Jihad S. Daba

Statistics of the scattering cross-section of a small number of random scatterers

Complex radar targets are often modeled as a number of individual scattering elements randomly distributed throughout the spatial region containing the target. While it is known that as the number of scatterers grows large the distribution of the scattered signal power or intensity is asymptotically exponential, this is not true for a small number of scatterers. The authors study the statistics of measured power or intensity, and hence scattering cross section, resulting from a small number of constant amplitude scatterers each having a random phase. They derive closed-form expressions for the probability density function (pdf) of the scattered signal intensity for one, two, and three scatterers having arbitrary amplitudes. For n>3 scatterers, they derive expressions for the pdf when the individual scatterers have identical constant amplitudes and independent random phases; these expressions are Gram-Charlier type expansions with weighting functions determined by the asymptotic form of the intensity pdf for a large number of scatterers n. The Kolmogorov-Smirnov goodness-of-fit test is used to show that the series expansions are a good fit to empirical pdfs computed using Monte-Carlo simulation of targets made up of a small number of constant amplitude scatterers with random phase. >

Statistical distributions of partially developed speckle based on a small number of constant scatterers with random phase

The speckle phenomenon is observed in coherent imaging systems such as synthetic aperture radar. The authors deal with situations in which the speckle arises from a small random number of constant amplitude scattering points within the resolution cell. Speckle in this context is referred to as partially developed. They first model the surface scattering statistics as a marked point process. They then derive closed form expressions and accurate approximations for the intensity probability density function of single look and multilook speckle using an orthogonal Gram-Charlier type series expansion having gamma-weighted generalized Laguerre polynomials as the basis functions. Using the Kolmogorov-Smirnov test, they show that the series expansions are a good approximation to the actual pdfs.<<ETX>>

Synthetic-aperture-radar surface reflectivity estimation using a marked point-process speckle model

This paper presents stochastic models and estimation algorithms for speckled images, with an emphasis on synthetic-aperture-radar images, and where the speckle may not be fully developed. We treat speckle from a novel point of view: as a carrier of useful surface information rather than as contaminating noise. The stochastic models for surface scattering are based on a doubly stochastic marked Poisson point process. For each of these surface-scattering statistical models, we present estimation algorithms to determine the average surface reflectivity and scatterer density within a resolution cell, using intensity measurements of speckled images. We show that the maximum-likelihood estimator is optimal in the sense that the variance of the error is the smallest possible using any conceivable estimate having the same bias with the same data.

Object discrimination and orientation determination in speckled images

Detection and identification of objects in images formed by coherent imaging systems are complicated by the presence of speckle. Speckle not only complicates these problems for human observers, but also for machine detection and identification algorithms. We investigate optimal statistical tests for object discrimination and orientation determination in speckle and compare their performance to that of human observers for the same problems. We formulate maximum likelihood tests for determining the orientation of an object and for discriminating among a set of known objects in a speckled image. We then analyze the performance of these tests to study the system requirements for reliable object discrimination and orientation determination. Next we generalize these tests and their corresponding pertormance analyses into three broad classes of pattern recognition problems, corresponding to orthogonal, antipodal, and biorthogonal signal problems in statistical communications theory. These generalizations make the design and analysis of a broad range of object discrimination and orientation determination straightforward. Finally we compare the performance of these tests to the results of Korwar and Pierce for human interpretation of objects in speckled images. We note that for fixed image contrast, number of looks, and image size in pixels, object shape has no effect on machine detection performance. This is not true for the human observer.

Segmentation of speckled images using a likelihood random field model

We devise a segmentation scheme aimed at extracting edge information from speckled images using a maximum likelihood edge detector. The scheme is based on finding a threshold for the probability density function of the summing average field over a neighborhood set and, in a general context, is founded on a likelihood random field model (LRFM). A rigorous stochastic analysis is used to derive an exact expression for the cumulative density function of the likelihood of the averaging sum image. Based on this, an accurate probability of error is derived and the performance of the scheme is analyzed. The segmentation performs reasonably well for both simulated and real images. The LRFM scheme is also compared with standard edge detection methods to quantify the significant gains obtained from the optimized edge detector. The importance of this work lies in the development of a stochastic-based segmentation, allowing an accurate quantification of the probability of false detection. Nonvisual quantification and misclassification in speckled images, such as synthetic aperture radar and medical ultrasound, is relatively new and is of interest to remote sensing human observers and clinicians.

Comments on "Statistics of the scattering cross section of small number of random scatterers" [with reply]

For original paper see IEEE Trans. Antennas Propag., vol.43, p.773-83 (1995 August). The present comment discusses the use of a recursive method and an orthonormal Laguerre polynomial representation in the original paper; a reply is given by the original authors.

Optimal Object Discrimination and Orientation Determination in Synthetic Aperture Radar Images

Detection and identification of objects in SAR images is complicated by the presence of speckle. This is true for both human and machine detection. We formulate and analyze the performance of maximum likelihood tests for determining the orientation of an object and for discriminating among a set of known objects in a speckled image. We then generalize the tests into three classes of pattern recognition problems, corresponding to orthogonal, antipodal, and biorthogonal signal detection problems. Finally, we compare the performance of these tests to the results of Korwar and Pierce for human interpretation of objects in speckled images.