Search

This paper studies a statistical model for heteroscedastic (i.e., power fluctuating) signals embedded in white Gaussian noise. Using the Riemannian geometry theory, we propose an unified approach to tackle several problems related to this model. The first axis of contribution concerns parameters (signal subspace and power factors) estimation, for which we derive intrinsic Cramér-Rao bounds and propose a flexible Riemannian optimization algorithmic framework in order to compute the maximum likelihood estimator (as well as other cost functions involving the parameters). Interestingly, the obtained bounds are in closed forms and interpretable in terms of problem’s dimensions and SNR. The second axis of contribution concerns the problem of clustering data assuming a mixture of heteroscedastic signals model, for which we generalize the Euclidean K-means++ to the considered Riemannian parameter space. We propose an application of the resulting clustering algorithm on the Indian Pines segmentation problem benchmark. [ABSTRACT FROM AUTHOR]

This paper proposes a new approximation of the theoretical signal to interference plus noise ratio (SINR) loss of the low-rank (LR) adaptive filter built on the eigenvalue decomposition of the sample covariance matrix. This new result is based on an analysis in the large dimensional regime, i.e., when the size and the number of data tend to infinity at the same rate. Compared to previous works, this new derivation allows us to measure the quality of the adaptive filter near the LR contribution. Moreover, we propose a new LR adaptive filter and we also derive its SINR loss approximation in a large dimensional regime. We validate these results on a jamming application and test their robustness in a multiple input multiple output space time adaptive processing application where the data size is large. [ABSTRACT FROM AUTHOR]

High resolution in synthetic aperture radar (SAR) leads to new physical characterizations of scatterers which are anisotropic and dispersive. These behaviors present an interesting source of diversity for target detection schemes. Unfortunately, such characteristics have been integrated and have been naturally lost in monovariate single-look SAR images. Modeling this behavior as nonstationarity, wavelet analysis has been successful in retrieving this information. However, the sharp-edge of the used wavelet functions introduces undesired high side-lobes for the strong scatterers present in the images. In this paper, a new family of parameterized wavelets, designed specifically to reduce those side lobes in the SAR image decomposition, is proposed. Target detection schemes are then explored using this spectro-angular diversity and it can be shown that in high-resolution SAR images, the non-Gaussian and robust framework leads to better results. [ABSTRACT FROM AUTHOR]

When a possible target is embedded in a low-rank (LR) Gaussian clutter (which is contained in a low-dimensional subspace) plus a white Gaussian noise, the detection process can be performed by applying the LR adaptive normalized matched filter (LR-ANMF), which is a function of the estimated projector. In a recent work, we derived an approximate distribution of the LR-ANMF under the $\mathcal {H}_0$ hypothesis by using a restrictive hypothesis (the target has to be orthogonal to the clutter subspace). In this paper, we propose to determine new approximations of the Pfa and the Pd of the LR-ANMF by relaxing this restrictive hypothesis. This new derivation is based on results concerning the convergence in a large dimension regime of quadratic forms. Simulations validate our result, in particular, when the tested signal is close to the clutter subspace. [ABSTRACT FROM AUTHOR]

We develop in this paper a new adaptive low-rank (LR) filter for MIMO-space time adaptive processing (STAP) application based on a tensorial modeling of the data. This filter is based on an extension of the higher order singular value decomposition (HOSVD) (which is also one possible extension of singular value decomposition to the tensor case), called alternative unfolding HOSVD (AU-HOSVD), which allows us to consider the combinations of dimensions. This property is necessary to keep the advantages of the STAP and the MIMO characteristics of the data. We show that the choice of a good partition (as well as the tensorial modeling) is not heuristic but have to follow several features. Thanks to the derivation of the theoretical formulation of multimode ranks for all partitions, the tensorial LR filters are easy to compute. Results on simulated data show the good performance of the AU-HOSVD LR filters in terms of secondary data and clutter notch. [ABSTRACT FROM AUTHOR]

In this paper, we propose to derive an approximate theoretical distribution under the null hypothesis of the low-rank adaptive normalized matched filter (LR-ANMF). This detector is used to detect a target when the disturbance is composed of a low-rank Gaussian contribution (called clutter) and an additive white Gaussian noise. In the LR-ANMF, the estimated covariance matrix is replaced by the estimated orthogonal projector onto the subspace clutter. The method to derive this distribution is based on perturbation analysis and assumes a steering vector far from the clutter and a large clutter-to-noise ratio. Simulations on a space?time adaptive processing example validate our theoretical result. The impact of both hypotheses is also studied. [ABSTRACT FROM PUBLISHER]

This paper addresses the problem of the clutter subspace projector estimation in the context of a disturbance composed of a low rank heterogeneous (Compound Gaussian) clutter and white Gaussian noise. In such a context, adaptive processing based on an estimated orthogonal projector onto the clutter subspace (instead of an estimated covariance matrix) requires less samples than classical methods. The clutter subspace estimate is usually derived from the eigenvalue decomposition of a covariance matrix estimate. However, it has been previously shown that a direct maximum likelihood estimator of the clutter subspace projector can be obtained for the considered context. In this paper, we derive two algorithms based on the block majorization-minimization framework to reach this estimator. These algorithms are shown to be computationally faster than the state of the art, with guaranteed convergence. Finally, the performance of the related estimators is illustrated on realistic Space Time Adaptive Processing for airborne radar simulations. [ABSTRACT FROM PUBLISHER]

We develop a new synthetic aperture radar (SAR) algorithm based on physical models for the detection of a man-made target (MMT) embedded in strong interferences (trunks of a forest). These physical models for the MMT and the interferences are integrated in low-rank subspaces and are based on scattering and polarimetric properties. Several images, called subspace SAR images, can be generated and combined considering these subspace models. We then propose a new approach for target detection and interference reduction based on the combination of SAR subspace images. We show that our SAR algorithm outperforms the classical SAR imagery algorithm on both simulated data and real data in the context of foliage penetration detection. [ABSTRACT FROM PUBLISHER]

We have developed a new synthetic aperture radar (SAR) algorithm based on physical models for the detection of a man-made target (MMT) embedded in strong clutter (trunks in a forest). The physical models for the MMT and the clutter are represented by low-rank subspaces and are based on scattering and polarimetric properties. Our SAR algorithm applies the oblique projection of the received signal along the clutter subspace onto the target subspace. We compute its statistical performance in terms of probabilities of detection and false alarms. The performances of the proposed SAR algorithm are improved compared to those obtained with existing SAR algorithms: the MMT detection is greatly improved, and the clutter is rejected. We also studied the robustness of our SAR algorithm to interference modeling errors. Results on real foliage penetration data showed the usefulness of this approach. [ABSTRACT FROM AUTHOR]

In a previous work, we have developed a low-rank (LR) spatio-temporal adaptive processing (STAP) filter when the disturbance is modeled as the sum of a low-rank spherically invariant random vector (SIRV) clutter and a zero-mean white Gaussian noise. This LR-STAP filter is built from the normalized sample covariance matrix (NSCM) and exhibits good robustness properties to secondary data contamination by target components. In this correspondence, we derive the bias of the NSCM with this noise model. We show that the eigenvectors estimated from the NSCM are unbiased. The new expressions of the expectation of NSCM eigenvalues are also given. From these results, we also show that the estimate of the clutter subspace projector based on the NSCM used in our LR-STAP is a consistent estimate of the true one. Results on numerical data validates the theoretical approach. [ABSTRACT FROM PUBLISHER]

The detection of a target echo in a sonar image is usually a difficult task since the reverberation, consisting of a large number of spurious echoes, generates a lot of false alarms. In this paper, we propose two new detectors derived from image processing algorithms. These detectors are respectively based on a morphological and a statistical contrast. Each detector only requires setting a few parameters. This setting is done using some prior knowledge about the data (shape of the emitted signal and the used antenna, characteristics of the reverberation). Nevertheless, an extensive statistical study of the detection performances proves that the proposed methods are robust and that even an imprecise setting of the parameters leads to satisfactory results. Applied to the real data, these detectors and their sequential combination lead to a significant improvement on the performances: The false alarm rate is drastically reduced while the detection probability is preserved. Based on different contrasts, these detectors have complementary behaviors. Therefore, a further improvement is achieved by a fusion of the different results to classify the remaining echoes as whether spurious or true detection. [ABSTRACT FROM AUTHOR]

Proposes an algorithm for Principal Component Inverse (PCI) which allows better echo separation. Detection problem in the presence of reverberation; Information on one-dimensional PCI method; Description of the PCI algorithm; Analysis of the reverberation subspace rank.

A new version of the signal subspace detector synthetic aperture radar (SSDSAR) processor developed in [1] is proposed. Actually, the SSDSAR processor can be divided in two different parts: a subspace basis computation part and an imaging part. The new version proposed here consists in performing the imaging part on fast-time compressed data and not raw data in order to reduce the computational cost from O(N^4) to O(N^3). We note that this new processor is the subspace detector version of the classical back projection SAR processor [2]. [ABSTRACT FROM PUBLISHER]

In this paper, we present a new synthetic aperture radar (SAR) processor relying on subspace detectors. The scattering pattern of the constituent element of the man-made target (MMT) to detect is used to improve the detection capabilities. In the particular case of foliage penetration (FOPEN), we propose to reduce the probability of false alarms by considering the scattering pattern of almost vertical trunks (modeled here as dielectric cylinders). New subspace detectors are derived to look for either an interference or a target element in a noisy environment. A new processor based on these subspace detectors is successively applied to simulated data. In addition, results obtained with real data reveal a significant improvement in the detection capabilities both in comparison with a classical SAR processor and with the subspace signal detector SAR (SSDSAR) processor (without interference model). [ABSTRACT FROM PUBLISHER]