Abraão D. C. Nascimento

Hypothesis Testing in Speckled Data With Stochastic Distances

Images obtained with coherent illumination, as is the case of sonar, ultrasound-B, laser, and synthetic aperture radar, are affected by speckle noise which reduces the ability to extract information from the data. Specialized techniques are required to deal with such imagery, which has been modeled by the G 0 distribution and, under which, regions with different degrees of roughness and mean brightness can be characterized by two parameters; a third parameter, which is the number of looks, is related to the overall signal-to-noise ratio. Assessing distances between samples is an important step in image analysis; they provide grounds of the separability and, therefore, of the performance of classification procedures. This paper derives and compares eight stochastic distances and assesses the performance of hypothesis tests that employ them and maximum likelihood estimation. We conclude that tests based on the triangular distance have the closest empirical size to the theoretical one, while those based on the arithmetic-geometric distances have the best power. Since the power of tests based on the triangular distance is close to optimum, we conclude that the safest choice is using this distance for hypothesis testing, even when compared with classical distances as Kullback-Leibler and Bhattacharyya.

Analytic Expressions for Stochastic Distances Between Relaxed Complex Wishart Distributions

The scaled complex Wishart distribution is a widely used model for multilook full polarimetric synthetic aperture radar data whose adequacy is attested in this paper. Classification, segmentation, and image analysis techniques that depend on this model are devised, and many of them employ some type of dissimilarity measure. In this paper, we derive analytic expressions for four stochastic distances between relaxed scaled complex Wishart distributions in their most general form and in important particular cases. Using these distances, inequalities are obtained that lead to new ways of deriving the Bartlett and revised Wishart distances. The expressiveness of the four analytic distances is assessed with respect to the variation of parameters. Such distances are then used for deriving new tests statistics, which are proved to have asymptotic chi-square distribution. Adopting the test size as a comparison criterion, a sensitivity study is performed by means of Monte Carlo experiments suggesting that the Bhattacharyya statistic outperforms all the others. The power of the tests is also assessed. Applications to actual data illustrate the discrimination and homogeneity identification capabilities of these distances.

Entropy-Based Statistical Analysis of PolSAR Data

Images obtained from coherent illumination processes are contaminated with speckle noise, with polarimetric synthetic aperture radar (PolSAR) imagery as a prominent example. With adequacy widely attested in the literature, the scaled complex Wishart distribution is an acceptable model for PolSAR data. In this perspective, we derive analytical expressions for the Shannon, Rényi, and restricted Tsallis entropy measurements 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 entropy measurements when replacing distribution parameters by maximum-likelihood estimators. As a consequence, confidence intervals based on the Shannon and Rényi entropy measurements 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 entropy.

Comparing Edge Detection Methods Based on Stochastic Entropies and Distances for PolSAR Imagery

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 likelihood 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.

Beta generalized normal distribution with an application for SAR image processing

In this paper, we introduce the beta generalized normal distribution, which is obtained by compounding the beta and generalized normal [S. Nadarajah, A generalized normal distribution, J. Appl. Stat. 32 (2005), pp. 685–694] distributions. The new model includes as sub-models the beta normal, beta Laplace, normal, and Laplace distributions. The shape of the new distribution is quite flexible, especially skewness and tail weights, due to two additional parameters. We obtain general expansions for the moments. We investigate the estimation of the parameters by maximum likelihood. We also propose a random number generator for the new distribution. We analyse and model actual synthetic aperture radars after the new distribution. The results could outperform the 0, Κ, and Γ distributions in several scenarios.

The Marshall-Olkin extended Weibull family of distributions

We introduce a new class of models called the Marshall-Olkin extended Weibull family of distributions based on the work by Marshall and Olkin (Biometrika 84:641–652, 1997). The proposed family includes as special cases several models studied in the literature such as the Marshall-Olkin Weibull, Marshall-Olkin Lomax, Marshal-Olkin Fréchet and Marshall-Olkin Burr XII distributions, among others. It defines at least twenty-one special models and thirteen of them are new ones. We study some of its structural properties including moments, generating function, mean deviations and entropy. We obtain the density function of the order statistics and their moments. Special distributions are investigated in some details. We derive two classes of entropy and one class of divergence measures which can be interpreted as new goodness-of-fit quantities. The method of maximum likelihood for estimating the model parameters is discussed for uncensored and multi-censored data. We perform a simulation study using Markov Chain Monte Carlo method in order to establish the accuracy of these estimators. The usefulness of the new family is illustrated by means of two real data sets.Mathematics Subject Classification (2010)60E05; 62F03; 62F10; 62P10

Parametric and nonparametric tests for speckled imagery

Synthetic aperture radar (SAR) has a pivotal role as a remote imaging method. Obtained by means of coherent illumination, SAR images are contaminated with speckle noise. The statistical modeling of such contamination is well described according to the multiplicative model and its implied

Bias Correction and Modified Profile Likelihood Under the Wishart Complex Distribution

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