Stian Normann Anfinsen

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

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.

Application of the Matrix-Variate Mellin Transform to Analysis of Polarimetric Radar Images

In this paper, we propose to use a matrix-variate Mellin transform in the statistical analysis of multilook polarimetric radar data. The domain of the transform integral is the cone of complex positive definite matrices, which allows for transformation of the distributions used to model the polarimetric covariance and coherency matrix. Based on the matrix-variate Mellin transform, an alternative characteristic function is defined, from which we can retrieve a new kind of matrix log-moments and log-cumulants. It is demonstrated that the matrix log-cumulants are of great value to analysis of polarimetric radar data, and that they can be used to derive estimators for the distribution parameters with low bias and variance.

Classification With a Non-Gaussian Model for PolSAR Data

In this paper, we present a generalized Wishart classifier derived from a non-Gaussian model for polarimetric synthetic aperture radar (PolSAR) data. Our starting point is to demonstrate that the scale mixture of Gaussian (SMoG) distribution model is suitable for modeling PolSAR data. We show that the distribution of the sample covariance matrix for the SMoG model is given as a generalization of the Wishart distribution and present this expression in integral form. We then derive the closed-form solution for one particular SMoG distribution, which is known as the multivariate K-distribution. Based on this new distribution for the sample covariance matrix, termed as the K -Wishart distribution, we propose a Bayesian classification scheme, which can be used in both supervised and unsupervised modes. To demonstrate the effect of including non-Gaussianity, we present a detailed comparison with the standard Wishart classifier using airborne EMISAR data.

Automated Non-Gaussian Clustering of Polarimetric Synthetic Aperture Radar Images

This paper presents an automatic image segmentation method for polarimetric synthetic aperture radar data. It utilizes the full polarimetric information and incorporates texture by modeling with a non-Gaussian distribution for the complex scattering coefficients. The modeling is based upon the well-known product model, with a Gamma-distributed texture parameter leading to the K-Wishart model for the covariance matrix. The automatic clustering is achieved through a finite mixture model estimated with a modified expectation maximization algorithm. We include an additional goodness-of-fit test stage that allows for splitting and merging of clusters. This not only improves the model fit of the clusters, but also dynamically selects the appropriate number of clusters. The resulting image segmentation depicts the statistically significant clusters within the image. A key feature is that the degree of sub-sampling of the input image will affect the detail level of the clustering, revealing only the major classes or a variable level of detail. Real-world examples are shown to demonstrate the technique.

Goodness-of-Fit Tests for Multilook Polarimetric Radar Data Based on the Mellin Transform

The advent of polarimetric synthetic aperture radar has spurred a growing interest in statistical models for complex-valued covariance matrices, which is the common representation of multilook polarimetric radar images. In this paper, we respond to an emergent need by proposing statistical tests for the simple and composite goodness-of-fit (GoF) problem for a class of compound matrix distributions. The tests are based on Mellin-kind matrix cumulants. These are derived from a novel characteristic function for positive definite Hermitian random matrices, defined in terms of a matrix-variate Mellin transform instead of the conventional Fouriér transform, and belong to a new framework for statistical analysis of multilook polarimetric radar data recently introduced by the authors. The cumulant-based tests are easy to compute, and the asymptotic sampling distribution of the test statistic is chi-square distributed in the simple hypothesis case. Under the composite hypothesis, the sampling distribution is obtained by Monte Carlo simulations. We evaluate the power of the proposed GoF tests with simulated data. We also use them to assess the fit of several matrix distributions to real data acquired by Radarsat-2 in fine-quad polarization mode.

A Textural–Contextual Model for Unsupervised Segmentation of Multipolarization Synthetic Aperture Radar Images

This paper proposes a novel unsupervised, non-Gaussian, and contextual segmentation method that combines an advanced statistical distribution with spatial contextual information for multilook polarimetric synthetic aperture radar (PolSAR) data. This extends on previous studies that have shown the added value of both non-Gaussian modeling and contextual smoothing individually or for intensity channels only. The method is based on a Markov random field (MRF) model that integrates a K-Wishart distribution for the PolSAR data statistics conditioned to each image cluster and a Potts model for the spatial context. Specifically, the proposed algorithm is constructed based upon the stochastic expectation maximization (SEM) algorithm. A new formulation of SEM is developed to jointly perform clustering of the data and parameter estimation of the K-Wishart distribution and the MRF model. Experiments on simulated and real PolSAR data demonstrate the added value of using an appropriate statistical representation, in combination with contextual smoothing.

Robust CFAR Detector Based on Truncated Statistics in Multiple-Target Situations

A new and robust constant false alarm rate (CFAR) detector based on truncated statistics (TSs) is proposed for ship detection in single-look intensity and multilook intensity synthetic aperture radar data. The approach is aimed at high-target-density situations such as busy shipping lines and crowded harbors, where the background statistics are estimated from potentially contaminated sea clutter samples. The CFAR detector uses truncation to exclude possible statistically interfering outliers and TSs to model the remaining background samples. The derived truncated statistic CFAR (TS-CFAR) algorithm does not require prior knowledge of the interfering targets. The TS-CFAR detector provides accurate background clutter modeling, a stable false alarm regulation property, and improved detection performance in high-target-density situations.

Ship Detection in Ice-Infested Waters Based on Dual-Polarization SAR Imagery

This letter discusses the potential of automatic ship detection in ice-infested waters based on satellite synthetic aperture radar (SAR) imagery. The popular K -distribution is used to model the backscatter statistics of sea ice clutter. The goodness of fit of this model is assessed with the Kolmogorov-Smirnov and Anderson-Darling test statistics for both VV and VH polarizations. We also test the impact of introducing the Method of Log Cumulant (MoLC) estimator for the shape parameter of the K-distribution. Finally, a constant false-alarm rate ship detection algorithm, applying the K -distribution with the MoLC estimator, is evaluated on dual-polarization RADARSAT-2 SAR data. Our results demonstrate that this is a viable approach to ship detection in ice-infested waters.

Subband Extraction Strategies in Ship Detection With the Subaperture Cross-Correlation Magnitude

The subaperture cross-correlation magnitude (SCM) has previously been proposed as a statistic that improves the contrast between small ship targets and the surrounding sea in synthetic-aperture-radar images. This preprocessing technique utilizes the fast decorrelation of open-water surface ripples on the scale of the SAR wavelength relative to coherent targets such as a ship. However, optimization of the bandwidth splitting in the subband extraction has not received any attention. The aim of this letter is twofold: 1) to describe the technical details of the algorithm, including modifications that are necessary to allow overlapping subapertures; and 2) to study the effect of splitting the bandwidth into two azimuth subapertures with respect to varying bandwidths and subaperture overlap. The impact on the SCM is investigated in terms of measures of speckle reduction and target-to-clutter contrast. Experiments are performed on real single-look complex SAR data containing repeated acquisitions of a vessel in open sea. The results indicate that the subband extraction strategy has a clear impact on performance.

A Multitexture Model for Multilook Polarimetric Synthetic Aperture Radar Data

A statistical model for multilook polarimetric radar data is presented where the polarimetric channels are associated with individual texture variables having potentially different statistical properties. The feasibility of producing closed-form probability density functions under certain restrictions is outlined. Mellin kind statistics is derived under various assumptions on the texture variables, and the potential for model fit assessment and hypothesis testing in the Mellin domain is demonstrated. Application to real data proves the usefulness of the analytic approach.