Convolutional neural networks have shown remarkable performance in recent years on various computer vision problems. However, the traditional convolutional neural network architecture lacks a critical property: shift equivariance and invariance, broken by downsampling and upsampling operations. Although data augmentation techniques can help the model learn the latter property empirically, a consistent and systematic way to achieve this goal is by designing downsampling and upsampling layers that theoretically guarantee these properties by construction. Adaptive Polyphase Sampling (APS) introduced the cornerstone for shift invariance, later extended to shift equivariance with Learnable Polyphase up/downsampling (LPS) applied to real-valued neural networks. In this paper, we extend the work on LPS to complex-valued neural networks both from a theoretical perspective and with a novel building block of a projection layer from C to R before the Gumbel Soft-max. We finally evaluate this extension on several computer vision problems, specifically for either the invariance property in classification tasks or the equivariance property in both reconstruction and semantic segmentation problems, using polarimetric Synthetic Aperture Radar images.

This paper presents a novel approach to radar target detection using Variational AutoEncoders (VAEs). Known for their ability to learn complex distributions and identify out-of-distribution samples, the proposed VAE architecture effectively distinguishes radar targets from various noise types, including correlated Gaussian and compound Gaussian clutter, often combined with additive white Gaussian thermal noise. Simulation results demonstrate that the proposed VAE outperforms classical adaptive detectors such as the Matched Filter and the Normalized Matched Filter, especially in challenging noise conditions, highlighting its robustness and adaptability in radar applications.

Complex-valued neural networks (CVNN) have attracted increasing attention in recent years, although their definition dates back to the mid-20th century. Indeed, several domains naturally process complex-valued signals, such as when sensing involves the response to an electromagnetic wave, such as remote sensing, MRI, etc. These domains would benefit from breakthroughs in complex-valued neural networks (CVNNs). We believe independent contributions to CVNNs must be gathered in a single, easy-to-use library. torchcvnn is an effort in that direction and provides several complex-valued building blocks, allowing us to experiment with CVNNs easily. The library is available at https://github.com/torchcvnn/torchcvnn alongside examples available at https://github.com/torchcvnn/examples.

The increased availability of SAR data has raised a growing interest in applying deep learning algorithms. However, the limited availability of labeled data poses a significant challenge for supervised training. This article introduces a new method for classifying SAR data with minimal labeled images. The method is based on a feature extractor Vit trained with contrastive learning. It is trained on a dataset completely different from the one on which classification is made. The effectiveness of the method is assessed through 2D visualization using t-SNE for qualitative evaluation and k-NN classification with a small number of labeled data for quantitative evaluation. Notably, our results outperform a k-NN on data processed with PCA and a ResNet-34 specifically trained for the task, achieving a 95.9% accuracy on the MSTAR dataset with just ten labeled images per class.

In the state-of-the-art, the Probability of False Alarm (PFA)- threshold relationship for the popular Matched Filter (MF) is often derived assuming that unknown non-linear parameters lie on a grid. However, these parameters vary continuously in practice. This is known as the off-grid case. In this article, an asymptotic PFA-threshold relationship for the popular Matched Filter is derived in the off-grid case under complex white Gaussian noise hypothesis using expected Euler characteristics. This asymptotic relationship fits very well with corresponding Monte-Carlo trials in the moderate to low PFAregime.

This article analyzes a kernel-based transfer learning method, under a k-class Gaussian mixture model for the input data. Following recent advances in random matrix theory, we propose new insights in transfer learning schemes for challenging cases, when the first-order statistics of all data classes coincide. The article proves the asymptotic normality of the LS-SVM decision function for any smooth kernel function. As a result, an optimization scheme is proposed to minimize the classification error rate. Our theoretical results are corroborated through simulations and then successfully applied to the context of transfer learning for PolSAR image classification.

Anomaly detection in Synthetic Aperture Radar (SAR) images is an important topic. However, the task is challenging due to the scarcity of anomalous samples and the lack of annotated data, which has led most algorithms in this field to be unsupervised. To address the issue, this article proposes a new loss that adds prior information. One of the main functions of an autoencoder is to reconstruct the input data as accurately as possible after encoding them in a latent vector. The proposed loss function guides the network using the Reed-Xiaoli (RX) detector and replaces any pixels in the input data deemed too abnormal with normal surrounding values. This approach incorporates a priori information in addition to the assumption that anomalies are largely under-represented compared to the rest of the image. An ablation study demonstrates that the proposed loss function improves detection performance.

This paper presents a new classification framework for both first and second order statistics, i.e. mean/location and covariance matrix. In the last decade, several covariance matrix classification algorithms have been proposed. They often leverage the Riemannian geometry of symmetric positive definite matrices (SPD) with its affine invariant metric and have shown strong performance in many applications. However, their underlying statistical model assumes a zero mean hypothesis. In practice, it is often estimated and then removed in a preprocessing step. This is of course damaging for applications where the mean is a discriminative feature. Unfortunately, the distance associated to the affine invariant metric for both mean and covariance matrix remains unknown. Leveraging previous works on geodesic triangles, we propose two affine invariant divergences that use both statistics. Then, we derive an algorithm to compute the associated Riemannian centers of mass. Finally, a divergence based Nearest centroid, applied on the crop classification dataset Breizhcrops, shows the interest of the proposed framework.

Off-grid targets are known to induce a mismatch that dramatically impacts the detection probability of the popular Normalized Matched Filter. To overcome this problem, the unknown target parameter is usually estimated through a Maximum Likelihood strategy resulting in a GLRT detection scheme. While the test statistic for the null hypothesis is well known in the on-grid case, the off-grid scenario is more involved and, to the best of our knowledge, no such theoretical result is available. This paper fills this gap by proposing such an expression under circular compound Gaussian noise with known covariance matrix thanks to a geometrical approach.

In this paper, we investigated the semantic segmentation of Polarimetric Synthetic Aperture Radar (PolSAR) using Complex-Valued Neural Network (CVNN). Although the use of the coherency matrix is ubiquitous as the input of CVNN [1]–[7], Pauli vector is also a relevant representation despite the noise. Two equivalent networks Complex-Valued Fully Convolutional Neural Network (CV-FCNN) and Real-Valued Fully Convolutional Neural Network (RV-FCNN), equivalence in terms of trainable parameters, are compared using both Pauli vector and the coherency matrix as the input feature. Experimentation on San Francisco dataset illustrated a better accuracy of CV-FCNN against its real-valued equivalent.

In the context of a growing popularity of Complex-Valued Neural Network (CVNN) for Polarimetric Synthetic Aperture Radar (PoISAR) applications, the input features often play a central role in classification and segmentation tasks. The socalled coherency matrix, widely used in the radar community, might limit the full potential of CVNNs. Particularly, complex-valued Pauli representation contains richer information than the coherency matrix. And the spatial coherent/local summation can also be performed by the first convolutional layers of CVNN. Letting this network learn itself the filters weights will further enhance its performance. In this paper, we propose a Complex-Valued Fully Convolutional Neural Network (CV-FCNN) which directly infers on the Pauli vector representation rather than on the coherency matrix to perform PolSAR image segmentation. The performance of CV-FCNN is then statistically evaluated on Bretigny PolSAR dataset and compared against an equivalent real-valued model.

This paper shows the benefits of using Complex-Valued Neural Network (CVNN) on classification tasks for non-circular complex-valued datasets. Motivated by radar and especially Synthetic Aperture Radar (SAR) applications, we propose a statistical analysis of fully connected feed-forward neural networks performance in the cases where real and imaginary parts of the data are correlated through the non-circular property. In this context, comparisons between CVNNs and their real-valued equivalent models are conducted, showing that CVNNs provide better performance for multiple types of non-circularity. Notably, CVNNs statistically perform less overfitting, higher accuracy and provide shorter confidence intervals than its equivalent Real-Valued Neural Network (RVNN).

We consider the problem of jointly estimating the location and scatter matrix of a Compound Gaussian distribution with unknown deterministic texture parameters. When the location is known, the Maximum Likelihood Estimator (MLE) of the scatter matrix corresponds to Tyler’s M-estimator, which can be computed using fixed point iterations. However, when the location is unknown, the joint estimation problem remains challenging since the associated standard fixed-point procedure to evaluate the solution may often diverge. In this paper, we propose a stable algorithm based on Riemannian optimization for this problem. Finally, numerical simulations show the good performance and usefulness of the proposed algorithm.

The Doppler frequency signature and the cadence frequency of a couple of people moving simultaneously into the forest are presented in this paper. A brisk walk and a run have been analyzed in L-band. The results are based on measured data that have been collected by a bistatic radar working in continuous wave (CW). The purpose of the analysis is to assess the reliability of the short-time Fourier transform (STFT) and of the cadence frequency diagram to distinguish two physical activities performed simultaneously in a forested area and recorded at 1 GHz. Obstructing trees and small movements of the undergrowth largely impacted the spectrogram, making it difficult to interpret. Instead, the cadence frequency looks reliable for detecting the two activities and distinguishing them from the surrounding vegetation.

In classical detection framework, the parameter space is usually discretized, so that in reality received parameter dependent signals are never perfectly aligned with the signal model under test: it leads to the off-grid signal mismatch. In a Gaussian adaptive context (i.e. the noise covariance is unknown), Kelly GLRT and AMF detectors are well established techniques that can suffer severe performance degradation in presence of this kind of mismatch. We propose here to use adaptive subspace detectors to solve this issue, a suitable subspace (that coincides with the Discrete Prolate Spheroidal Sequences basis when the signal model is that of sinusoids in noise) is proposed that offers robust performance. The interest lies in the fact that such detectors are really easy to implement and we are able to derive their analytic performance.

This paper presents how the most recent improvements made on covariance matrix estimation and model order selection can be applied to the portfolio optimization problem. Our study is based on the case of the Maximum Variety Portfolio and may be obviously extended to other classical frameworks with analogous results. We focus on the fact that the assets should preferably be classified in homogeneous groups before applying the proposed methodology which is to whiten the data before estimating the covariance matrix using the robust Tyler M-estimator and the Random Matrix Theory (RMT). The proposed procedure is applied and compared to standard techniques on real market data showing promising improvements.

The Doppler frequency signature of a man walking into the forest is presented in this paper. The results are based on measured data that have been collected by a bistatic radar working in continuous wave (CW) in the UHF-band. VV and HH polarizations have been employed for our study. The spectrograms have been generated at 1 GHz and 435 MHz by using a Short-Time Fourier Transform (STFT). The purpose of the analysis is to highlight the impact of both the chosen frequencies and the VV and HH polarizations on the Doppler spectrum of a target moving in a cluttered environment. The Doppler signal has been detected at both used frequencies, but it has appeared strongly fragmented by using the VV polarization nevertheless. The HH polarization instead has proved to be more efficient in detecting the Doppler return of the subject moving around the obstructing trees.

A new lower bound is proposed in this article. Like Levenshtein bound, it relates to the maximum correlation value (autocorrelation and cross-correlation) a set of sequences can achieve. The novelty introduced here is that each sequence is associated with a mismatched filter. The proposed bound is inspired from Levenshtein's, holds for any set of unimodular sequences and can be applied in both aperiodic and periodic cases. It appears that the obtained expression does not deviate a lot from the (matched) Levenshtein, which indicates that the use of a mismatched filter will not guarantee much better sidelobe performance, as the number fo sequences is significant, contrary to the popular belief.

A growing problem in the remote sensing community concerns the estimation of change-points in a time series of Synthetic Aperture Radar (SAR) images. Although the methodologies of change-point estimation have already been investigated in the literature, there are, to the best of our knowledge, no study on the expected performance for the estimation of change-points in a Wishart distributed time series. This is mainly due to the fact that few results exist on change-point estimation performance in the mathematical literature: the classical central limit theorem does not apply and the classical Cramer-Rao Bound does not exist due to the discrete nature of the parameters. To fill this gap, this paper proposes to use a lower-bound on the Mean Square Error (MSE) with fewer regularity conditions. To this end, recent works on hybrid Cramer-Rao/Weiss-Weinstein bound have been adapted to the specific SAR problematic of interest. Since estimation strategies usually rely on a set of parameters which have to be set by the user, we show how the proposed lower bound allows performing an appropriate tuning. Moreover, the proposed bound is computationally efficient which enables an extensive analysis without a high computational cost.

A preliminary Doppler analysis on a man walking in free space at 1 GHz is presented in this paper. Firstly, the back-scattered response of the moving target has been provided by a simulation tool based on physical optics (PO) theory. Then, a short-time Fourier transform (STFT), a reassignment spectrogram (RE-Spect) and a Wigner-Ville distribution (WVD) have been employed to the data, in order to characterize the micro-Doppler signature of the walking human body. The results are based entirely on numerical tests. The investigation on the time variations of the Doppler spectrum of moving targets at lower frequencies is of interest for the emerging radar applications devoted to the detection and tracking of people in highly cluttered environment.

This paper considers the problem of detecting changes in multivariate Synthetic Aperture Radar image time series. Classical methodologies based on covariance matrix analysis are usually built upon the Gaussian assumption, as well as an unstructured signal model. Both of these hypotheses may be inaccurate for high-dimension/resolution images, where the noise can be heterogeneous (non-Gaussian) and where all channels are not always informative (low-rank structure). In this paper, we tackle these two issues by proposing a new detector assuming a robust low-rank model. Analysis of the proposed method on a UAVSAR dataset shows promising results.

Given a target prior information, our goal is to propose a method for automatically separating targets of interests from the background in hyperspectral imagery. More precisely, we regard the given hyperspectral image (HSI) as being made up of the sum of low-rank background HSI and a sparse target HSI that contains the targets based on a prelearned target dictionary constructed from some online spectral libraries. Based on the proposed method, two strategies are briefly outlined and evaluated to realize the target detection on both synthetic and real experiments.

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.

In this paper, we propose a method for separating known targets of interests from the background in hyperspectral imagery. More precisely, we regard the given hyperspectral image (HSI) as being made up of the sum of low-rank background HSI and a sparse target HSI that contains the known targets based on a pre-learned target dictionary specified by the user. Based on the proposed method, two strategies are outlined and evaluated independently to realize the target detection on both synthetic and real experiments.

In this paper, we propose new detectors for Change Detection between two multivariate images. The data is supposed to fol-Iowa Compound Gaussian distribution. By using Likelihood Ratio Test (LRT) and Generalised LRT (GLRT) approaches, we derive our detectors. The CFAR behaviour has been studied and the simulations show that they outperform the classic Gaussian Detector when the data is highly heterogeneous.

This paper presents a new algorithm to estimate the number of sources embedded in a correlated Complex Elliptically Distributed (CES) noise in the context of large dimensional regime. The proposed method is a two-steps ones: first the data covariance matrix is estimated with a robust and consistent estimator exploiting the Toeplitz structure assumption of the true scatter matrix. Then, after whitening the signal thanks to the first estimator, the distribution of its Tyler estimator eigenvalues is studied, as in [1]. This allows to derive a threshold, estimated thanks to the Marchenko-Pastur law, to separate the eigenvalues corresponding to the noise and those corresponding to the sources. The number of sources can therefore be deduced. The proposed method is compared to classical ones as the Akaike Information Criterion (AIC) or other algorithms recently developed.

In this paper, a simultaneous sparsity representation-based binary hypothesis (S-SRBBH) model for target detection in hyperspectral image (HSI) is proposed. The S-SRBBH exploits the interpixel correlation within neighboring pixels in HSI, and then, each test pixel is represented by only the background dictionary (Ab) under null hypothesis or from the union of Aband target dictionary (At) under alternative hypothesis. Usually, an inner window region (IWR) centered within an outer window region (OWR) contribute in constructing Ab. Indeed, the use of IWR has a huge effect on the detection performance since it encloses the targets of interests, but its use requires the information of the size of the targets which is usually hardly available. That is why, this paper also serves to construct Abwithout IWR by exploiting the low-rank and sparse matrix decomposition (LRaSMD) technique to decompose the HSI into low-rank background HSI and sparse target HSI. Then for each test pixel, a concentric window is located on the low-rank background HSI, and all the pixels within the window contribute to form Ab. Two real HSIs are used to demonstrate that S-SRBBH achieves good target detection especially when the LRaSMD technique is exploited to construct Ab.

Usually, in radar imaging, the scatterers are supposed to respond the same way regardless of the angle from which they are viewed and have the same properties within the emitted spectral bandwidth. Nevertheless, new capacities in SAR imaging (large bandwidth, large angular extent) make this assumption obsolete. An original application of the Linear Time-Frequency Distributions (LTFD) in SAR imaging allows to highlight the spectral and angular diversities of these reflectors. This methodology allows to transform a monovariate SAR image onto multivariate SAR image. Robust detection schemes in Gaussian or non-Gaussian background (Adaptive Matched Filter (AMF), Adaptive Normalized Matched Filter (ANMF), Anomaly Kelly Detector) associated with classical or robust Covariance Matrix Estimates (Sample Covariance Matrix (SCM), M-estimators) can then be applied exploiting these diversities. The combined two-methodologies show their very good performance for target detection.

One of the most general and acknowledged models for background statistics characterization is the family of elliptically symmetric distributions. They account for heterogeneity and non-Gaussianity of real data. Today, although nonGaussian models are assumed for background modeling and design of detectors, the parameters estimation is usually performed using classical Gaussian-based estimators. This letter analyzes robust estimation techniques in a nonGaussian environment and highlights their interest as an alternative to classical procedures for target detection purposes. The goal of this letter is to extend well-known detection methodologies to nonGaussian framework, when the statistical mean is nonnull and unknown. Furthermore, a theoretical closed-form expression for false-alarm regulation is derived and the Constant False Alarm Rate property is pursued to allow the detector to be independent of nuisance parameters. The experimental validation is conducted on simulations.

Classical target detection schemes are usually obtained by deriving the likelihood ratio under Gaussian hypothesis and replacing the unknown background parameters by their estimates. In most applications, interference signals are assumed to be Gaussian with zero mean [or with a known mean vector (MV)] and with an unknown covariance matrix (CM). When the MV is unknown, it has to be jointly estimated with the CM. In this paper, adaptive versions of the classical matched filter (MF) and the normalized MF, as well as two versions of the Kelly detector are first derived and then analyzed for the case where the MV of the background is unknown. More precisely, theoretical closed-form expressions for false alarm (FA) regulation are derived and the constant FA rate property is pursued to allow the detector to be independent of nuisance parameters. Finally, the theoretical contributions are validated through simulations.

This paper presents two approaches to derive an asymptotic distribution of the robust Adaptive Normalized Matched Filter (ANMF). More precisely, the ANMF has originally been derived under the assumption of Gaussian distributed noise where the variance is different between the observation under test and the set of secondary data. We propose in this work to relax the Gaussian hypothesis: we analyze the ANMF built with robust estimators, namely the M-estimators and the Tyler's estimator, under the Complex Elliptically Symmetric (CES) distributions framework. In this context, we derive two asymptotic distributions for this robust ANMF. Firstly, we combine the asymptotic properties of the robust estimators and the Gaussian-based distribution of the ANMF at finite distance. Secondly, we directly derive the asymptotic distribution of the robust ANMF. Then, Monte-Carlo simulations show the good approximation provided by the proposed methods. Moreover, for a non-asymptotic regime, the simulations provide very promising results.

Infrastructure monitoring applications can require the tracking of slowly moving points of a certain structure. Given a certain point from a structure to be monitored, in the context of available spaceborne synthetic aperture radar (SAR) products, where the image is already focused in a slant range-azimuth grid, it is not obvious if this point is the scattering center, if it is in layover or if it is visible from the respective orbit. This paper proposes a scattering centers detection and tracking procedure based on refocusing a set of SAR images on a provided high-resolution grid of the structure. The refocusing procedure is designed for high-resolution spotlight and sliding spotlight SAR images and consists of an azimuth defocusing followed by a modified back-projection algorithm on the given set of points. The scattering centers of the refocused image are detected in the 4-D tomography framework by testing if the main response is at zero elevation in the local elevation-velocity spectral distribution obtained using the Capon estimator. The mean displacement velocity is estimated from the peak response on the zero elevation axis, whereas the displacements time series for detected single scatterers is obtained as phase difference of complex amplitudes. The algorithm is tested by simulations with an emphasis on its behavior for a low number of satellite passes and applied on real data acquired with the TerraSAR-X satellite over the Puylaurent dam. The relative displacements between scattering regions show very good agreement with in situ measurements.

The Reed-Xiaoli (RX) is considered as the benchmark algorithm in multidimensional anomaly detection (AD). However, the RX detector performance decreases when the statistical parameters estimation is poor. This could happen when the background is non-homogeneous or the noise independence assumption is not fulfilled. For a better performance, the statistical parameters are estimated locally using a sliding window approach. In this approach, called adaptive RX, a window is centered over the pixel under the test (PUT), so the background mean and covariance statistics are estimated using the data samples lying inside the window's spatial support, named the secondary data. Sometimes, a smaller guard window prevents those pixels close to the PUT to be used, in order to avoid the presence of outliers in the statistical estimation. The size of the window is chosen large enough to ensure the invertibility of the covariance matrix and small enough to justify both spatial and spectral homogeneity. We present here an alternative methodology to select the secondary data for a PUT by means of a binary partition tree (BPT) representation of the image. We test the proposed BPT-based adaptive hyperspectral RX AD algorithm using a real dataset provided by the Target Detection Blind Test project.

Infrastructure monitoring applications can require the tracking of slowly moving points of a certain structure. Given a certain point from a structure to be monitored, in the context of available SAR products where the image is already focused in a slant range - azimuth grid, it is not obvious if this point is the scattering center, if it is in layover or if it is visible from the respective orbit. This paper proposes a scattering center monitoring procedure based on refocusing a set of SAR images on a provided high-resolution DEM of the structure. The scattering centers of the refocused image are detected in the 4-D tomography framework by testing if the main response is at zero elevation in the local elevation-velocity spectral distribution obtained using the Capon estimator. The algorithm is validated on real data acquired with the TerraSAR-X satellite over the Puylaurent water dam in France during March-June 2012. The relative displacements between scattering regions show very good agreement with the in situ measurements.

This paper deals with the energetic analysis of non-stationary scatterers in High-Resolution laboratory radar imaging. A method based on the well-known Multi-Dimensional Time-Frequency Analysis is proposed to extract marginal densities and highlights the frequency and angle (azimuth) signatures associated to a scatterer. Then, basic statistics are processed to characterize the frequency and/or aspect angle signatures. All in all, the efficiency of this technique is demonstrated, in an anechoic chamber experiment. On the one hand, statistics are linked to target characteristics, on the other hand the experiment shows the meaning of parameters and the efficiency of statistics can be discussed.

Anomaly Detection methods are used when there is not enough information about the target to detect. These methods search for pixels in the image with spectral characteristics that differ from the background. The most widespread detection test, the RX-detector, is based on the Mahalanobis distance and on the background statistical characterization through the mean vector and the covariance matrix. Although non-Gaussian distributions have already been introduced for background modeling in Hyperspectral Imaging, the parameters estimation is still performed using the Maximum Likelihood Estimates for Gaussian distribution. This paper describes robust estimation procedures more suitable for non-Gaussian environment. Therefore, they can be used as plug-in estimators for the RX-detector leading to some great improvement in the detection process. This theoretical improvement has been evidenced over two real hyperspectral images.

Recently, a general approach for high-resolution polarimetric SAR (POLSAR) data classification in heterogeneous clutter was presented, based on a statistical test of equality of covariance matrices. Here, we extend that approach by taking advantage of the Constant False Alarm Ratio (CFAR) property of the statistical test in order to improve the clustering process. We show that the CFAR property can be used in the hierarchical segmentation of the POLSAR data images to automatically detect the number of clusters. The proposed method will be applied on a high-resolution polarimetric data set acquired by the ONERA RAMSES system.

When accounting for heterogeneity and non-Gaussianity of real hyperspectral data, elliptical distributions provide reliable models for background characterization. Through these assumptions, this paper highlights the fact that robust estimation procedures are an interesting alternative to classical methods and can bring some great improvement to the detection process. The goal of this paper is then not only to recall well-known methodologies of target detection but also to propose ways to extend them for taking into account the heterogeneity and non-Gaussianity of the hyperspectral images.

This paper provides comprehensive analysis of the dry snow pack backscattering coefficient dependence on the density change, for various SAR sensor parameters and chosen dry snow pack parameters, characteristic for the region of French Alps. As the result, qualitative conclusions, based on applying fundamental scattering theories (Rayleigh scattering model, Quasi Crystalline Approximation, Integral Equation Model) on the particular distributed target are presented. They represent the ground for semi-empirical models, which may provide a satisfactory link between backscattering coefficient and snow density (as one of the quantities defining SWE), as well as the guidelines for the further radar acquisitions over the Alpine region in France.

This paper proposes the new method for wet snow mapping using SAR data. It represents a modified version of the existing Nagler's mapping method, based on winter/summer image comparison, which is considered as the classic one. Instead of the existing unique threshold, a variable threshold matrix (function of the local incidence angle for each pixel) is proposed, based on dry and wet snow backscattering simulation results. The new membership decision method (with the respect to the dry/snow classes) is introduced. It considers the intensity ratio as a stochastical process: the probability that “the intensity ratio is smaller than the corresponding dry/wet snow determined threshold” is larger than the desired confidence level.

When dealing with impulsive background echoes, Gaussian model is no longer pertinent. We study in this paper the class of elliptically contoured (EC) distributions. They provide a multivariate location-scatter family of distributions that primarily serve as long tailed alternatives to the multivariate normal model. They are proven to represent a more accurate characterization of HSI data than models based on the multivariate Gaussian assumption. For data in ℝk, robust proposals for the sample covariance estimate are the M-estimators. We have also analyzed the performance of an adaptive non- Gaussian detector built with these improved estimators. Constant False Alarm Rate (CFAR) is pursued to allow the detector independence of nuisance parameters and false alarm regulation.

We discuss in the paper the use of the Riemannian mean given by the differential geometric tools. This geometric mean is used in this paper for computing the centers of class in the polarimetric H/α unsupervised classification process. We can show that the centers of class will remain more stable during the iteration process, leading to a different interpretation of the H/α/A classification. This technique can be applied both on classical SCM and on Fixed Point covariance matrices. Used jointly with the Fixed Point CM estimate, this technique can give nice results when dealing with high resolution and highly textured polarimetric SAR images classification.

This paper deals with hyperspectral detection in impulsive and/or non homogeneous background contexts. In hyperspectral imaging applications, the detection performance of the detectors (target detection or anomaly detection like Mahalanobis distance) is typically evaluated on Gaussian assumption. However, it is well known that hyperspectral imaging data exhibit spatial heterogeneity and non-Gaussian behavior leading to a poor performance for all the conventional Gaussian detectors. Many works have been already derived in the context of radar detection in non-homogeneous and non-Gaussian clutter. These works can be easily extended in the context of hyperspectral detection. The aim of this pa per is twofold. In the context of Spherically Invariant Random Vectors (SIRV) modeling for the background, we re call some properties of different non-Gaussian detectors built with a nice and robust estimate of the background Covariance Matrix. Secondly, we present some results on regulation of false alarm obtained on experimental background hyper spectral data. These results demonstrate the interest of the proposed detection scheme, and show an excellent correspondence between experimental and theoretical results.

This paper presents a new estimation scheme for optimally deriving clutter parameters with high resolution POLSAR data. The heterogeneous clutter in POLSAR data is described by the Spherically Invariant Random Vectors model. Three parameters are introduced for the high resolution POLSAR data clutter: the span, the normalized texture and the speckle normalized covariance matrix. The asymptotic distribution of the novel span estimator is investigated. A novel heterogeneity test for the POLSAR clutter is also discussed. The proposed method is tested with airborne POLSAR images provided by the ONERA RAMSES system.

This letter presents a new estimation scheme for optimally deriving clutter parameters with high-resolution polarimetric synthetic aperture radar (POLSAR) data. The heterogeneous clutter in POLSAR data is described by the spherically invariant random vector model. Three parameters are introduced for the high-resolution POLSAR data clutter: the span, the normalized texture, and the speckle normalized covariance matrix. The asymptotic distribution of the novel span estimator is investigated. A novel heterogeneity test for the POLSAR clutter is also discussed. The proposed method is tested with airborne POLSAR images provided by the Office National d'Études et de Recherches Aerospatiales Radar Aéroporté Multi-spectral d'Etude des Signatures system.

Previously, the well-known Optimum Gaussian Detector (OGD) has been extended to the Multiple-Input Multiple-Output (MIMO) case where all transmit-receive subarrays are considered jointly as a system such that only one detection threshold is used. In this extension, all subarrays have been assumed to be widely separated and the transmitted waveforms are assumed to be orthogonal. However, the necessary separation needed for each subarray to be uncorrelated depends on several factors and it might not be possible to ensure that this condition is always respected, especially in the case of moving platforms. Moreover, perfectly orthogonal waveforms do not exist. Hence, we consider in this paper, a new robust MIMO detector that is able to maintain the same Probability of False Alarm (Pfa) irregardless of the correlation between the subarrays.

Based on the Kennaugh-Huynen decomposition, the Target Scattering Vector Model (TSVM) allows to extract four roll-invariant parameters. Those parameters are necessary for an unambiguous description of the target scattering mechanism. The proposed method consists in applying the TSVM prior to the GLRT-LQ detector for the detection of any oriented target.

Modern SAR systems have high resolution which leads the backscattering clutter to be non-Gaussian. In order to properly classify images from these systems, a non-Gaussian noise model is considered: the SIRV model. A statistical test of equality of covariance matrices is used to classify pixels, taking into account the critical region of the test which rejects the likeliness of a covariance matrix to any of the class centers. This test is applied on experimental data obtained with the ONERA RAMSES system in X-band. The results show a good separation between natural and man-made areas of the image.

This paper presents a new estimation scheme for optimally deriving clutter parameters with high resolution POLSAR data. The heterogeneous clutter in POLSAR data was described by the Spherically Invariant Random Vectors model. Three parameters were introduced for the high resolution POLSAR data clutter: the span, the normalized texture and the speckle normalized covariance matrix. The asymptotic distribution of the novel span estimator is also investigated. The proposed method is tested with airborne POLSAR images provided by the ONERA RAMSES system.

This paper presents an application of the recent advances in the field of spherically invariant random vector (SIRV) modeling for coherency matrix estimation in heterogeneous clutter. The complete description of the polarimetric synthetic aperture radar (POLSAR) data set is achieved by estimating the span and the normalized coherency independently. The normalized coherency describes the polarimetric diversity, while the span indicates the total received power. The main advantages of the proposed fixed-point (FP) estimator are that it does not require anya prioriinformation about the probability density function of the texture (or span) and that it can directly be applied on adaptive neighborhoods. Interesting results are obtained when coupling this FP estimator with an adaptive spatial support based on the scalar span information. Based on the SIRV model, a new maximum-likelihood distance measure is introduced for unsupervised POLSAR classification. The proposed method is tested with both simulated POLSAR data and airborne POLSAR images provided by the Radar Ae¿roporte¿ Multi-Spectral d'Etude des Signatures system. Results of entropy/alpha/anisotropy decomposition, followed by unsupervised classification, allow discussing the use of the normalized coherency and the span as two separate descriptors of POLSAR data sets.

Reducing the number of secondary data used to estimate the Clutter Covariance Matrix (CCM) for Space Time Adaptive Processing (STAP) techniques is still an active research topic. Low rank CCM estimates have already been proposed but only for homogeneous and Gaussian clutter. We propose in this paper to extend the low-rank CCM methods for heterogeneous and/or non-Gaussian clutter. We derive a new detector based on low-rank techniques and exploiting properties of the Normalized Sample Covariance Matrix (NSCM). This detector is shown to exhibit a smaller SNR loss than classical STAP detectors. Moreover, the new detector has a texture-CFAR property with respect to non-Gaussian SIRV model and has more robust behavior when some targets are present in the secondary data. We also give experimental comparison results between the classical STAP detectors and the new one for STAP data.

In this paper, heterogeneous clutter models are introduced to describe Polarimetric Synthetic Aperture Radar (PolSAR) data. Based on the Spherically Invariant Random Vectors (SIRV) estimation scheme, the scalar texture parameter and the normalized covariance matrix are extracted. If the texture parameter is modeled by a Fisher PDF, the observed target scattering vector follows a KummerU PDF. Then, this PDF is implemented in a hierarchical segmentation algorithm. Segmentation results are shown on high resolution PolSAR data at L and X band.

This paper deals with the analysis of non-stationary scatterers in SAR images. Indeed, SAR imaging makes the assumptions that the scatterers are isotropic and white in the emitted frequency band. However, new SAR applications use a large bandwidth and a strong angular excursion. These assumptions become obsolete and the behavior of scatterers becomes non-stationary. The basic tool to study non-stationary signals is the time-frequency analysis. Recent studies based on multidimensional Time-Frequency Analysis describing the angular and frequency behavior of scatterers has highlighted anisotropic and dispersive behavior of bright points. This paper generalizes the hyperimage concept to study scatterers. Multidimensional Time-Frequency distributions are tested on simulations, then they are applied to very high resolution SAR images and show some scatterers are anisotropic and dispersive.

In radar imaging, the assumption is made that scatterers are white in the emitted frequency band and isotropic for all direction of observation. Nevertheless, new capacities in radar imaging, using a wideband and a large angular excursion, make these hypotheses not valid. Time-frequency analysis highlight this point of view and show some scatterers are anisotropic and/or dispersive. This information source can be completed by radar polarimetry. This paper suggests a supervised classification of scatterers using neural networks based on polarimetric time-frequency signatures. This method is applied here on anechoic chamber data, however can be generalized to SAR or circular SAR imaging.

In the context of non-Gaussian polarimetric clutter models, this paper presents an application of the recent advances in the field of Spherically Invariant Random Vectors (SIRV) modelling for coherency matrix estimation in heterogeneous clutter. The complete description of the POLSAR data set is achieved by estimating the span and the normalized coherency independently. The normalized coherency describes the polarimetric diversity, while the span indicates the total received power. Based on the SIRV model, a new maximum likelihood distance measure is introduced for unsupervised POLSAR segmentation. The proposed method is tested with airborne POLSAR images provided by the RAMSES system.

In the general area of radar detection, estimation of the clutter covariance matrix is an important point. This matrix commonly exhibits a persymmetric structure: this is the case for instance for active systems using a symmetrically spaced linear array or pulse train. In this context, this paper provides a new Gaussian adaptive detector called the persymmetric adaptive matched filter (P-AMF). Its theoretical distribution is derived allowing adjustment of the detection threshold for a given probability of false alarm (PFA). Simulations results highlight the improvement in term of probability of detection (PD) of the P-AMF in comparison with the classical adaptive matched filter (AMF).

This paper presents an application of the recent advances in the field of Spherically Invariant Random Vectors modelling. We propose the use of the Fixed Point (FP) estimator for deriving normalized polarimetric coherency matrices in compound Gaussian clutter. The main advantages of the FP estimator are that it does not require any "a priori" information about the probability density function of the texture and it can be directly applied on adaptive neighborhoods. Interesting results are obtained when coupling this FP estimator with an adaptive spatial support driven on the scalar span information. The proposed method is tested with both simulated POLSAR data and high resolution POLSAR data acquired over the French Alps.

Synthetic Aperture Radar (SAR) images built from received signals are high-resolution maps of the spatial distribution of the reflectivity function of targets. Conventional radar imaging assumes that all the scatterers are considered as bright points (isotropic for all observation angles and white in the frequency band) [1]. Recent studies based on multidimensional Time-Frequency Analysis describe the angular and frequency behavior of scatterers and show that they are anisotropic and dispersive [2]. Another useful information source in radar imaging is the polarimetry Studies based on multidimensional wavelet and coherent decompositions allow to represent the angular and frequency polarimetric behavior and show the non-stationarity of this behavior. The aim is to characterize scatterers by time-frequency analysis and polarimetry.

Under Gaussian assumptions, the sample covariance matrix (SCM) is encountered in many covariance based processing algorithms. In case of impulsive noise, this estimate is no more appropriate. This is the reason why when the noise is modeled by spherically invariant random vectors (SIRV), a natural extension of the SCM is extensively used in the literature: the well-known normalized sample covariance matrix (NSCM), which estimates the covariance of SIRV. Indeed, this estimate gets rid of a fluctuating noise power and is widely used in radar applications. The aim of this paper is to derive closed-form expressions of the first- and second-order moments of the NSCM

This paper presents a detailed theoretical analysis of a recently introduced covariance matrix estimator, called the fixed point estimate (FPE). It plays a significant role in radar detection applications. This estimate is provided by the maximum likelihood estimation (MLE) theory when the non-Gaussian noise is modelled as a spherically invariant random process (SIRP). We study in details its properties: existence, uniqueness, unbiasedness, consistency and asymptotic distribution. We propose also an algorithm for its computation and prove the convergence of this numerical procedure. These results allow us to study the performance analysis of the adaptive CFAR radar detectors (GLRT-LQ, BORD, ...).

In this paper, a theoretical expression of the optimum non-Gaussian radar detector is derived from the non-Gaussian SIRP model (Spherically Invariant Random Process) clutter and a bayesian estimator of the characteristic function of the SIRP. The SIRP model is used to perform coherent detection and to modelize the clutter as a complex Gaussian process whose variance is itself a positive random variable (r.v.). The PDF of the variance characterizes the statistics of the SIRP and after performing a bayesian estimation of this PDF from reference clutter cells we derive the Bayesian Optimum Radar Detector (BORD) and its statistical asymptotic form without any knowledge about the statistics of the clutter. We evaluate BORD performance for an unknown target signal embedded in K-distributed clutter and compare with optimum detectors performance (such as Optimum K Detector - OKD - in K-distributed clutter).

Original methods of radar detection performance analysis are derived for a fluctuating or non-fluctuating target embedded in additive and a priori unknown noise. This kind of noise can be, for example, the sea or ground clutter encountered in surface-sited radar for the detection of a target illuminated at low grazing angles or in high resolution radar. For these cases, the spiky clutter tends to have a statistic which strongly differs from the gaussian assumption. Therefore, the detection theory becomes difficult to perform since the nature of the statistics has to be known. The new methods proposed here are based on the parametric modelisation of the moment generating function of the noise envelope by Pade approximation and lead to a powerful estimation of its probability density function. They allow to evaluate the radar detection performance of a target embedded in any noise without knowledge of the closed form of its statistic and allow in the same way to take into account any possible fluctuation of the target. These methods have been tested successfully on synthetic signals and have been performed on experimental signals such as ground clutter.

In signal analysis, the joint estimation of the time-scale parameters which can affect a known signal (Doppler effect or scale effect, delay...) may be a problem of interest. An important result has shown that, even if the quality of the time delay estimation is classically given by the inverse spread of the signal spectral density, the quality of the scale estimation only depends on the inverse of the signal spread in Mellin space. This spread has a direct interpretation in the time-frequency plane and can be precisely estimated when duration, bandwidth and relative bandwidth of the signal are known. We propose here to develop two methods of optimum signal synthesis which minimize the variance of the estimates given by the Cramer-Rao lower bounds. The first method is based on the stationary phase principle, applied on frequency and Mellin spaces, which allows to construct signals with given autocorrelation functions in scale and time spaces. The second method is devoted to the construction of a frequency phase law depending on the Mellin variable with the spreads in frequency and Mellin spaces related to the expected scale and time-delay resolutions.

The theoretical approach to broadband time-frequency problems has led to consideration of new time-frequency distributions affiliated with the affine group of clock changes. Due to their origin these distributions involve stretched forms of the signals which are not easy to compute by standard techniques. An attempt is made to solve this difficulty by giving efficient algorithms founded on the use of the fast Mellin transform.>

Wavelet analysis is characterized by the constructive intervention of dilations, and dilations in physics are associated with changes of measurement units. This double observation is at the basis of the introduction of the dimensionalized wavelet transform as a technique that allows the adaptation of the representation of dilations to the physical dimension of the field under study. An imaging process can then be built in accordance with the physical meaning required for the description. Lengthy general developments are avoided by illustrating the method with the practical problem of radar (or sonar) imaging of targets.>

Theoretical wideband studies generally provide expressions involving stretched forms of the signal. This feature complicates implementation of the results and suggests the use of a Mellin transform to process dilations efficiently. A tool for the practical development of this idea is given. The definition, properties, and time-frequency interpretation of the relevant Mellin transform are given. The discretization is developed, leading to a form which can run with any FFT (fast Fourier transform) routine. The advantage of the technique is illustrated by computing broadband radar ambiguity functions and affine time-frequency representations.>