Scattering statistics of rock outcrops: Model-data comparisons and Bayesian inference using mixture distributions

The probability density function of the acoustic field amplitude scattered by the seafloor was measured in a rocky environment off the coast of Norway using a synthetic aperture sonar system, and is reported here in terms of the probability of false alarm. Interpretation of the measurements focused on finding appropriate class of statistical models (single versus two-component mixture models), and on appropriate models within these two classes. It was found that two-component mixture models performed better than single models. The two mixture models that performed the best (and had a basis in the physics of scattering) were a mixture between two K distributions, and a mixture between a Rayleigh and generalized Pareto distribution. Bayes' theorem was used to estimate the probability density function of the mixture model parameters. It was found that the K-K mixture exhibits significant correlation between its parameters. The mixture between the Rayleigh and generalized Pareto distributions also had significant parameter correlation, but also contained multiple modes. We conclude that the mixture between two K distributions is the most applicable to this dataset.Comment: 15 pages, 7 figures, Accepted to the Journal of the Acoustical Society of Americ

Statistical Modeling of SAR Images: A Survey

Statistical modeling is essential to SAR (Synthetic Aperture Radar) image interpretation. It aims to describe SAR images through statistical methods and reveal the characteristics of these images. Moreover, statistical modeling can provide a technical support for a comprehensive understanding of terrain scattering mechanism, which helps to develop algorithms for effective image interpretation and creditable image simulation. Numerous statistical models have been developed to describe SAR image data, and the purpose of this paper is to categorize and evaluate these models. We first summarize the development history and the current researching state of statistical modeling, then different SAR image models developed from the product model are mainly discussed in detail. Relevant issues are also discussed. Several promising directions for future research are concluded at last

MIMO Radar Target Localization and Performance Evaluation under SIRP Clutter

Multiple-input multiple-output (MIMO) radar has become a thriving subject of research during the past decades. In the MIMO radar context, it is sometimes more accurate to model the radar clutter as a non-Gaussian process, more specifically, by using the spherically invariant random process (SIRP) model. In this paper, we focus on the estimation and performance analysis of the angular spacing between two targets for the MIMO radar under the SIRP clutter. First, we propose an iterative maximum likelihood as well as an iterative maximum a posteriori estimator, for the target's spacing parameter estimation in the SIRP clutter context. Then we derive and compare various Cram\'er-Rao-like bounds (CRLBs) for performance assessment. Finally, we address the problem of target resolvability by using the concept of angular resolution limit (ARL), and derive an analytical, closed-form expression of the ARL based on Smith's criterion, between two closely spaced targets in a MIMO radar context under SIRP clutter. For this aim we also obtain the non-matrix, closed-form expressions for each of the CRLBs. Finally, we provide numerical simulations to assess the performance of the proposed algorithms, the validity of the derived ARL expression, and to reveal the ARL's insightful properties.Comment: 34 pages, 12 figure

Ship Wake Detection in SAR Images via Sparse Regularization

In order to analyse synthetic aperture radar (SAR) images of the sea surface, ship wake detection is essential for extracting information on the wake generating vessels. One possibility is to assume a linear model for wakes, in which case detection approaches are based on transforms such as Radon and Hough. These express the bright (dark) lines as peak (trough) points in the transform domain. In this paper, ship wake detection is posed as an inverse problem, which the associated cost function including a sparsity enforcing penalty, i.e. the generalized minimax concave (GMC) function. Despite being a non-convex regularizer, the GMC penalty enforces the overall cost function to be convex. The proposed solution is based on a Bayesian formulation, whereby the point estimates are recovered using maximum a posteriori (MAP) estimation. To quantify the performance of the proposed method, various types of SAR images are used, corresponding to TerraSAR-X, COSMO-SkyMed, Sentinel-1, and ALOS2. The performance of various priors in solving the proposed inverse problem is first studied by investigating the GMC along with the L1, Lp, nuclear and total variation (TV) norms. We show that the GMC achieves the best results and we subsequently study the merits of the corresponding method in comparison to two state-of-the-art approaches for ship wake detection. The results show that our proposed technique offers the best performance by achieving 80% success rate.Comment: 18 page

SAR Amplitude Probability Density Function Estimation Based on a Generalized Gaussian Model

International audienceIn the context of remotely sensed data analysis, an important problem is the development of accurate models for the statistics of the pixel intensities. Focusing on synthetic aperture radar (SAR) data, this modeling process turns out to be a crucial task, for instance, for classification or for denoising purposes. In this paper, an innovative parametric estimation methodology for SAR amplitude data is proposed that adopts a generalized Gaussian (GG) model for the complex SAR backscattered signal. A closed-form expression for the corresponding amplitude probability density function (PDF) is derived and a specific parameter estimation algorithm is developed in order to deal with the proposed model. Specifically, the recently proposed “method-of-log-cumulants” (MoLC) is applied, which stems from the adoption of the Mellin transform (instead of the usual Fourier transform) in the computation of characteristic functions and from the corresponding generalization of the concepts of moment and cumulant. For the developed GG-based amplitude model, the resulting MoLC estimates turn out to be numerically feasible and are also analytically proved to be consistent. The proposed parametric approach was validated by using several real ERS-1, XSAR, E-SAR, and NASA/JPL airborne SAR images, and the experimental results prove that the method models the amplitude PDF better than several previously proposed parametric models for backscattering phenomena

Maximum Likelihood Estimation of Compound-Gaussian Clutter and Target Parameters

Compound-Gaussian models are used in radar signal processing to describe heavy-tailed clutter distributions. The important problems in compound-Gaussian clutter modeling are choosing the texture distribution, and estimating its parameters. Many texture distributions have been studied, and their parameters are typically estimated using statistically suboptimal approaches. We develop maximum likelihood (ML) methods for jointly estimating the target and clutter parameters in compound-Gaussian clutter using radar array measurements. In particular, we estimate i) the complex target amplitudes, ii) a spatial and temporal covariance matrix of the speckle component, and iii) texture distribution parameters. Parameter-expanded expectation-maximization (PX-EM) algorithms are developed to compute the ML estimates of the unknown parameters. We also derived the Cramer-Rao bounds (CRBs) and related bounds for these parameters. We first derive general CRB expressions under an arbitrary texture model then simplify them for specific texture distributions. We consider the widely used gamma texture model, and propose an inverse-gamma texture model, leading to a complex multivariate t clutter distribution and closed-form expressions of the CRB. We study the performance of the proposed methods via numerical simulations

Statistical modeling of polarimetric SAR data: a survey and challenges

Knowledge of the exact statistical properties of the signal plays an important role in the applications of Polarimetric Synthetic Aperture Radar (PolSAR) data. In the last three decades, a considerable research effort has been devoted to finding accurate statistical models for PolSAR data, and a number of distributions have been proposed. In order to see the differences of various models and to make a comparison among them, a survey is provided in this paper. Texture models, which could capture the non-Gaussian behavior observed in high resolution data, and yet keep a compact mathematical form, are mainly explained. Probability density functions for the single look data and the multilook data are reviewed, as well as the advantages and applicable context of those models. As a summary, challenges in the area of statistical analysis of PolSAR data are also discussed.Peer ReviewedPostprint (published version

Biologically Inspired Sensing and MIMO Radar Array Processing

The contributions of this dissertation are in the fields of biologically inspired sensing and multi-input multi-output: MIMO) radar array processing. In our research on biologically inspired sensing, we focus on the mechanically coupled ears of the female Ormia ochracea. Despite the small distance between its ears, the Ormia has a remarkable localization ability. We statistically analyze the localization accuracy of the Ormia\u27s coupled ears, and illustrate the improvement in the localization performance due to the mechanical coupling. Inspired by the Ormia\u27s ears, we analytically design coupled small-sized antenna arrays with high localization accuracy and radiation performance. Such arrays are essential for sensing systems in military and civil applications, which are confined to small spaces. We quantitatively demonstrate the improvement in the antenna array\u27s radiation and localization performance due to the biologically inspired coupling. On MIMO radar, we first propose a statistical target detection method in the presence of realistic clutter. We use a compound-Gaussian distribution to model the heavy tailed characteristics of sea and foliage clutter. We show that MIMO radars are useful to discriminate a target from clutter using the spatial diversity of the illuminated area, and hence MIMO radar outperforms conventional phased-array radar in terms of target-detection capability. Next, we develop a robust target detector for MIMO radar in the presence of a phase synchronization mismatch between transmitter and receiver pairs. Such mismatch often occurs due to imperfect knowledge of the locations as well as local oscillator characteristics of the antennas, but this fact has been ignored by most researchers. Considering such errors, we demonstrate the degradation in detection performance. Finally, we analyze the sensitivity of MIMO radar target detection to changes in the cross-correlation levels: CCLs) of the received signals. Prior research about MIMO radar assumes orthogonality among the received signals for all delay and Doppler pairs. However, due to the use of antennas which are widely separated in space, it is impossible to maintain this orthogonality in practice. We develop a target-detection method considering the non-orthogonality of the received data. In contrast to the common assumption, we observe that the effect of non-orthogonality is significant on detection performance