This paper deals with batch normalization for SPDnet, a deep learning architecture specifically designed to handle covariance matrices. Current SPDnet batch normalization relies on geometric means, which require expensive iterative computations and lacks formal backpropagation derivations. These limitations are addressed through two contributions: (i) formal backpropagation derivation for SPDnet batch normalization, and (ii) computationally efficient closed-form alternatives to the geometric mean: log-Euclidean, arithmetic and harmonic means, and the geometric mean of arithmetic and harmonic means. Simulation results on the batch normalization layer with different means demonstrate significant reductions in memory consumption and comparable training time by avoiding automatic differentiation, demonstrating the effectiveness of our approach. Numerical experiments on three real datasets show that simpler means can outperform the geometric mean with up to 5% accuracy improvements while reducing training time by a factor of 5.

Multi-Temporal Interferometric Synthetic Aperture Radar (MT-InSAR) exploits Synthetic Aperture Radar images time series (SAR-TS) for surface deformation monitoring via phase difference (with respect to a reference image) estimation. Most of the actual state-of-the-art MT-InSAR rely on temporal covariance matrix of the SAR-TS, assuming Gaussian distribution. However, these approaches become computationally expensive when the time series lengthens and new images are added to the data vector. This paper proposes a novel approach to sequentially integrate each newly acquired image using Phase Linking (PL) and Maximum Likelihood Estimation (MLE). The methodology divides the data into blocks, using previous images and estimations as a prior to sequentially estimate the phase of the new image. Actually, this framework allows to consider non Gaussian distributions, such as a mixture of scaled Gaussian distribution, which is particularly important to consider when dealing with urban areas.

Traditional Phase-Linking (PL) algorithms are known for their high cost, especially with the huge volume of Synthetic Aperture Radar (SAR) images generated by Sentinel-1 SAR missions. Recently, a COvariance Fitting Interferometric Phase Linking (COFI-PL) approach has been proposed, which can be seen as a generic framework for existing PL methods. Although this method is less computationally expensive than traditional PL approaches, COFI-PL exploits the entire covariance matrix, which poses a challenge with the increasing time series of SAR images. However, COFI-PL, like traditional PL approaches, cannot accommodate the efficient inclusion of newly acquired SAR images. This paper overcomes this drawback by introducing a sequential integration of a block of newly acquired SAR images. Specifically, we propose a method for effectively addressing optimization problems associated with phase-only complex vectors on the torus based on the Majorization-Minimization framework. The proposed approach demonstrates comparable performance to the offline COFI-PL method while achieving a reduction in computation time , of approximately 15% in both simulations and real data experiments. Moreover, it outperforms state-of-the-art sequential approaches in terms of both accuracy and speed.

Interferometric phase linking (IPL) has become a prominent technique for processing images of areas containing distributed scatterers in SAR interferometry. Traditionally, IPL consists in estimating consistent phase differences between all pairs of SAR images in a time series from the sample covariance matrix (SCM) of pixel patches on a sliding window. This article reformulates this task as a covariance fitting problem; IPL appears then as a form of projection of an input covariance matrix so that it satisfies the phase closure property. This approach yields a systematic methodology to frame IPL as an optimization problem on the torus of phase-only complex vectors. On the modeling side, the formulation is modular and allows for a flexible choice of covariance matrix estimates, regularization options, and matrix distances. In particular, we demonstrate that most existing IPL algorithms appear as special instances of this framework. In addition, we propose some new options, which were not covered by the state of the art, whose merits are illustrated through simulations and a real-world case study. On the computational side, another contribution of this article is the derivation of generic and computationally efficient algorithms for IPL using majorization-minimization (MM) and Riemannian optimization.

We introduce a new method for Through-the-Wall Radar Imaging (TWRI) that detects the location of stationary targets hidden by a wall. A crucial step is the mitigation of wall returns which obscure the scene and which are characterized by their low-rankedness given the radar measurement setup. Whereas existing methods make use of nuclear norm minimization or Truncated Singular Value Decomposition (TSVD), we propose to leverage Riemannian optimization over the manifold of fixed-rank matrices in order to use robust estimation while keeping the original rank constraint without relaxation. A detection step via sparse recovery is then performed and the overall method is compared with existing methods over simulated scenes. The results show that the proposed method achieves a better performance.

In this study, we consider the realm of covariance matrices in machine learning, particularly focusing on computing Fréchet means on the manifold of symmetric positive definite matrices, commonly referred to as Karcher or geometric means. Such means are leveraged in numerous machine learning tasks. Relying on advanced statistical tools, we introduce a random matrix theory based method that estimates Fréchet means, which is particularly beneficial when dealing with low sample support and a high number of matrices to average. Our experimental evaluation, involving both synthetic and real-world EEG and hyperspectral datasets, shows that we largely outperform state-of-the-art methods.

This paper introduces a novel approach for sequential estimation of the interferometric phase in the context of long Synthetic Aperture Radar (SAR) image time series. When newly acquired data arrive, the data set expands and can be partitioned into two distinct blocks. One represents the previous SAR images and the other represents the newly acquired data. The proposed approach (S-MLE-PL) exploits sequential maximum likelihood estimation of the covariance matrix of the whole data set, taking the existing data set as prior information. This approach facilitates the continuous interferometric phase estimation by incorporating the new data into the previous context. In addition, it presents the advantage of reduced computation time compared to the traditional approaches, making it a more efficient solution for operational displacement estimation.

We propose a new pipeline to classify Ground Penetrating Radar (GPR) images, based upon the use of second-orders statistics computed over convolutional features of a ResNet-like architecture. In particular, the architecture consists in an end-to-end training phase with backpropagation from convolutional filters from layers adapted to Symmetric Positive Definite (SPD) matrices. The developed approach is tested and compared to a shallow network given in the GPR literature and a deep Computer Vision model like ResNet. Thorugh experiments on real data, we show that we outperform these methods in various scenarios: when the number of training data is small and when some of them are mislabelled.

This paper presents a new performance bound for estimation problems where the parameter to estimate lies in a Riemannian manifold (a smooth manifold endowed with a Riemannian metric) and follows a given prior distribution. In this setup, the chosen Riemannian metric induces a geometry for the parameter manifold, as well as an intrinsic notion of the estimation error measure. Performance bounds for such error measure were previously obtained in the non-Bayesian case (when the unknown parameter is assumed to deterministic), and referred to as intrinsic Cramér-Rao bound. The presented result then appears either as: a) an extension of the intrinsic Cramér-Rao bound to the Bayesian estimation framework; b) a generalization of the Van-Trees inequality (Bayesian Cramér-Rao bound) that accounts for the aforementioned geometric structures. In a second part, we leverage this formalism to study the problem of covariance matrix estimation when the data follow a Gaussian distribution, and whose covariance matrix is drawn from an inverse Wishart distribution. Performance bounds for this problem are obtained for both the mean squared error (Euclidean metric) and the natural Riemannian distance for Hermitian positive definite matrices (affine invariant metric). Numerical simulation illustrate that assessing the error with the affine invariant metric is revealing of interesting properties of the maximum a posteriori and minimum mean square error estimator, which are not observed when using the Euclidean metric.

This paper proposes an algorithm for phase differences estimation in multi-temporal InSAR. The proposed approach is based on covariance fitting estimation and the majorization-minimization algorithm. Experiments with Sentinel-1 images of Mexico City demonstrate that the proposed approach compares favorably to the state-of-the-art phase linking (i.e., maximum likelihood-based approaches) when the sample support is low (i.e., when the number of pixels in the multi-look window cannot scale with the number of SAR images). Hence, the proposed approach can improve the spatial resolution of phase difference estimation in case of large SAR image time series.

In this paper, we propose two algorithms to enhance the interpretability of the hyperbola in B-scans obtained with a Ground Penetrating Radar (GPR). These hyperbolas are the responses of buried objects or cavities. To correctly detect and classify them, a denoising is typically necessary for GPR images as the signal-to-noise ratio is low, and the various interfaces naturally present in the earth have a strong response. Both algorithms are based on a sparse convolutional coding model plus a low rank component. It is solved through an Alternating Direction Method of Multipliers (ADMM) framework. In order to take into account the presence of outliers and the artifacts caused by the acquisition, the second algorithm is based on the Huber norm instead of the classicL2-norm. These algorithms are tested on a real dataset labeled by geophysicists. The results show the denoising efficiency of this approach, and in particular the robustness of the second algorithm.

Phase linking is a prominent methodology to estimate coherence and phase difference in interferometric synthetic-aperture radar. This method is driven by a maximum likelihood estimation approach, which allows to fully exploit all the possible interferograms from a time series. Its performance is, however, known to be affected by the accuracy of the covariance matrix estimation step, which usually requires to introduce additional prior information on its structure when there is a small sample support (spatial window). Moreover, most phase linking algorithms are built upon the sample covariance matrix, due to the assumption of an underlying Gaussian distribution. In a scenario where SAR data is high resolution, or when the study area is spatially heterogeneous (e.g., urban area), this assumption can also limit the accuracy of the covariance matrix estimation step. Considering the two aforementioned issues, we introduce alternative statistical models, whose maximum likelihood estimators then yield new phase linking algorithms. In order to be robust to non-Gaussian data, we consider the use of a more general model of scaled mixture of Gaussian. To address small sample support issues, we also generalize this approach to a possibly low-rank structured covariance matrix. A unified algorithm to perform phase linking given these models is then derived and validated by simulations and a real data case (Sentinel-1 data).

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.

We consider the problem of classifying Ground Penetrating Radar (GPR) signals by using covariance matrices descriptors computed on convolutional features obtained from MobileNetV2 Convolutional Neural Network (CNN) first layers. This approach allows to leverage the rich data representation obtained from CNNs and the low-dimensionality of second-order statistics. Then the Riemannian geometry of covariance matrices is leveraged to improve classification rate. The proposed approach allows then to perform automatic classification of buried objects with few labeled data available. We also consider the scenario of an airbone radar and provide results at different elevations.

This paper presents a new algorithm for improving the estimation of interferometric SAR (InSAR) phases in the context of time series and phase linking approach. Based on maximum likelihood estimator of a multivariate Gaussian model, the estimation of the InSAR phases is solved using a Block Coordinate Descent algorithm. Compared to the state-of-the-art approaches, the main improvement lies on the joint estimation of the covariance matrix and the InSAR phases instead of using a plug-in coherence estimate obtained from the sample covariance of the data or the modeling of the temporal decorrelation of the target under observation. Results of synthetic simulations confirm the improvement brought by the proposed estimator.

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.

This paper aims at providing an original Riemannian geometry to derive robust covariance matrix estimators in spiked models (i.e. when the covariance matrix has a low-rank plus identity structure). The considered geometry is the one induced by the product of the Stiefel manifold and the manifold of Hermitian positive definite matrices, quotiented by the unitary group. One of the main contributions is to consider a Riemannian metric related to the Fisher information metric of elliptical distributions, leading to new representations for the tangent spaces and a new retraction. A new robust covariance matrix estimator is then obtained as the minimizer of Tyler's cost function, redefined directly on the set of low-rank plus identity matrices, and computed with the aforementioned tools. The main interest of this approach is that it appears well suited to the cases where the sample size is lower than the dimension, as illustrated by numerical experiments.

We consider the optimal performance of blind separation of Gaussian sources. In practice, this estimation problem is solved by a two-step procedure: estimation of a set of covariance matrices from the observed data and approximate joint diagonalization of this set to find the unmixing matrix. Rather than studying the theoretical performance of a specific method, we are interested in the optimal attainable performance of any estimator. To do so, we consider the so-called intrinsic Cramér-Rao bound, which exploits the geometry of the parameters of the model. Unlike previous works developing a Cramér-Rao bound in this context, our solution does not require any additional hypotheses. To obtain our bound, we define and study a new Riemannian manifold holding the parameters of interest. An original estimation error measure is defined with the help of our Riemannian distance function. The corresponding Fisher information matrix is then obtained from the Fisher information metric and orthonormal bases on the tangent spaces of the manifold. Finally, our theoretical results are validated on simulated data.

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.

This paper introduces an improved Low Rank Adaptive Normalized Matched Filter (LR-ANMF) detector in a high dimensional (HD) context where the observation dimension is large and of the same order of magnitude than the sample size. To that end, the statistical analysis of the LR-ANMF, in a context where the target signal is disturbed by a spatially correlated Gaussian clutter and a spatially white Gaussian noise, is addressed. More specifically, the asymptotic distribution under the null hypothesis is derived, in the regime where both the dimension M of the observations and the number N of samples converge to infinity at the same rate and when the clutter covariance matrix has fixed rank K. In particular, it is shown that the LR-ANMF test statistic does not exhibit the CFAR property in the previous asymptotic regime. A correction to the LR-ANMF test is then proposed to ensure the asymptotic CFAR property, providing the improved LR-ANMF, termed as HD-LR-ANMF. Its asymptotic distribution is derived under both the null and the alternative hypotheses. Numerical simulations illustrate the fact that, despite the asymptotic nature of the analysis, the results obtained are accurate for reasonable values of M, N.

Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to largely outperform the sample covariance matrix estimate and to compete with state-of-the-art methods, while at the same time being computationally simpler and faster. Applications to linear and quadratic discriminant analyses also show significant gains, therefore suggesting practical interest to statistical machine learning.

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.

Scatter matrix and its normalized counterpart, referred to as shape matrix, are key parameters in multivariate statistical signal processing, as they generalize the concept of covariance matrix in the widely used Complex Elliptically Symmetric distributions. Following the framework of [1], intrinsic Cramér-Rao bounds are derived for the problem of scatter and shape matrices estimation with samples following a Complex Elliptically Symmetric distribution. The Fisher Information Metric and its associated Riemannian distance (namely, CES-Fisher) on the manifold of Hermitian positive definite matrices are derived. Based on these results, intrinsic Cramér-Rao bounds on the considered problems are then expressed for three different distances (Euclidean, natural Riemannian, and CES-Fisher). These contributions are therefore a generalization of Theorems 4 and 5 of [1] to a wider class of distributions and metrics for both scatter and shape matrices.

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 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.

Regularized Tyler Estimator's (RTE) have raised attention over the past years due to their attractive performance over a wide range of noise distributions and their natural robustness to outliers. Developing adaptive methods for the selection of the regularisation parameter α is currently an active topic of research. Indeed, the bias-performance compromise of RTEs highly depends on the considered application. Thus, finding a generic rule that is optimal for every criterion and/or data configurations is not straightforward. This issue is addressed in this paper for undersampled configurations (number of samples lower than the dimension of the data). The paper proposes a new regularisation parameter selection based on a subspace reduction approach. The performance of this method is investigated in terms of estimation accuracy and for adaptive detection purposes, both on simulation and real data.

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.

The paper addresses the problem of approximating the detector distribution used in target detection embedded in a disturbance composed of a low rank Gaussian noise and a white Gaussian noise. In this context, it is interesting to use an adaptive version of the Low Rank Normalized Matched Filter (LR-ANMF) detector, which is a function of the estimated projector onto the low rank noise subspace. We will show that the traditional approximation of the LR-ANMF detector distribution is not always the better one. In this paper, we propose to perform its limits when the number of secondary data K and the data dimension m both tend to infinity at the same rate m/K → c∈2 (0;∞). Then, we give the theoretical distributions of these limits in the large dimensional regime and approximate the LR-ANMF detector distribution by them. The comparison of empirical and theoretical distributions on a jamming application shows the interest of our approach.

In the context of an heterogeneous disturbance with a Low Rank (LR) structure (called clutter), one may use the LR approximation for filtering and detection process. These methods are based on the projector onto the clutter subspace instead of the noise covariance matrix. In such context, adaptive LR schemes have been shown to require less secondary data to reach equivalent performances as classical ones. The main problem is then the estimation of the clutter subspace instead of the noise covariance matrix itself. Maximum Likelihood estimator (MLE) of the clutter subspace has been recently studied for a noise composed of a LR Spherically Invariant Random Vector (SIRV) plus a white Gaussian Noise (WGN). This paper focuses on environments with a high Clutter to Noise Ratio (CNR). An original MLE of the clutter subspace is proposed in this context. A cross-interpretation of this new result and previous ones is provided. Validity and interest - in terms of performance and robustness - of the different approaches are illustrated through simulation results.

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.

In this paper the contribution of the polarimetric information to discriminate signal from interference subspaces is presented. By using only one single polarization, it is shown that the target and the interferences responses are similar; the reduction of false alarms due to the trunk is there fore not possible. The use of double polarization allows to discriminate the target response from the interferences ones. False alarms can then be reduced. These results show that the polarimetric information greatly contributes to increase the difference between the signal and the interference subspaces. We expect to include the cross-polarizations (HV and VH) to improve the encouraging results presented here.

In this paper, we consider that the disturbance of a STAP system is composed of a low-rank Gaussian clutter and a white Gaussian noise. From this model, the theoretical SNR Loss of a Robust Low-Rank STAP filter based on the Normalized Sample Covariance Matrix is derived by means of a perturbation analysis. Theoretical results are shown to be in good agreement with simulations for a realistic STAP configuration. Our analysis extends previous result on the SNR loss of Low-Rank STAP filtering based on the Sample Covariance Matrix.

We develop a new SAR processor based on several orthogonal projections.We take into account the scattering properties of the target and the interferences by using subspace models. To detect the target without detecting the interferences, we process images from the orthogonal projection of the received signal into the target subspace and from the orthogonal projection of the received signal into a part of the interference subspace. We can combine these two images to firstly detect the target and to secondly reduce interference. This new SAR processor is applied to realistic simulated data for FoPen (Foliage Penetration) application.

We develop a new SAR processor based on oblique projection. We take into account the scattering properties of the target and the interferences by using subspace models. To detect the target and to reject the interferences, we process images with the oblique projection of the received signal into the target subspace along the interference one. This new SAR processor is applied to realistic simulated data for FoPen (Foliage Penetration) application.

This paper deals with three new polarimetric SAR processors based on subspace detectors. These algorithms aim at using models with physical and polarimetric scattering properties not exploited by the isotropic point model. These processors are implemented by computing the corresponding target subspaces. Results on simulated data with realistic targets show the interest of these new processors.

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.

This paper presents research results in space-surface multistatic synthetic aperture radar (SS-MSAR) with non-cooperative GPS satellites. The effect of the system's geometry is investigated. We will show that in SS-MSAR, the spatial resolution depends on the geometry of the system, i.e. satellite-receiver-target positions relative to each other. General ambiguity function (GAF) and the point spread function (PSF) are defined in our case in a 3D case corresponding to our study. These criteria are then computed, and compared, for several scenarios including one (bistatic case) to three emitters (multistatic case).

This paper deals with two new SAR processors based on CFAR subspaces detector. These two algorithms aim at improving man made target detection performances in a forest clutter by using electromagnetic scattering models. The implementation of the two detectors is described. An application on simulated data shows the interest of the two methods.

This paper deals with the capability of a SAR processor based on a subspace detector to get better performance than a classical SAR processor for Man Made Target (MMT) detection in a forest. The new algorithm aims at using new models, different from the isotropic point one commonly used in SAR processors. The implementation of the Subspace Detector SAR (SDSAR) algorithm is described and detection performances between a classical SAR (CSAR) algorithm and the SDSAR one are compared when detecting a MMT in white Gaussian noise and in a simulated forest.