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.

This paper introduces Generalized Nonnegative Structured Kruskal Tensor Regression (NS-KTR), a novel tensor regression framework that enhances interpretability and performance through mode-specific hybrid regularization and nonnegativity constraints. Our approach accommodates both linear and logistic regression formulations for diverse response variables while addressing the structural heterogeneity inherent in multidimensional tensor data. We integrate fused LASSO, total variation, and ridge regularizers — each tailored to specific tensor modes — and develop an efficient alternating direction method of multipliers (ADMM)-based algorithm for parameter estimation. Comprehensive experiments on synthetic signals and real hyperspectral datasets demonstrate that NS-KTR consistently outperforms conventional tensor regression methods. The framework’s ability to preserve distinct structural characteristics across tensor dimensions while ensuring physical interpretability makes it especially suitable for applications in signal processing and hyperspectral image analysis. • NS-KTR: nonnegative structured Kruskal tensor regression with hybrid regularization. • Mode-specific regularization: LASSO, total variation, and ridge across tensor modes. • Unified framework supports linear and logistic regression for diverse responses. • ADMM-based optimization achieves superior accuracy with significant speedups.

We consider the problem of classifying a pair of Synthetic Aperture Radar (SAR) images by proposing an explainable and frugal algorithm that integrates a set of divergences. The approach relies on a statistical framework that takes standard probability distributions into account for modelling SAR data. Then, by learning a combination of parameterized Renyi divergences and their parameters from the data, we are able to classify the pair of images with fewer parameters than regular machine learning approaches while also allowing an interpretation of the results related to the priors used. Experiments on real multi-class data demonstrate the virtues of the suggested method when compared to both Random Forest and Convolutional Neural Networks (CNN) classifiers, showing its resilience to disturbances such as polluted labels and variations in the percentage of training data.

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.

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.

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.

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.

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 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.

Testing the similarity of covariance matrices (CMs) from groups of observations has been shown to be a relevant approach for change and/or anomaly detection in synthetic aperture radar images. Although the term “similarity” usually refers to equality or proportionality, we explore the testing of shared properties in the structure of low rank (LR) plus identity CM, which are appropriate for radar processing. Specifically, we derive two new generalized likelihood ratio tests to infer: 1) on the equality of the LR signal component of CMs and 2) on the proportionality of the LR signal component of CMs. The formulation of the second test involves nontrivial optimization problems for which we tailor efficient majorization-minimization algorithms. Eventually, the proposed detection methods enjoy interesting properties that are illustrated on simulations and on an application to real data for change detection.

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.