Unsupervised Classification of Polarimetric SAR Images via Riemannian Sparse Coding

Unsupervised classification plays an important role in understanding polarimetric synthetic aperture radar (PolSAR) images. One of the typical representations of PolSAR data is in the form of Hermitian positive definite (HPD) covariance matrices. Most algorithms for unsupervised classification using this representation either use statistical distribution models or adopt polarimetric target decompositions. In this paper, we propose an unsupervised classification method by introducing a sparsity-based similarity measure on HPD matrices. Specifically, we first use a novel Riemannian sparse coding scheme for representing each HPD covariance matrix as sparse linear combinations of other HPD matrices, where the sparse reconstruction loss is defined by the Riemannian geodesic distance between HPD matrices. The coefficient vectors generated by this step reflect the neighborhood structure of HPD matrices embedded in the Euclidean space and hence can be used to define a similarity measure. We apply the scheme for PolSAR data, in which we first oversegment the images into superpixels, followed by representing each superpixel by an HPD matrix. These HPD matrices are then sparse coded, and the resulting sparse coefficient vectors are then clustered by spectral clustering using the neighborhood matrix generated by our similarity measure. The experimental results on different fully PolSAR images demonstrate the superior performance of the proposed classification approach against the state-of-the-art approachesThis work was supported in part by the National Natural Science Foundation of China under Grant 61331016 and Grant 61271401 and in part by the National Key Basic Research and Development Program of China under Contract 2013CB733404. The work of A. Cherian was supported by the Australian Research Council Centre of Excellence for Robotic Vision under Project CE140100016.

Multi-Frequency Polarimetric SAR Classification Based on Riemannian Manifold and Simultaneous Sparse Representation

Normally, polarimetric SAR classification is a high-dimensional nonlinear mapping problem. In the realm of pattern recognition, sparse representation is a very efficacious and powerful approach. As classical descriptors of polarimetric SAR, covariance and coherency matrices are Hermitian semidefinite and form a Riemannian manifold. Conventional Euclidean metrics are not suitable for a Riemannian manifold, and hence, normal sparse representation classification cannot be applied to polarimetric SAR directly. This paper proposes a new land cover classification approach for polarimetric SAR. There are two principal novelties in this paper. First, a Stein kernel on a Riemannian manifold instead of Euclidean metrics, combined with sparse representation, is employed for polarimetric SAR land cover classification. This approach is named Stein-sparse representation-based classification (SRC). Second, using simultaneous sparse representation and reasonable assumptions of the correlation of representation among different frequency bands, Stein-SRC is generalized to simultaneous Stein-SRC for multi-frequency polarimetric SAR classification. These classifiers are assessed using polarimetric SAR images from the Airborne Synthetic Aperture Radar (AIRSAR) sensor of the Jet Propulsion Laboratory (JPL) and the Electromagnetics Institute Synthetic Aperture Radar (EMISAR) sensor of the Technical University of Denmark (DTU). Experiments on single-band and multi-band data both show that these approaches acquire more accurate classification results in comparison to many conventional and advanced classifiers

Wave Propagation and Source Localization in Random and Refracting Media

This thesis focuses on understanding the way that acoustic and electromagnetic waves propagate through an inhomogeneous or turbulent environment, and analyzes the effect that this uncertainty has on signal processing algorithms. These methods are applied to determining the effectiveness of matched-field style source localization algorithms in uncertain ocean environments, and to analyzing the effect that random media composed of electrically large scatterers has on propagating waves. The first half of this dissertation introduces the frequency-difference autoproduct, a surrogate field quantity, and applies this quantity to passive acoustic remote sensing in waveguiding ocean environments. The frequency-difference autoproduct, a quadratic product of frequency-domain complex measured field values, is demonstrated to retain phase stability in the face of significant environmental uncertainty even when the related pressure field’s phase is as unstable as noise. This result demonstrates that a measured autoproduct (at difference frequencies less than 5 Hz) that is associated with a pressure field (measured in the hundreds of Hz) and which has propagated hundreds of kilometers in a deep ocean sound channel can be consistently cross-correlated with a calculated autoproduct. This cross-correlation is shown to give a cross-correlation coefficient that is more than 10 dB greater than the equivalent cross-correlation coefficient of the measured pressure field, demonstrating that the autoproduct is a stable alternative to the pressure field for array signal processing algorithms. The next major result demonstrates that the frequency-difference autoproduct can be used to passively localize remote unknown sound sources that broadcast sound hundreds of kilometers to a measuring device at hundreds of Hz frequencies. Because of the high frequency content of the measured pressure field, an equivalent conventional localization result is not possible using frequency-domain methods. These two primary contributions, recovery of frequency-domain phase stability and robust source localization, represent unique contributions to existing signal processing techniques. The second half of this thesis focuses on understanding electromagnetic wave propagation in a random medium composed of metallic scatterers placed within a background medium. This thesis focuses on developing new methods to compute the extinction and phase matrices, quantities related to Radiative Transfer theory, of a random medium composed of electrically large, interacting scatterers. A new method is proposed, based on using Monte Carlo simulation and full-wave computational electromagnetics methods simultaneously, to calculate the extinction coefficient and phase function of such a random medium. Another major result of this thesis demonstrates that the coherent portion of the field scattered by a configuration of the random medium is equivalent to the field scattered by a homogeneous dielectric that occupies the same volume as the configuration. This thesis also demonstrates that the incoherent portion of the field scattered by a configuration of the random medium, related to the phase function of the medium, can be calculated using buffer zone averaging. These methods are applied to model field propagation in a random medium, and propose an extension of single scattering theory that can be used to understand mean field propagation in relatively dense (tens of particles per cubic wavelength) random media composed of electrically large (up to 3 wavelengths long) conductors and incoherent field propagation in relatively dense (up to 5 particles per cubic wavelength) media composed of electrically large (up to two wavelengths) conductors. These results represent an important contribution to the field of incoherent, polarimetric remote sensing of the environment.PHDApplied PhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/169886/1/geroskdj_1.pd

The Fifteenth Marcel Grossmann Meeting

The three volumes of the proceedings of MG15 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 40 morning plenary talks over 6 days, 5 evening popular talks and nearly 100 parallel sessions on 71 topics spread over 4 afternoons. These proceedings are a representative sample of the very many oral and poster presentations made at the meeting.Part A contains plenary and review articles and the contributions from some parallel sessions, while Parts B and C consist of those from the remaining parallel sessions. The contents range from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theory, to precision tests of general relativity including progress towards the detection of gravitational waves, and from supernova cosmology to relativistic astrophysics, including topics such as gamma ray bursts, black hole physics both in our galaxy and in active galactic nuclei in other galaxies, and neutron star, pulsar and white dwarf astrophysics. Parallel sessions touch on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, white dwarfs, binary systems, radiative transfer, accretion disks, quasars, gamma ray bursts, supernovas, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, numerical relativity, gravitational lensing, large scale structure, observational cosmology, early universe models and cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, global structure, singularities, chaos, Einstein-Maxwell systems, wormholes, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors and data analysis, precision gravitational measurements, quantum gravity and loop quantum gravity, quantum cosmology, strings and branes, self-gravitating systems, gamma ray astronomy, cosmic rays and the history of general relativity