Paul R. Kersten

Unsupervised classification of polarimetric synthetic aperture Radar images using fuzzy clustering and EM clustering

Five clustering techniques are compared by classifying a polarimetric synthetic aperture radar image. The pixels are complex covariance matrices, which are known to have the complex Wishart distribution. Two techniques are fuzzy clustering algorithms based on the standard /spl lscr//sub 1/ and /spl lscr//sub 2/ metrics. Two others are new, combining a robust fuzzy C-means clustering technique with a distance measure based on the Wishart distribution. The fifth clustering technique is an application of the expectation-maximization algorithm assuming the data are Wishart. The clustering algorithms that are based on the Wishart are demonstrably more effective than the clustering algorithms that appeal only to the /spl lscr//sub p/ norms. The results support the conclusion that the pixel model is more important than the clustering mechanism.

Motion Analysis in SAR Images of Unfocused Objects Using Time–Frequency Methods

Synthetic aperture radar (SAR) image formation processing assumes that the scene is stationary, and to focus an object, one coherently sums a large number of independent returns. Any target motion introduces phases that distort and/or translate the targets image. Target motion produces a smear primarily in the azimuth direction of the SAR image. Time-frequency (TF) modeling is used to analyze and correct the residual phase distortions. An interactive focusing algorithm based on TF modeling demonstrates how to correct the phase and to rapidly focus the mover. This is demonstrated on two watercraft observed in a SAR image. Then, two time-frequency representations (TFRs) are applied to estimate the motion parameters of the movers or refocus them or both. The first is the short-time Fourier transform, from which a velocity profile is constructed based on the length of the smear. The second TFR is the time-frequency distribution series, which is a robust derivative of the Wigner-Ville distribution that works well in this SAR environment. The smear is a modulated chirp, from which a velocity profile is plotted and the phase corrections are integrated to focus the movers. The relationship between these two methods is discussed. Both methods show good agreement on the example.

A comparison of change detection statistics in POLSAR images

Abstract : Change detection in polarimetric SAR (POLSAR) images is an important topic. Three statistics are compared on both simulated and real data for their efficacy in change detection. The three statistics are the contrast ratio, the ellipticity and the Bartlett test. The relative performance for these three test statistics on the two simulations is dramatically different. The results are illustrated and explained.

Estimating Surface Water Speeds With a Single-Phase Center SAR Versus an Along-Track Interferometric SAR

Synthetic aperture radar (SAR) single-aperture systems are designed to image fixed scenes. Dual-antenna along-track interferometric (ATI) SAR systems are designed to detect moving targets and estimate their motion parameters. Although SAR systems are not designed to characterize moving targets, for localized targets, such as vehicles or ships, this problem has been addressed in the literature with some success. Distributed moving targets are hard to characterize, even for ATI systems. Estimating surface water speeds is an ideal example of this since the water returns are generated from weak returns randomly distributed in both time and space. The question asked here is can one measure surface water speeds with a single-phase center SAR system? The answer presented is a qualified yes, with the aid of an upper bound on the water speed, but not with the same accuracy as an ATI system. This upper bound and the collection geometry provide design criteria for the filtering of the phase information. Time-frequency (TF) methods provide another speed estimate as well as a rough profile of the speed across the water channel. A robust nonparametric TF method was developed and applied to estimate the speed. Comparisons between the ATI estimate and single-phase estimates are made using data from an X-band ATI-SAR system.

Implementation of the Time-Frequency Distribution Series for SAR Applications

Joint Time Frequency Analysis (JTFA) of SAR imagery is a natural generalization of the sub-aperture image processing used by the remote sensing community for years. At the heart of this process is the Time-Frequency Representations (TFR’s) such as the Wigner-Ville (WV) transform, which is difficult to use because of its large cross-product terms. The Time-Frequency Distribution Series (TFDS) mitigates the cross product terms by averaging in only those terms close to the signal. However, designing an efficient implementation of this series is not easy. Some of the details are explained and an example of a SAR application given. Keywordsjoint time-frequency analysis, JTFS, SAR, WignerVille Transfom, time-frequency distribution series, TFDS.

Scene Analysis of SAR Images using Joint Time-Frequency Analysis

SAR image formation assumes the returns are from stationary objects; however, if the objects move they appear displaced and distorted because the phases needed to focus the object are incorrect. One method to obtain the phase correction to focus the object is interactive search. Another method obtains if one knows the motion of the object. Conversely, for some conditions, one can estimate the object motion from the blurred image. This paper examines a SAR image of two craft moving in an azimuth direction and applies three time-frequency methods to focus the objects and determine the craft’s velocity-profile. Keywordsjoint time-frequency analysis (JTFA), SAR, WignerVille Transform, time-frequency (TF), moving targets, focus tool.

The Wishart-Kotz classifier for multilook polarimetric SAR data

We presents a classifier for multilook polarimetric synthetic aperture radar (PolSAR) data based upon a new distribution model for the polarimetric sample covariance matrix: the complex Wishart-Kotz distribution. This is a highly flexible model, which exhibits the heavy tails needed to fit the data found in high resolution PolSAR images. In addition, they do not contain the mathematical special functions that limit the usefulness of alternative heavy-tailed distributions by inflicting high computational cost and numerical instability. Classification results on simulated and real data are presented.

A Novel Method for Removal of Emitter Noise in SAR Images

Traditionally, interfering emitter signatures have been removed through notched filtering in the range (fast-time) dimension. This works well when a narrowband emitter interferes with a wideband radar pulse; however, when the emitter and radar signal bandwidths are comparable, then this approach fails since the noise is distributed throughout the pulse and the image as well. In cases where the interfering signal is localized in the cross range, joint time-frequency methods can often focus this interference signal, thereby transforming the image. In this transformed image, the interferer is the foreground, and the desired synthetic aperture radar image is blurred and now the background. The focused compressed interferer can be analyzed and censored from the transformed image. Back transformation restores the image with the interference removed. This technique has been fully automated and applied to an Electromagnetics Institute Synthetic Aperture Radar (EMISAR) image contaminated by a nonstationary emitter. The cleansed image is virtually free of the emitter interference

Classification of POLSAR images using a fast fuzzy c-medians clustering algorithm

The fuzzy c-medians clustering (FCMED) clustering algorithm is known to be a robust l/sub 1/ fuzzy clustering algorithm that works well even in the presence of outliers or remote small clusters. The well-known fuzzy c-means (FCM) clustering algorithm often performs poorly in this environment. Unfortunately, the FCMED has a high space-complexity, which makes its application impractical for large images. A new fast fuzzy c-medians clustering (FFCMED) algorithm is presented, which may be applied to any clustering problem, but is demonstrated here by classifying a POLSAR image. The FFCMED provides a robust clustering tool that works well for large images and data sets. A relative speed up over the FCMED of at least 3-to-1 was observed for the image illustrated in this paper.

Classification of polarimetric synthetic aperture radar images using fuzzy clustering

Clustering is a well known technique for classification in polarimetric synthetic aperture radar (POLSAR) images. Pixels are represented as complex covariance matrices, which demand dissimilarity measures that can capture the phase relationships between the polar components of the returns. Four dissimilarity measures are compared to judge their efficacy to separate complex covariances within the fuzzy clustering process. When these four measures are used to classify, a POLSAR image, the measures that are based upon the Wishart distribution outperform the standard metrics because they better represent the total information contained in the polarimetric data. The Expectation Maximization (EM) algorithm is applied to a mixture of complex Wishart distributions to classify the image. Its performance matches the FCM clustering results yielding a tentative conclusion that the Wishart distribution model is more important than the clustering mechanism itself.