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.

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.

Complex-Valued (CV) Synthetic Aperture Radar (SAR) image generation and augmentation is an important pillar to enhance deep learning performance for SAR applications such as detection, classification, segmentation, super-resolution etc. Usual transformations (flip, rotation, translation, scaling, etc.) are mostly inapplicable to SAR images due to the radar characteristics and the processing pipeline. In this paper, we explore the applicability of Wasserstein Generative Adversarial Networks (WGANs) to SAR data. The latter, being complex, require CV generator and a discriminator taking as input a complex-valued signal, to capture the underlying distribution. In particular, we show the applicability of CV-WGANs for the synthesis of (i) Fourier spectrum of various MNIST like datasets as toy example and (ii) L-band UAVSAR dataset.

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.

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.

Much work has been dedicated to estimating and optimizing workloads in high-performance computing (HPC) and deep learning. However, researchers have typically relied on few metrics to assess the efficiency of those techniques. Most notably, the accuracy, the loss of the prediction, and the computational time with regard to GPUs or/and CPUs characteristics. It is rare to see figures for power consumption, partly due to the difficulty of obtaining accurate power readings. In this paper, we introduce a composite score that aims to characterize the trade-off between accuracy and power consumption measured during the inference of neural networks. For this purpose, we present a new open-source tool allowing researchers to consider more metrics: granular power consumption, but also RAM/CPU/GPU utilization, as well as storage, and network input/output (I/O). To our best knowledge, it is the first fit test for neural architectures on hardware architectures. This is made possible thanks to reproducible power efficiency measurements. We applied this procedure to state-of-the-art neural network architectures on miscellaneous hardware. One of the main applications and novelties is the measurement of algorithmic power efficiency. The objective is to allow researchers to grasp their algorithms' efficiencies better. This methodology was developed to explore trade-offs between energy usage and accuracy in neural networks. It is also useful when fitting hardware for a specific task or to compare two architectures more accurately, with architecture exploration in mind.

Radar is an extremely valuable sensing technology for detecting moving targets and measuring their range, velocity, and angular positions. When people are monitored at home, radar is more likely to be accepted by end-users, as they already use WiFi, is perceived as privacy-preserving compared to cameras, and does not require user compliance as wearable sensors do. Furthermore, it is not affected by lighting conditions nor requires artificial lights that could cause discomfort in the home environment. So, radar-based human activities classification in the context of assisted living can empower an aging society to live at home independently longer. However, challenges remain as to the formulation of the most effective algorithms for radar-based human activities classification and their validation. To promote the exploration and cross-evaluation of different algorithms, our dataset released in 2019 was used to benchmark various classification approaches. The challenge was open from February 2020 to December 2020. A total of 23 organizations worldwide, forming 12 teams from academia and industry, participated in the inaugural Radar Challenge, and submitted 188 valid entries to the challenge. This paper presents an overview and evaluation of the approaches used for all primary contributions in this inaugural challenge. The proposed algorithms are summarized, and the main parameters affecting their performances are analyzed.

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.

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.

Deploying neural networks models over embedded devices have an increased interest and many works is ongoing on that topic. Energy consumption, model sizes and inference time are critical issues as explained in the literature. In the context of IoT and edge computing, tradeoff have been studied in order to get a low cost but rapid answer, robust to connection issue exploiting early exiting or distributing deep neural networks. Those approaches exploits the cloud as an endpoint, balancing the load with respect to different computing capabilities. In this paper, we propose to extend those approaches to networks of embedded devices such as a swarm of drones, where every device has the same computing capabilities (in terms of energy and speed). Computing load may be balanced among the whole swarm in order to maximise either the lifetime of specific devices or lifetime of the whole swarm. We develop criteria to best cut and distribute those networks, validate them through power measurement and express the different tradeoffs we have to address.

The joint estimation of means and scatter matrices is often a core problem in multivariate analysis. In order to overcome robustness issues, such as outliers from Gaussian assumption,M-estimators are now preferred to the traditional sample mean and sample covariance matrix. These estimators are well established and studied in the real case since the seventies. Their extension to the complex case has drawn recent interest. In this letter, we derive the asymptotic performance of complexM-estimators for multivariate location and scatter matrix estimation.

This paper addresses structured covariance matrix estimation under t -distribution. Covariance matrices frequently reveal a particular structure due to the considered application and taking into account this structure usually improves estimation accuracy. In the framework of robust estimation, the t -distribution is particularly suited to describe heavy-tailed observation. In this context, we propose an efficient estimation procedure for covariance matrices with convex structure under t -distribution. Numerical examples for Hermitian Toeplitz structure corroborate the theoretical analysis.

In this letter, we study the behavior of the maximum likelihood estimator (MLE) in the framework of low noise level (or high signal-to-noise ratio), when the data follow a unimodal elliptical distribution. The MLE appears to be the same as in the Gaussian context, regardless the noise distribution. We also show that the asymptotic distribution of this estimator is unimodal elliptical, where the law is intimately linked to that of the noise distribution. Additionally, this estimator is shown to be not efficient, except in the Gaussian noise case. Finally, we validate our analytic results by some simulations.

In this letter, we investigated the connection between information and estimation measures for mismatched Gaussian models. In addition to the input prior mismatch, we take into account the noise mismatch and establish a new relation between relative entropy and excess mean square error. The derived formula shows that the input prior mismatch may be canceled by the noise mismatch. Finally, an example illustrates the impact of model mismatches on estimation accuracy.

In statistical signal processing, hybrid parameter estimation refers to the case where the parameters vector to estimate contains both non-random and random parameters. Numerous works have shown the versatility of deterministic constrained Cramér-Rao bound for estimation performance analysis and design of a system of measurement. However in many systems both random and non-random parameters may occur simultaneously. In this communication, we propose a constrained hybrid lower bound which take into account of equality constraint on deterministic parameters. The usefulness of the proposed bound is illustrated with an application to radar Doppler estimation

This letter investigates hybrid lower bounds on the mean square error in order to predict the so-called threshold effect. A new family of tighter hybrid large error bounds based on linear transformations (discrete or integral) of a mixture of the McAulay-Seidman bound and the Weiss-Weinstein bound is provided in multivariate parameters case with multiple test points. For use in applications, we give a closed-form expression of the proposed bound for a set of Gaussian observation models with parameterized mean, including tones estimation which exemplifies the threshold prediction capability of the proposed bound.

In statistical signal processing, hybrid parameter estimation refers to the case where the parameters vector to estimate contains both non-random and random parameters. As a contribution to the hybrid estimation framework, we introduce a recursive hybrid Cramér–Rao lower bound for discrete-time Markovian dynamic systems depending on unknown deterministic parameters. Additionally, the regularity conditions required for its existence and its use are clarified.

In statistical signal processing, hybrid parameter estimation refers to the case where the parameters vector to estimate contains both non-random and random parameters. In this communication, we propose a new hybrid lower bound which, for the first time, includes the Ziv-Zakaï bound well known for its tightness in the Bayesian context (random parameters only). For the general case of parameterized mean model with Gaussian noise, closed-form expressions of the proposed bound are provided.

This article investigates hybrid lower bounds in order to predict the estimators mean square error threshold effect. A tractable and computationally efficient form is derived. This form combines the Barankin and the Weiss-Weinstein bounds. This bound is applied to a frequency estimation problem for which a closed-form expression is provided. A comparison with results on the hybrid Barankin bound shows the superiority of this new bound to predict the mean square error threshold.