Oscar H. Bustos

Robust Estimates for ARMA Models

Abstract Two new classes of robust estimates for ARMA models are introduced: estimates based on residual autocovariances (RA estimates), and estimates based on truncated residual autocovariances (TRA estimates). A heuristic derivation of the asymptotic normal distribution is given. We also perform a Monte Carlo study to compare the robustness properties of these estimates with the least squares, M, and GM estimates. In this study we consider observations that correspond to a Gaussian model with additive outliers. The Monte Carlo results show that RA and TRA estimates compare favorably with respect to least squares, M, and GM estimates.

Classification of SAR images using a general and tractable multiplicative model

Among the frameworks for Synthetic Aperture Radar (SAR) image modelling and analysis, the multiplicative model is very accurate and successful. It is based on the assumption that the observed random field is the result of the product of two independent and unobserved random fields: X and Y. The random field X models the terrain backscatter and, thus, depends only on the type of area to which each pixel belongs. The random field Y takes into account that SAR images are the result of a coherent imaging system that produces the well-known phenomenon called speckle noise, and that they are generated by performing an average of n statistically independent images (looks) in order to reduce the noise effect. There are various ways of modelling the random field X; recently the Γ−1/2(α, γ) distribution was proposed. This, with the usual Γ1/2(n, n) distribution for the amplitude speckle, resulted in a new distribution for the return: the (α, γ, n) law. The parameters α and γ depend only on the ground truth, and n is the number of looks. The advantage of this distribution over the ones used in the past is that it models very well extremely heterogeneous areas like cities, as well as moderately heterogeneous areas like forests and homogeneous areas like pastures. As the ground data can be characterized by the parameters α and γ, their estimation in each pixel generates parameter maps that can be used as the input for classification methods. In this work, moment estimators are used on simulated and on real SAR images and, then, a supervised classification technique (Gaussian maximum likelihood) is performed and evaluated. Excellent classification results are obtained.

General M-estimates for contaminated p th-order autoregressive processes: Consistency and asymptotic normality

SummaryThis work is concerned with simultaneous estimation of coefficients and a scale parameter of a p th-order autoregressive process (Xt). The observations are Yt=VtZt+(1-Vt)Xt where (Zt) is a contaminating process and (Vt) represents the proportion of contamination. If (Xt) or (Zt) have heavy tails both least squares estimates and ordinary M-estimates are seriously affected. Under general conditions we prove consistency and asymptotic normality of a general class of M-estimates which contains some M-estimates studied by Denby and Martin [6].

The influence of training errors, context and number of bands in the accuracy of image classification

We present the assessment of two classification procedures using both a Monte Carlo experiment and real data. Classification performance is hard to assess with generality due to the huge number of variables involved. We consider the problem of classifying multispectral optical imagery with pointwise Gaussian Maximum Likelihood (ML) and contextual ICM (Iterated Conditional Modes), with and without errors in the training stage. Two experimental setups were considered in order to assess the influence of using partial and low‐quality information and to make a quantitative comparison of ML and ICM in real situations. Using simulation the ground truth is known and, therefore, precise comparisons are possible. The contextual approach proved to be superior to the pointwise one, at the expense of requiring more computational resources. Quantitative and qualitative results are discussed.

Statistical functions and procedures in IDL 5.6 and 6.0

Abstract This work presents the results of assessing the accuracy of statistical routines as implemented in the IDL platform, versions 5.6 and 6.0 for Windows XP and Linux. This is “a complete computing environment for the interactive analysis and visualization of data. IDL integrates a powerful, array-oriented language with numerous mathematical analysis and graphical display techniques (Research Systems Inc., IDL Versions 5.6 for Microsoft Windows, 2003 and 6.0.1 for Linux x86 m32, 2004. URL http://www.rsinc.com )”. It is shown that, though it is an excellent platform for signal and image processing and analysis, it has flaws when statistical computing is concerned, mainly when dealing with non-linear regression by least squares fitting and, in particular, when computing in single precision floating point.

A new image segmentation algorithm with applications to image inpainting

This article describes a new approach to perform image segmentation. First an image is locally modeled using a spatial autoregressive model for the image intensity. Then the residual autoregressive image is computed. This resulting image possesses interesting texture features. The borders and edges are highlighted, suggesting that our algorithm can be used for border detection. Experimental results with real images are provided to verify how the algorithm works in practice. A robust version of our algorithm is also discussed, to be used when the original image is contaminated with additive outliers. A novel application in the context of image inpainting is also offered.

Generalized method for sampling spatially correlated heterogeneous speckeled imagery

This paper presents a general result for the simulation of correlated heterogeneous targets, which are present in images corrupted by speckle noise. This technique is based on the use of a correlation mask and Gaussian random variables, in order to obtain spatially dependent Gamma deviates. These Gamma random variables, in turn, allow the obtainment of correlated deviates with specified correlation structure. The theoretical properties of the procedure are presented, along with the corresponding algorithm.

Simulation of correlated intensity SAR images

This paper discusses some methods already available for the simulation of correlated heterogeneous targets in synthetic aperture radar (SAR) images, and extends one of these methods. This new technique is based on the use of a correlation mask and Gaussian random variables, in order to obtain spatially dependent Gamma deviates. Its theoretical properties are presented, along with an algorithm. These Gamma random variables, in turn, allow the obtainment of correlated /spl Kscr/ deviates.

Robust classification of SAR imagery

In this work the G/sub A//sup 0/ distribution is assumed as the universal model for amplitude synthetic aperture radar (SAR) imagery data under the multiplicative model. The observed data, therefore, is assumed to obey a G/sub A//sup 0/ (/spl alpha/, /spl gamma/, n) law, where the parameter n is related to the speckle noise, and (/spl alpha/, /spl gamma/) are related to the ground truth, giving information about the background. Therefore, maps generated by the estimation of (/spl alpha/, /spl gamma/) in each coordinate can be used as the input for classification methods. Maximum likelihood estimators are derived and used to form estimated parameter maps. This estimation can be hampered by the presence of corner reflectors, man-made objects used to calibrate SAR images that produce large return values. In order to alleviate this contamination, robust (M) estimators are also derived for the universal model. Gaussian maximum likelihood classification is used to obtain maps using hard-to-deal-with simulated data, and the superiority of robust estimation is quantitatively assessed.

Simulation of Spatially Correlated Clutter Fields

Correlated 𝒢 distributions can be used to describe the clutter seen in images obtained with coherent illumination, as is the case of B-scan ultrasound, laser, sonar, and synthetic aperture radar (SAR) imagery. These distributions are derived using the square root of the generalized inverse Gaussian distribution for the amplitude backscatter within the multiplicative model. A two-parameter particular case of the amplitude 𝒢 distribution, called , constitutes a modeling improvement with respect to the widespread 𝒦 A distribution when fitting urban, forested, and deforested areas in remote sensing data. This article deals with the modeling and the simulation of correlated -distributed random fields. It is accomplished by means of the Inverse Transform method, applied to Gaussian random fields with spatial correlation. The main feature of this approach is its generality, since it allows the introduction of negative correlation values in the resulting process, necessary for the proper explanation of the shadowing effect in many SAR images.