the propagation environment. Channel estimation methods can exploit the resulting sparsity to estimate parameters(delay and angles) of each propagation path, which in turn can be exploited for positioning and mapping. When paths exhibit significant spread in either angle or delay, these methods breakdown or lead to significant biases. We present a novel tensor-based method for channel estimation that allows estimation of mmWave channel parameters in a non-parametric form. The method is able to accurately estimate the channel, even in the absence of a specular component. This in turn enables positioning and mapping using only diffuse multipath. Simulation results are provided to demonstrate the efficacy of the proposed approach