Polarimetric and interferometric SAR data are frequently multilook processed for speckle reduction and data compression. The statistical characteristics of multilook data are quite different from those of single-look data. The authors investigate the statistics of their intensity and phase. Probability density function (PDF's) of the multilook phase difference, magnitude of complex product, and intensity and amplitude ratios between two components of the scattering matrix are derived, and expressed in closed forms. The PDF's depend on the complex correlation coefficient and the number of looks. Comparisons of these theoretically derived PDF's are made to measurements from NASA/JPL AIRSAR data. The results of this paper can be applied to feature classification using polarimetric SAR and to the estimation of decorrelation effects of the interferometric SAR. >

Intensity and phase statistics of multilook polarimetric and interferometric SAR imagery

In dual- or multiple-channel synthetic aperture radar (SAR) imaging modes, cross-channel correlation is a potential source of information. The sample coherence magnitude is calculated over a moving window to generate a coherence magnitude map. High-resolution coherence maps may be useful to discriminate fine structures. Coarser resolution is needed for a more accurate estimation of the coherence magnitude. In this study, the accuracy of coherence estimation is investigated as a function of the coherence map resolution. It is shown that the space-averaged coherence magnitude is biased toward higher values. The accuracy of the coherence magnitude estimate obtained is a function of the number of pixels averaged and the number of independent samples per pixel (i.e., the coherence map resolution). A method is proposed to remove the bias from the space-averaged sample coherence magnitude. Coherence magnitude estimation from complex (magnitude and phase) coherence maps is also considered. It is established that the magnitude of the averaged sample coherence estimate is slightly biased for high-resolution coherence maps and that the bias reduces with coarser resolution. Finally, coherence estimation for nonstationary targets is discussed. It is shown that the averaged sample coherence obtained from complex coherence maps or coherence magnitude maps is suitable for estimation of nonstationary coherence. The averaged sample (complex) coherence permits the calculation of an unbiased coherence estimate, provided that the original signals can be assumed to be locally stationary over a sufficiently coarse resolution cell.

Coherence estimation for SAR imagery

High-frequency radar measurements of man-made targets are dominated by returns from isolated scattering centers, such as corners and flat plates. Characterizing the features of these scattering centers provides a parsimonious, physically relevant signal representation for use in automatic target recognition (ATR). In this paper, we present a framework for feature extraction predicated on parametric models for the radar returns. The models are motivated by the scattering behaviour predicted by the geometrical theory of diffraction. For each scattering center, statistically robust estimation of model parameters provides high-resolution attributes including location, geometry, and polarization response. We present statistical analysis of the scattering model to describe feature uncertainty, and we provide a least-squares algorithm for feature estimation. We survey existing algorithms for simplified models, and derive bounds for the error incurred in adopting the simplified models. A model order selection algorithm is given, and an M-ary generalized likelihood ratio test is given for classifying polarimetric responses in spherically invariant random clutter.

Attributed scattering centers for SAR ATR

This study provides an update of the polarimetric tools currently being used for optimum information extraction from polarimetric synthetic aperture radar (SAR) images. The basics of polarimetric theory are summarized and discussed in the context of SAR. Calibration of polarimetric SAR, which is an important issue for the extraction of meaningful polarization information, is reviewed. Information extraction using the scattered and received wave parameters and target decomposition theory is considered. In particular, the use of coherent versus incoherent target decomposition is discussed and the practical limitations of these target decompositions are outlined. Speckle filtering and classification of polarimetric SAR images are also thoroughly analyzed, and the important directions for future research are outlined.

A review of polarimetry in the context of synthetic aperture radar: concepts and information extraction

This paper addresses estimation of the equivalent number of looks (ENL), an important parameter in statistical modeling of multilook synthetic aperture radar (SAR) images. Two new ENL estimators are discovered by looking at certain moments of the multilook polarimetric covariance matrix, which is commonly used to represent multilook polarimetric SAR (PolSAR) data, and assuming that the covariance matrix is complex Wishart distributed. First, a second-order trace moment provides a polarimetric extension of the ENL definition and also a matrix-variate version of the conventional ENL estimator. The second estimator is obtained from the log-determinant matrix moment and is also shown to be the maximum likelihood estimator under the Wishart model. It proves to have much lower variance than any other known ENL estimator, whether applied to single-polarization or PolSAR data. Moreover, this estimator is less affected by texture and thus provides more accurate results than other estimators should the assumption of Gaussian statistics for the complex scattering coefficients be violated. These are the first known estimators to use the full covariance matrix as input, rather than individual intensity channels, and therefore to utilize all the statistical information available. We finally demonstrate how an ENL estimate can be computed automatically from the empirical density of small sample estimates calculated over a whole scene. We show that this method is more robust than procedures where the estimate is calculated in a manually selected region of interest.

Estimation of the Equivalent Number of Looks in Polarimetric Synthetic Aperture Radar Imagery

A multivariate K-distribution is proposed to model the statistics of fully polarimetric radar data from earth terrain with polarizations HH, HV, VH, and VV. In this approach, correlated polarizations of radar signals, as characterized by a covariance matrix, are treated as the sum of N n-dimensional random vectors; N obeys the negative binomial distribution with a parameter alpha and mean N-bar. Subsequently, an n-dimensional K-distribution, with either zero or nonzero mean, is developed in the limit of infinite N-bar or illuminated area. The probability density function (PDF) of the K-distributed vector normalized by its Euclidean norm is independent of the parameter alpha and is the same as that derived from a zero-mean Gaussian-distributed random vector.

K-distribution and polarimetric terrain radar clutter

A multivariate K-distribution, well supported by experimental data, is proposed to model the statistics of fully polarimetric radar clutter of earth terrain. In this approach, correlated polarizations of backscattered radar returns are characterized by a covariance matrix and homogeneity of terrain scatterers is characterized by a parameter . As compared with C-, L- and P-band polarimetric SAR image simultaneously measured by Jet Propulsion Laboratory (JPL) on Mt. Shasta, it is found that appears to decrease from C- to P-band for both the forest and burned areas.

J. K. Jao

Papers

K-distribution and polarimetric terrain radar clutter

K-Distribution and Multi-Frequency Polarmetric Terrain Radar Clutter