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**1 - 7**of**7**### Non-Gaussian Statistical Analysis of Polarimetric Synthetic Aperture Radar Images

, 2011

"... This thesis describes general methods to analyse polarimetric synthetic aperture radar images. The primary application is for unsupervised image segmentation, and fast, practical methods are sought. The fundamental assumptions and statistical modelling are derived from the phys-ics of electromagneti ..."

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This thesis describes general methods to analyse polarimetric synthetic aperture radar images. The primary application is for unsupervised image segmentation, and fast, practical methods are sought. The fundamental assumptions and statistical modelling are derived from the phys-ics of electromagnetic scattering from distributed targets. The physical basis directly leads to the image phenomenon called speckle, which is shown to be potentially non-Gaussian and several statistical distributions are investigated. Speckle non-Gaussianity and polarimetry both hold pertinent information about the target medium and methods that utilise both attributes are developed. Two distinct approaches are proposed: a local feature extraction method; and a model-based clustering algorithm. The local feature extraction approach creates a new six-dimensional description of the image that may be used for subsequent image analysis or for physical parameter extraction (inversion). It essentially extends standard polarimetric features with the addition of a non-Gaussianity measure for texture. Importantly, the non-Gaussianity

### 1Bias Correction and Modified Profile Likelihood under the Wishart Complex Distribution

"... Abstract—This paper proposes improved methods for the maximum likelihood (ML) estimation of the equivalent number of looks L. This parameter has a meaningful interpretation in the context of polarimetric synthetic aperture radar (PolSAR) images. Due to the presence of coherent illumination in their ..."

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Abstract—This paper proposes improved methods for the maximum likelihood (ML) estimation of the equivalent number of looks L. This parameter has a meaningful interpretation in the context of polarimetric synthetic aperture radar (PolSAR) images. Due to the presence of coherent illumination in their processing, PolSAR systems generate images which present a granular noise called speckle. As a potential solution for reducing such interference, the parameter L controls the signal-noise ratio. Thus, the proposal of efficient estimation methodologies for L has been sought. To that end, we consider firstly that a PolSAR image is well described by the scaled complex Wishart distribution. In recent years, Anfinsen et al. derived and analyzed estimation methods based on the ML and on trace statistical moments for obtaining the parameter L of the unscaled version of such probability law. This paper generalizes that approach. We present the second-order bias expression proposed by Cox and Snell for the ML estimator of this parameter. Moreover, the formula of the profile likelihood modified by Barndorff-Nielsen in terms of L is discussed. Such derivations yield two new ML estimators for the parameter L, which are compared to the estimators proposed by Anfinsen et al.. The performance of these estimators is assessed by means of Monte Carlo experiments, adopting three statistical measures as comparison criterion: the mean square error, the bias, and the coefficient of variation. Equivalently to the simulation study, an application to actual PolSAR data concludes that the proposed estimators outperform all the others in homogeneous scenarios. I.

### Classification of Segments in PolSAR Imagery by Minimum Stochastic Distances Between Wishart

"... A new classifier for Polarimetric SAR (PolSAR) images is proposed and assessed in this paper. Its input consists of segments, and each one is assigned the class which minimizes a stochastic distance. Assuming the complex Wishart model, several stochastic distances are obtained from the h-φ family of ..."

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A new classifier for Polarimetric SAR (PolSAR) images is proposed and assessed in this paper. Its input consists of segments, and each one is assigned the class which minimizes a stochastic distance. Assuming the complex Wishart model, several stochastic distances are obtained from the h-φ family of divergences, and they are employed to derive hypothesis test statistics that are also used in the classification process. This article also presents, as a novelty, analytic expressions for the test statistics based on the following stochastic distances between complex Wishart models: Kullback-Leibler, Bhattacharyya, Hellinger, Rényi, and Chi-Square; also, the test statistic based on the Bhattacharyya distance between multivariate Gaussian distributions is presented. The classifier performance is evaluated using simulated and real PolSAR data. The simulated data are based on the complex Wishart model, aiming at the analysis of the proposal well controlled data. The real data refer to the complex L-band image, acquired during the 1994 SIR-C mission. The results of the proposed classifier are compared with those obtained by a Wishart per-pixel/contextual classifier, and we show the better performance of the region-based classification. The influence of the statistical modeling is assessed by comparing the results using the Bhattacharyya distance between multivariate Gaussian distributions for amplitude data. The results with simulated data indicate that the proposed classification method has a very good performance when the data follow the Wishart model. The proposed classifier also performs better than the per-pixel/contextual classifier and the Bhattacharyya Gaussian distance using SIR-C PolSAR data.

### IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 1 Entropy-based Statistical Analysis of PolSAR Data

"... Abstract—Images obtained from coherent illumination pro-cesses are contaminated with speckle noise, with polarimetric synthetic aperture radar (PolSAR) imagery as a prominent example. With an adequacy widely attested in the literature, the scaled complex Wishart distribution is an acceptable model f ..."

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Abstract—Images obtained from coherent illumination pro-cesses are contaminated with speckle noise, with polarimetric synthetic aperture radar (PolSAR) imagery as a prominent example. With an adequacy widely attested in the literature, the scaled complex Wishart distribution is an acceptable model for PolSAR data. In this perspective, we derive analytic expressions for the Shannon, Rényi, and restricted Tsallis entropies under this model. Relationships between the derived measures and the parameters of the scaled Wishart law (i.e., the equivalent number of looks and the covariance matrix) are discussed. In addition, we obtain the asymptotic variances of the Shannon and Rényi entropies when replacing distribution parameters by maximum likelihood estimators. As a consequence, confidence intervals based on these two entropies are also derived and proposed as new ways of capturing contrast. New hypothesis tests are additionally proposed using these results, and their performance is assessed using simulated and real data. In general terms, the test based on the Shannon entropy outperforms those based on Rényi’s. Index Terms—Information theory, SAR polarimetry, contrast measures. I.

### Index Terms Statistical Information Theory · Hypothesis Test · Asymptotic Theory · Signal Processing · PolSAR Image · Hermitian

"... This work presents a comprehensive examination of the use of information theory for understanding Polarimetric Synthetic Aperture Radar (PolSAR) images by means of contrast measures that can be used as test statistics. Due to the phenomenon called ‘speckle’, common to all images obtained with cohere ..."

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This work presents a comprehensive examination of the use of information theory for understanding Polarimetric Synthetic Aperture Radar (PolSAR) images by means of contrast measures that can be used as test statistics. Due to the phenomenon called ‘speckle’, common to all images obtained with coherent illumination such as PolSAR imagery, accurate modelling is required in their processing and analysis. The scaled multilook complex Wishart distribution has proven to be a successful approach for modelling radar backscatter from forest and pasture areas. Classification, segmentation, and image analysis techniques which depend on this model have been devised, and many of them employ some kind of dissimilarity measure. Specifically, we introduce statistical tests for analyzing contrast in such images. These tests are based on the chi-square, Kullback-Leibler, Rényi, Bhattacharyya, and Hellinger distances. Results obtained by Monte Carlo experiments reveal the Kullback-Leibler distance as the best one with respect to the empirical test sizes under several situations which include pure and contaminated data. The proposed methodology was applied to actual data, obtained by an E-SAR sensor over surroundings of Weßling, Bavaria, Germany.

### 1Comparing Edge Detection Methods based on Stochastic Entropies and Distances for PolSAR Imagery

"... Abstract—Polarimetric synthetic aperture radar (PolSAR) has achieved a prominent position as a remote imaging method. However, PolSAR images are contaminated by speckle noise due to the coherent illumination employed during the data acquisition. This noise provides a granular aspect to the image, ma ..."

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Abstract—Polarimetric synthetic aperture radar (PolSAR) has achieved a prominent position as a remote imaging method. However, PolSAR images are contaminated by speckle noise due to the coherent illumination employed during the data acquisition. This noise provides a granular aspect to the image, making its processing and analysis (such as in edge detection) hard tasks. This paper discusses seven methods for edge detection in multilook PolSAR images. In all methods, the basic idea consists in detecting transition points in the finest possible strip of data which spans two regions. The edge is contoured using the transitions points and a B-spline curve. Four stochastic distances, two differences of entropies, and the maximum like-lihood criterion were used under the scaled complex Wishart distribution; the first six stem from the h-φ class of measures. The performance of the discussed detection methods was quantified and analyzed by the computational time and probability of correct edge detection, with respect to the number of looks, the backscatter matrix as a whole, the SPAN, the covariance an the spatial resolution. The detection procedures were applied to three real PolSAR images. Results provide evidence that the methods based on the Bhattacharyya distance and the difference of Shannon entropies outperform the other techniques. Index Terms—Image analysis, information theory, polarimetric SAR, edge detection.

### Information Theoretic SAR Boundary Detection with User Interaction

"... Detection of region boundaries is a very challenging task especially in the presence of noise or speckle as in synthetic aperture radar images. In this work, we propose an interactive boundary detection technique which makes use of B-splines and well-known powerful tools of information theory such a ..."

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Detection of region boundaries is a very challenging task especially in the presence of noise or speckle as in synthetic aperture radar images. In this work, we propose an interactive boundary detection technique which makes use of B-splines and well-known powerful tools of information theory such as the Kullback-Leibler divergence (KLD) and Bhattacharyya distance. The proposed architecture consists of the following four main steps: (1) The user selects points inside and outside of a region. (2) Profiles that link these inside and outside points are extracted. (3) Boundary points that lie on the profile are located. (4) Finally, the B-splines that provide both elasticity and smoothness are used for connecting boundary points together to obtain an accurate estimate of the actual boundary. Existing work related to this approach are extended in two axes. First the use of multiple points both inside and outside of a region made possible to obtain a few times more boundary points. A tracking stage is proposed to put the boundary points in the right order and at the same time eliminate some of them that are erroneously detected as boundary points as well. Experiments were conducted using simulated and real SAR images.