Inverse Gaussian Texture Research Articles

Mixture texture model with weighted generalized inverse Gaussian distribution for target detection

With the improvement of radar resolution, the amplitude distribution of sea clutter has begun to exhibit significant heavy-tailed characteristics. Existing models for sea clutter amplitude distribution do not sufficiently solve this problem, which results in a diminished target detection probability in two-step generalized likelihood ratio test (GLRT) based target detectors. To address this issue and to enhance the radar target detection capabilities, we propose a new compound-Gaussian clutter model based on a weighted mixture of generalized inverse Gaussian distributions to model the texture. The CG-WGIG model demonstrates greater flexibility and effectively captures the characteristics of sea clutter amplitude distributions with heavy tails, thus affording a better fit. We combine this model with the two-step GLRT criterion to propose a GLRT detector endowed with a weighted generalized inverse Gaussian texture (GLRT-WGIG), specifically tailored for detecting range-spread targets (RSTs). We have conducted a rigorous mathematical proof to demonstrate that the constant false alarm rate (CFAR) characteristic of the proposed GLRT-WGIG detector is independent of the covariance matrix, thereby ensuring its robustness in various operational scenarios. Using measured data, we demonstrate that the proposed model and detector are flexible and outperform the existing methods in terms of fitting and detection performance, where we obtain a mean 12.02% MSE of fitting performance promotion.

Persymmetric adaptive subspace detection in compound Gaussian sea clutter with generalized inverse Gaussian texture

This paper considers the detection problem of subspace targets in compound Gaussian sea clutter with generalized inverse Gaussian (GIG) texture. Based on the Wald test, the gradient test, and the Durbin test, we propose three novel subspace detectors. And the criterion above are first applied to the detection problem in compound Gaussian (CG) sea clutter with GIG texture. In the first step, assuming that the speckle covariance matrix (CM) and the texture component are unknown to obtain the test statistics of the proposed detectors. In the second step, we exploit the persymmetric property of speckle CM and the maximum a posteriori (MAP) criterion to obtain the estimation of speckle CM and the GIG texture parameters. Moreover, the constant false alarm rate (CFAR) properties of the three proposed detectors have been proven with respect to the speckle CM and the scale parameter of the texture component. We verify the detection performance of the three proposed detectors by the numerical experiments both in simulated data and real sea clutter data, and the simulated results show the proposed detectors are robust in the case of limited training and mismatched signals.

Optimum and Near-Optimum Coherent CFAR Detection of Radar Targets in Compound-Gaussian Clutter With Generalized Inverse Gaussian Texture

In this article, we propose optimum and near-optimum adaptive coherent detectors of radar targets in compound-Gaussian clutter with generalized inverse Gaussian texture (CG-GIG clutter). The target amplitude and the speckle covariance matrix are modeled as unknown quantities to be estimated. On the basis of the two-step generalized likelihood ratio test (GLRT) and the estimate of the speckle covariance matrix, the optimum coherent detector and its adaptive version are designed in this article. It is demonstrated that the proposed optimum coherent detector contains three common detectors, which are the optimum K detector, the generalized likelihood ratio test linear-threshold detector (GLRT-LTD), and the GLRT detector for compound-Gaussian clutter with inverse Gaussian texture. Due to the existence of the modified Bessel function depending on data, the optimum coherent detector is computationally unrealizable. Therefore, a near-optimum coherent detector with a new structure named $\alpha$ matched filter ($\alpha$-MF) detector and its adaptive version are proposed, which decreases the computational cost. The proposed near-optimum coherent detector contains two common detectors, the GLRT-LTD and the $\alpha$-MF detector in K-distributed clutter, and has a comparable detection performance of the near-optimum detector in compound-Gaussian clutter with inverse Gaussian texture, which was proposed before. Theoretical analysis and numerical experiments illustrate that the proposed two detectors for CG-GIG clutter have the constant false alarm ratio property relative to the estimate of the speckle covariance matrix and the Doppler steering vector. Moreover, the detection performance of the two coherent detectors are evaluated by the simulated and real data.

Polarimetric Target Detection in Compound Gaussian Sea Clutter With Inverse Gaussian Texture

This letter addresses the polarimetric target detection problem in compound Gaussian sea clutter. In view of the heavy-tailed characteristic of sea clutter, we model the sea clutter as compound Gaussian distribution with inverse Gaussian texture (IGCG). We propose three polarimetric compound Gaussian detectors based on the two-step Rao test, the Wald test, and the generalized likelihood ratio test (GLRT). Specifically, we assume that the polarimetric clutter covariance matrix (PCCM) and the inverse Gaussian textures are known in the first step, and the test statistics of the proposed polarimetric detectors are derived. In the second step, we use the training data to estimate PCCM and maximum <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> (MAP) to estimate the inverse Gaussian textures, and we obtain the fully adaptive detectors. Then, we give proof of the constant false alarm rate (CFAR) properties of the proposed detectors. We validate the performance of the proposed polarimetric detectors by conducting experiments based on simulated and real sea clutter data. Finally, the numerical results indicate that the proposed detectors exhibit better detection performance than their competitors and are robust when the mismatched signal occurs.

Persymmetric Range-Spread Targets Detection in Compound Gaussian Sea Clutter With Inverse Gaussian Texture

This letter addresses the persymmetric adaptive detection problem of range-spread targets in compound Gaussian sea clutter. Based on the generalized likelihood ratio test (GLRT), Rao test, and Wald test, three novel compound Gaussian detectors are developed. Specifically, the sea clutter is modeled as compound Gaussian with inverse Gaussian distribution, and the detectors are derived by the two-step maximum <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posterior</i> (MAP) procedures. In the first step, we assume the clutter covariance matrix (CCM) and the inverse Gaussian texture are known and derive the proposed detectors’ test statistics. In the second step, we use the persymmetric property and MAP criterion to estimate the CCM and inverse Gaussian texture parameters. Then the proposed detectors are proved to be constant false alarm rate (CFAR) detectors with respect to the real CCM. The simulation experiments are conducted by comparing the proposed detectors with their counterparts on both synthetic data and real sea clutter data. The numerical results indicate that the novel detectors exhibit better detection performance than their competitors.

GLRT-Based Polarimetric Detection in Compound-Gaussian Sea Clutter With Inverse-Gaussian Texture

This letter presents the derivation of the generalized likelihood ratio test (GLRT)-based polarimetric detector in the non-Gaussian clutter. We model the non-Gaussian sea clutter as compound-Gaussian distribution with inverse-Gaussian texture (IG-CG), which has better goodness-of-fit for the high-resolution sea clutter. Based on the two-step GLRT criterion, we develop the test statistic of the proposed detector by assuming the texture component is known in the first step. In the second step, with the texture of the secondary data estimated as the power of the clutter, we insert the maximum <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> estimate (MAPE) of the texture of the primary data into the test statistic to achieve the fully adaptive detection. Furthermore, the model-based polarimetric detector, which exploits the independence between the co-polarized and the cross-polarized component, is derived. Finally, we conduct experiments with simulated clutter and real sea clutter to evaluate the performance of the proposed detector. The simulation results verify that the proposed detectors have better detection performance and the MAPE under different hypotheses leads to different levels of robustness to the mismatched signal.

Adaptive CFAR Detectors for Mismatched Signal in Compound Gaussian Sea Clutter With Inverse Gaussian Texture

This letter deals with the adaptive detection problem in compound Gaussian sea clutter with inverse Gaussian texture when the mismatched signal occurs. In order to reject the mismatched signal, we introduce a fictitious signal to the null hypothesis based on the adaptive beamformer orthogonal rejection test (ABORT). We adopt the two-step generalized likelihood ratio test (GLRT) criterion and develop two selective detectors, i.e., the ABORT-like compound Gaussian with inverse Gaussian (A-IGCG) detector and ABORT-like maximum <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> (MAP) compound Gaussian with inverse Gaussian (AM-IGCG) detector. Both the proposed detectors are proved to be constant false alarm rate (CFAR) detectors. The several experiments that compare the proposed detectors with other selective detectors and compound Gaussian detectors are conducted by using two types of real sea data, i.e., IPIX 1998 and 2019 real sea data. The numerical results indicate that the novel detectors exhibit significant tradeoffs between performances of detection and selectivity property.

Knowledge-based target detection in compound Gaussian clutter with inverse Gaussian texture

This paper addresses the problem of adaptive detection of radar targets embedded in heterogeneous compound-Gaussian clutter environments. Based on the Bayesian theory, a priori knowledge of clutter is utilized to improve detection performance. The clutter texture is modeled by the inverse Gaussian distribution to describe the heavy-tailed clutter. Furthermore, clutter's heterogeneity results in insufficient secondary data, and the inverse complex Wishart distribution is exploited to model the speckle covariance matrix. Based on a priori distributions of clutter, a novel detector without using secondary data is derived via the generalized likelihood ratio test (GLRT). Monte Carlo experiments are performed to evaluate the detection performance of the proposed detector. Experimental results illustrate that the proposed detector outperforms its competitors in scenarios with limited secondary data.

Adaptive target detection against spatially correlated compound‐Gaussian clutter with multivariate inverse Gaussian texture

To improve the detection performance in the presence of target-steering vector mismatches, a novel robust adaptive matched filter (AMF) detector for compound Gaussian clutter is proposed. First, the multivariate inverse Gaussian distribution is first introduced to compound Gaussian clutter model. Second, the texture value is estimated with maximum a posteriori (MAP) estimator in spatial domain, which has a closed form and is not affected by the target's steering vector mismatch. A robust AMF detector is derived based on this estimation. Simulation results demonstrate that the proposed detector can achieve better performance in the presence of target-steering vector mismatches.

Near-optimum coherent CFAR detection of radar targets in compound-Gaussian clutter with inverse Gaussian texture

This paper studies the design of efficient detector for radar targets in compound-Gaussian clutter with inverse Gaussian texture (CG-IG clutter). Due to inclusion of the modified Bessel function, the optimum coherent detector in CG-IG clutter cannot be easily implemented in radar systems. Through deriving the mathematical relationship between the shape parameters of the K and CG-IG distributions, the efficient α matched filter (α-MF) detector in K-distributed clutter, is improved to realize the near-optimum detection with real-time and fast implementation in CG-IG clutter. The control parameter α in CG-IG clutter is calculated by a new formula. The constant false alarm rate (CFAR) property of α-MF and adaptive α-MF (α-AMF) is proved in CG-IG clutter. Numerical results indicate that the α-AMF CFAR detector has almost the same detection performance as the adaptive optimum detector and outperforms the adaptive MF (AMF) and adaptive normalized MF (ANMF) in CG-IG clutter.

Adaptive subspace detection of range-spread target in compound Gaussian clutter with inverse Gaussian texture

In this paper, we investigate the adaptive subspace detection of range-spread target embedded in compound Gaussian clutter. The inverse Gaussian distribution is considered to describe the texture of the clutter in order to match the non-Gaussian characteristic of sea clutter. Moreover, the range-spread target's energy is assumed to be spread not only in range dimension but also in Doppler dimension, which is more suitable for the practical situation. Thus, the range-spread target is modeled as a subspace signal which describes the range-spread and Doppler-spread. In this paper, an adaptive detector for a subspace range-spread target is derived by using two-step generalized likelihood ratio test (GLRT). Finally, the detection performance of the proposed detector is verified by experiments based on measured data and simulation data. The experimental results show that the detection performance of the proposed detector is better than that of the existing detectors.

Closed‐form estimators of CGIG distributed parameters

The interpolation method has been employed in non-integer-order moments estimators obtained in a previous work for the parameters of compound-Gaussian clutter model with inverse Gaussian texture (CGIG). Closed-form parameter estimators for the CGIG distributed clutter are derived with no special functions. These are achieved after a simple combination of three basic expressions: non-integer positive moments, non-integer negative moments and Bessel recurrence relation. Simulation results show that the derived estimators are well suited for multilook data and have a comparable accuracy as well as the numerically solved maximum-likelihood approach, but they are much simpler and faster to compute

Iterative Maximum Likelihood and Outlier-robust Bipercentile Estimation of Parameters of Compound-Gaussian Clutter With Inverse Gaussian Texture

Compound-Gaussian model with the inverse Gaussian texture (IG–CG) is recognized to be one of the best models to characterize high-resolution sea clutter at low grazing angles. The model parameters are often estimated by the second- and fourth-order amplitude sample moments, which are of low precision and easily interfered by outliers of high power such as returns of ships and reefs and sea spikes. In this letter, an iterative maximum likelihood (ML) estimator and an outlier-robust bipercentile estimator are proposed and are compared with the moment-based estimator. The experimental results show that the iterative ML estimator is better in performance than the moment-based estimator when samples are without outliers and the bipercentile estimator behaves better when samples contain a small number of outliers.

Low‐order moment‐based estimation of shape parameter of CGIG clutter model

In this Letter, a low-order moment-based estimation of the parameters of compound-Gaussian clutter model with the inverse Gaussian texture (CGIG) is proposed. The CGIG clutter model proposed recently was known as an effective model to describe high-resolution sea clutter at low grazing angles. Its parameter estimation is often obtained by the explicit moment-based estimation using the second- and fourth-order moments, which is low precision in the case of small samples. Here, the first- and second-order moments are used to construct a higher precision estimator, where the look-up table method is employed to make up the lack of explicit expression of the shape parameter.

Adaptive detection of range-spread targets in compound Gaussian clutter with the square root of inverse Gaussian texture

The compound Gaussian clutter with the square root of inverse Gaussian texture component has been successfully used for modeling the heavy-tailed non-Gaussian clutter measured by high-resolution radars. In high-resolution radars, the targets may extend along multiple consecutive range cells, which are called range-spread targets. In this paper, we consider the range-spread target detection problem in the compound Gaussian clutter with the square root of inverse Gaussian texture. Three adaptive detectors are proposed based on Bayesian one-step generalized likelihood ratio test, maximum a posteriori generalized likelihood ratio test and Bayesian two-step generalized likelihood ratio test, respectively. Finally, the detection performances of the proposed detectors are evaluated by the Monte Carlo simulation. The simulation results show that the proposed detectors have better detection performance of range-spread target than the conventional generalized likelihood ratio test detector.

ADAPTIVE DETECTION IN COMPOUND-GAUSSIAN CLUTTER WITH INVERSE GAUSSIAN TEXTURE

This paper mainly deals with the problem of target detection in the presence of Compound-Gaussian (CG) clutter with the Inverse Gaussian (IG) texture and the unknown Power Spectral Density (PSD). The traditional CG distributions, in particular the K distribution and the complex multivariate t distribution, are widely used for modeling the real clutter data from the High-Resolution (HR) radars. Recently, the novel CG distribution with the IG texture is described as the IG-CG distribution and validated to provide the better flt with the recorded data of the HR clutter than the mentioned two competitors. Within the IG-CG framework, the detector is flrstly proposed here in terms of the two-step Generalized Likelihood Ratio Test (GLRT) criterion, and the empirical estimation method is resorted to estimate the unknown PSD in order to adapt the realistic scenario. The proposed detector is tested on the real-life HR clutter data, in comparison with the Adaptive Normalized Matched Filter (ANMF) processor, and the detection results illustrate that it outperforms the ANMF.

Compound-Gaussian Clutter Modeling With an Inverse Gaussian Texture Distribution

The compound-Gaussian (CG) distributions have been successfully used for modelling the non-Gaussian clutter measured by high-resolution radars. Within the CG class, the complex K -distribution and the complex t-distribution have been used for modelling sea clutter which is often heavy-tailed or spiky in nature. In this paper, a heavy-tailed CG model with an inverse Gaussian texture distribution is proposed and its distributional properties such as closed-form expressions for its probability density function (p.d.f.) as well as its amplitude p.d.f., amplitude cumulative distribution function and its kurtosis parameter are derived. Experimental validation of its usefulness for modelling measured real-world radar lake-clutter is provided where it is shown to yield better fits than its widely used competitors.