The real and imaginary components of the scattering matrix elements measured for each pixel in single look fully polarimetric SAR(POLSAR) are coherently combined from a large number of scatterers in each resolution bin. These components for the three independent Sinclair matrix scattering elements have normal distributions when collected over homogeneous regions. This is observed from the ocean surface, homogeneous desert regions, agricultural areas and more. These distributions are studied in this paper. Other distributions such as those for the amplitude ratios and the phase differences of the Sinclair matrix elements are addressed. This is done for single look fully polarimetric SIR-C data at L and C band and TerraSAR-X data. Distributions of observables from 4 look SIR-C data at L and C band are also addressed and compared to the single look distributions. All terrestial surfaces are considered where data is available.
We demonstrate an algorithm for determining low entropy fully polarimetric synthetic aperture radar (POLSAR) coherence matrices using inverse syntetic aperture radar (ISAR) data. Low entropy information is not accessible using the standard method of averaging pixels. Spatially averaging locally around a SAR pixel is not equivalent to time averaging necessary for low entropy measurement. A low entropy POLSAR measurement indicates the dominance of a single scatterer. Low entropy ocean scattering, primarily from Bragg scattering, will be discussed.
A large number of scatterers contribute to the total energy received from a resolution cell of a polarimetric synthetic aperture radar(POLSAR). The polarimetric response for each resolution cell is obtained by simultaneously measuring both the amplitude and phase of the scattered field using orthogonal channels. The POLSAR signature from ocean backscatter is primarily produced by the capillary and small gravity waves produced by the local wind. Measurement of low entropy cells from resonant ocean Bragg scatter requires proper multilook processing of the SAR phase histories. Low entropy information is not accessible using the standard averaging of pixels. Scattering entropy allows for the consideration of depolarization. Empirical observations are presented from four-look SIR-C L and C band data from a large set of global ocean surface data. The data trend of alpha versus incidence angle for the L Band four-look SIR-C scenes closely follows some behaviour predicted by an extended Bragg model. A survey is presented for a collection of terrestrial surfaces including agricultural areas, forests, desert terrain, and volcanic surfaces. Analysis of the normalized coherence matrices from four look SIR-C imagery is discussed.
The coherence matrix from the scattering matrix of a single look polarimetric SAR pixel will have an entropy of zero with the main eigenvalue being equal to the span and the other two eigenvalues being equal to zero. Each scattering matrix element from terrain scatter is a coherent sum from a large number of scatterers in a resolution cell. Entropy/alpha decomposition is only possible where the coherency matrix elements are determined from ensemble covariances. This is the case for multilook polarimetric SAR data where covariances from the exact same collection of scatterers are averaged using separate extraction filters in the SAR doppler direction. We report interesting observations from analysis of multilook SIR-C data at L and C bands from different oceans around the globe. We present a strategy for segmenting single look polarimetric TerraSAR ocean data using an algorithm we have previously developed with the averaging of the resulting like pixels used to generate coherence matrices. We give a brief discussion of desert surfaces.
We report results from the segmenting and study of terrain surface signatures of fully polarimetric multilook L-band and C-band SIR-C data. Entropy/alpha/anisotropy decomposition features are available from single multilook pixel data. This eliminates the need to average data from several pixels. Entropy and alpha are utilized in the segmentation along with features we have developed primarily from the eigenanalysis of the Kennaugh matrices of multilook data. We have previously reported on our algorithm for segmenting fully polarimetric single look TerraSAR-X, multilook SIR-C and 7 band Landsat 5 data featuring the iterative application of a feedforward neural network with one hidden layer. A comparison of signatures from simultaneously recorded data at L and C bands is presented. The terrain surfaces surveyed include the ocean, lakes, lake ice, bare ground, desert salt flats, lava beds, vegetation, sand dunes, rough desert surfaces, agricultural and urban areas.
We have developed an algorithm for segmenting fully polarimetric single look TerraSAR-X, multilook SIR-C and 7 band Landsat 5 imagery using neural nets. The algorithm uses a feedforward neural net with one hidden layer to segment different surface classes. The weights are refined through an iterative filtering process characteristic of a relaxation process. Features selected from studies of fully polarimetric complex single look TerraSAR-X data and multilook SIR-C data are used as input to the net. The seven bands from Landsat 5 data are used as input for the Landsat neural net. The Cloude-Pottier incoherent decomposition is used to investigate the physical basis of the polarimetric SAR data segmentation. The segmentation of a SIR-C ocean surface scene into four classes is presented. This segmentation algorithm could be a very useful tool for investigating complex polarimetric SAR phenomena.
We have previously shown that Stokes eigenvectors can be numerically extracted from the Kennaugh(Stokes)
matrices of both single-look and multilook fully polarimetric SIR-C data. The extracted orientation and ellipticity
parameters of the Stokes eigenvector were found to be related to the Huynen orientation and helicity parameters
for single-look fully polarimetric SIR-C data. We formally show in this paper that these two parameters, which
diagonalize the Sinclair matrices of the single-look data, belong to a set of parameters which diagonalize the
Kennaugh matrices of single-look data. Along with the cross sections kSvvk2, kShvk2, kShhk2 and the Span, the
eigenvalues of the Kennaugh matrix and the covariance matrix are used as input features in the development of
a neural net landcover classifier for SIR-C data.
We have previously reported on the analysis of fully polarimetric single look and multilook SIR-C data. We
have reported that the Stokes(Kennaugh) matrices for each pixel have one and only one eigenvector that satisfies
the property of a Stokes Vector. We now report on new analysis of fully polarimetric SIR-C data and ISAR
data from the Submillimeter-Wave Technology Laboratory at the University of Massachussetts Lowell which
shows that the remaining three eigenvectors of the Stokes matrix are quaternions which represent rotations.
Furthermore, the three direction vectors of these quaternions form an orthogonal cartesian set of axes. We also
discuss relationships between the angles of the Stokes Vector with the Euler parameters initially proposed by
Huynen.
We have completed the analysis of single look fully polarimetric data from SIR-C. The analysis of multilook fully
polarimetric data was reported at the SPIE Radar Sensor Technology XIII conference in April 13-15, 2009. The
title of the paper is Stokes Matrix Eigenvectors of Fully Polarimetric SAR Data. In addition to the property
that only one of the eigenvectors of the Stokes matrix satifies the condition for a Stokes Vector, the eigenvector
solutions for the single look data are fully polarized (no depolarized part). An interesting relationship between
the eigenvalue and span for a pixel will be shown. Results from the investigation of the copolarized phase
difference distributions for the ocean surface, lake surface, lake ice, bare ground, crop fields and vegetation are
reported. Similar analysis of high resolution data from such sensors as RADARSAT 2 and TerraSAR-X and
aircraft data will allow for detailed modeling studies of fully polarimetric signatures. We present a derivation of
the Stokes matrix elements and describe the delivery format of the SIR-C data.
The Stokes matrices of about 1 billion pixels of fully polarimetric single look and multilook SIR-C L-band data
were analyzed. The Stokes matrix is a 4×4 real symmetric matrix. The Jacobi eigenvalue algorithm was used to
determine the eigenvalues and eigenvectors of each matrix. A remarkable result is that all 1 billion pixels did not
have more than one eigenvector which satisfied the Stokes vector property where (equation) and S0 >0. Less than 1 percent of the pixels had no eigenvectors which satisfied this property. The equality
condition corresponds to cases where the eigenvector describes a fully polarized Stokes vector. Images were
generated from the fraction of the polarized part and unpolarized part of these Stokes vectors, the sine of the
ellipticity as well as the eigenvalue. Images were generated as well from the phase statistics generated from the
Mueller scattering matrix. These images strongly correlate with the span imagery. The reported resolution for
the multilook SIR-C data is 25 m. Each resolution cell is populated by a large number of scattering centers at
this relatively low resolution. RADARSAT-2, which was launched on Dec 14, 2007, is capable of much higher
resolution fully polarimetric data. Application of this type of analysis to such data will allow consideration of
the signatures of the more dominant scatterers in a resolution cell.
Present remote sensing systems are capable of producing digital image data at rates which far exceed the exploitation capabilities of existing processing systems. Automated image classification and interpretation tools are necessary to optimize the use of remotely sensed multispectral imagery. We have investigated the use of artificial neural networks (ANN) for spectral pattern recognition in multispectral imagery for both polarimetric synthetic aperture radar (SAR) and Landsat Thematic Mapper (TM) data. We have used ANN to segment SAR and TM scenes into a few broad land use/land cover (LU/LC) types (e.g., vegetation, bare soil, water, etc.). We believe that these broad landuse classes can be subclassified further into more refined types (e.g., vegetation, class can be partitioned into different vegetation types) using spectral information, spatial shape indicators, and contextual image information such as texture.
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