International audience

This letter considers two estimators of the intensity$\lambda$of the Shot Noise process for high values of$\lambda$. They are based on the first and the second empirical cumulants of the Shot Noise. For both statistics, it is shown that their respective variance grows respectively linearly and quadratically with$\lambda$. We construct Variance Stabilizing Transforms (and their corresponding inverse transforms) for both estimators thanks to the Delta method so as to make their respective variance constant (regardless of$\lambda$). Asymptotic distributions of the variance stabilized estimators are established. Finally, variance stabilization property is validated by Monte-Carlo simulations.

Distributed Acoustic Sensing (DAS) is a novel vibration sensing technology that can be employed to detect vehicles and to analyse traffic flows using existing telecommunication cables. DAS therefore has great potential in future “smart city” developments, such as real-time traffic incident detection. Though previous studies have considered vehicle detection under relatively light traffic conditions, in order for DAS to be a feasible technology in real-world scenarios, detection algorithms need to also perform robustly under a wide range of traffic conditions. In this study we investigate the potential of roadside DAS for the simultaneous detection and characterisation of the velocity of individual vehicles. To improve the temporal resolution and detection accuracy, we propose a self-supervised Deep Learning approach that deconvolves the characteristic car impulse response from the DAS data, which we refer to as a Deconvolution Auto-Encoder (DAE). We show that deconvolution of the DAS data with our DAE leads to better temporal resolution and detection performance than the original (non-deconvolved) data. We subsequently apply our DAE to a 24-hour traffic cycle, demonstrating the feasibility of our proposed method to process large volumes of DAS data, potentially in near-real time.

Fiber-optic distributed acoustic sensing (DAS) is an emerging technology for vibration measurements with numerous applications in seismic signal analysis, including microseismicity detection, ambient noise tomography, earthquake source characterization, and active source seismology. Using laser-pulse techniques, DAS turns (commercial) fiber-optic cables into seismic arrays with a spatial sampling density of the order of meters and a time sampling rate up to one thousand Hertz. The versatility of DAS enables dense instrumentation of traditionally inaccessible domains, such as urban, glaciated, and submarine environments. This in turn opens up novel applications such as traffic density monitoring and maritime vessel tracking. However, these new environments also introduce new challenges in handling various types of recorded noise, impeding the application of traditional data analysis workflows. In order to tackle the challenges posed by noise, new denoising techniques need to be explored that are tailored to DAS. In this work, we propose a Deep Learning approach that leverages the spatial density of DAS measurements to remove spatially incoherent noise with unknown characteristics. This approach is entirely self-supervised, so no noise-free ground truth is required, and it makes no assumptions regarding the noise characteristics other than that it is spatio-temporally incoherent. We apply our approach to both synthetic and real-world DAS data to demonstrate its excellent performance, even when the signals of interest are well below the noise level. Our proposed methods can be readily incorporated into conventional data processing workflows to facilitate subsequent seismological analyses.

Detecting changes in network-structured time series data is of utmost importance in critical applications as diverse as detecting denial of service attacks against online service providers or monitoring energy and water supplies. The aim of this paper is to address this challenge when anomalies activate unknown groups of nodes in a network. We devise an online change-point detection algorithm that fully benefits from the recent advances in graph signal processing to exploit the characteristics of the data that lie on irregular supports. Built upon the kernel machinery, it performs density ratio estimation in an online way. The algorithm is scalable in the sense that it is spatially distributed over the nodes to monitor large-scale dynamic networks. The detection and localization performances of the algorithm are illustrated with simulated data.

The performance of iterative algorithms aimed at solving a regularized least squares problem typically depends on the value of some regularization parameter. Tuning the regularization parameter value is a fundamental step necessary to control the strength of the regularization and hence ensure a good performance. We address the problem of finding the optimal regularization parameter in such iterative algorithms. We propose to adaptively adjust the regularization parameter throughout the iterations of the algorithm by minimizing an estimate of the current risk, typically the Weighted Stein unbiased risk estimate (WSURE). We then prove that, for the case of the Tikhonov regularization, the proposed ADAptive Parameter Tuning (ADA-PT) strategy provides a stationary point consistent with the risk minimizer. We illustrate the efficiency of ADA-PT on two image deconvolution problems: one with the Tikhonov regularization and one with the weighted ℓ-1 analysis wavelet regularization.

This paper investigates calibration of sensor arrays in the radio astronomy context. Current and future radio telescopes require computationally efficient algorithms to overcome the new technical challenges as large collecting area, wide field of view and huge data volume. Specifically, we study the calibration of radio interferometry stations with significant direction dependent distortions. We propose an iterative robust calibration algorithm based on a relaxed maximum likelihood estimator for a specific context: i) observations are affected by the presence of outliers and ii) parameters of interest have a specific structure depending on frequency. Variation of parameters across frequency is addressed through a distributed procedure, which is consistent with the new radio synthesis arrays where the full observing bandwidth is divided into multiple frequency channels. Numerical simulations reveal that the proposed robust distributed calibration estimator outperforms the conventional non-robust algorithm and/or the mono-frequency case.

This paper presents a kernel-based nonlinear mixing model for hyperspectral data, where the nonlinear function belongs to a Hilbert space of vector valued functions. The proposed model extends the existing ones by accounting for band-dependent and neighboring nonlinear contributions. The key idea is to work under the assumption that nonlinear contributions are dominant in some parts of the spectrum, while they are less pronounced in other parts. In addition to this, we motivate the need for taking into account nonlinear contributions originating from the ground covers of neighboring pixels by practical considerations, precisely the adjacency effect. The relevance of the proposed model is that the nonlinear function is associated with a matrix valued kernel that allows to jointly model a wide range of nonlinearities and includes prior information regarding band dependences. Furthermore, the choice of the nonlinear function input allows to incorporate neighboring effects. The optimization problem is strictly convex and the corresponding iterative algorithm is based on the alternating direction method of multipliers. Finally, experiments conducted using synthetic and real data demonstrate the effectiveness of the proposed approach.

This communication proposes an unsupervised neighbor dependent nonlinear unmixing algorithm for hyperspectral data. The proposed mixing scheme models the reflectance vector of a pixel as the sum of a linear combination of the endmem-bers plus a nonlinear function acting on neighboring spectra. The nonlinear function belongs to a reproducing kernel Hilbert space. The observations themselves are considered as the endmember candidates, and the group lasso regulariza-tion is used to enable selecting the purest pixels among the candidates. Experiments on synthetic data demonstrate the effectiveness of the proposed approach.

Diffusion LMS is an efficient strategy for solving distributed optimization problems with cooperating agents. In some applications, the optimum parameter vectors may not be the same for all agents. Moreover, agents usually exchange information through noisy communication links. In this work, we analyze the theoretical performance of the single-task diffusion LMS when it is run, intentionally or unintentionally, in a multitask environment in the presence of noisy links. To reduce the impact of these nuisance factors, we introduce an improved strategy that allows the agents to promote or reduce exchanges of information with their neighbors.

This paper introduces a graph Laplacian regularization in the hyperspectral unmixing formulation. The proposed regularization relies upon the construction of a graph representation of the hyperspectral image. Each node in the graph represents a pixel's spectrum, and edges connect similar pixels. The proposed graph framework promotes smoothness in the estimated abundance maps and collaborative estimation between homogeneous areas of the image. The resulting convex optimization problem is solved using the Alternating Direction Method of Multipliers (ADMM). A special attention is given to the computational complexity of the algorithm, and Graph-cut methods are proposed in order to reduce the computational burden. Finally, simulations conducted on synthetic and real data illustrate the effectiveness of the graph Laplacian regularization with respect to other classical regularizations for hyperspectral unmixing.

In this work, a diffusion-type algorithm is proposed to solve multitask estimation problems where each cluster of nodes is interested in estimating its own optimum parameter vector in a distributed manner. The approach relies on minimizing a global mean-square error criterion regularized by a term that promotes piecewise constant transitions in the parameter vector entries estimated by neighboring clusters. We provide some results on the mean and mean-square-error convergence. Simulations are conducted to illustrate the effectiveness of the strategy.

We consider the problem where a large known library of L alternatives is available and we wish to maximize the detection power in a worst case scenario. The considered minimax detection approach relies on a GLR test allied to a sparsity constraint. This approach conditions the optimization of the target subspaces, in number r ≪ L. While the exact solution of the minimax optimization problem can be found for r = 1, the problem for r > 1 is more intricate and we propose two algorithms aimed at finding an approximate solution. The proposed algorithms are illustrated on a face database and on hyperspectral data and are shown to improve on the r = 1 case.

We review several detection strategies that account for the possible sparsity of target sources in data cubes. The considered sparsity can exist in the data acquisition space, or in some transform domain. Theoretical aspects of the detection tests are first described. Emphasis is then put on practical issues that may arise in hyperspectral data, such as spatio-spectral dependencies or very low Signal-to-Noise Ratios. Applications are finally described in the framework of the hyperspectral data of MUSE (Multi-Unit Spectroscopic Explorer) instrument. MUSE is a powerful integral field spectrograph whose observational abilities should provide unprecedented insights about the formation and evolution of galaxies.

In the “Higher Criticism” framework for multiple hypothesis testing, the binomial counts of the empirical CDF of the P-values are standardized through Z-scores. In the asymptotic regime, the distribution of these standardized counts tends to be a standard Gaussian. In the non-asymptotic regime, these distributions depart from normality and generally differ from each other. As a result, comparable values of Z-scores obtained for different P-values reflect in fact different evidence against the joint null hypothesis. We show that such evidence can be computed in closed-form for finite sample size, resulting in an alternate standardization which leads to identically distributed and thus more comparable statistics. Numerical results illustrate some merits of the alternate standardization.

This paper addresses the problem of blind and fully constrained unmixing of hyperspectral images. Unmixing is performed without the use of any dictionary, and assumes that the number of constituent materials in the scene and their spectral signatures are unknown. The estimated abundances satisfy the desired sum-to-one and nonnegativity constraints. Two models with increasing complexity are developed to achieve this challenging task, depending on how noise interacts with hyperspectral data. The first one leads to a convex optimization problem and is solved with the alternating direction method of multipliers. The second one accounts for signal-dependent noise and is addressed with a reweighted least squares algorithm. Experiments on synthetic and real data demonstrate the effectiveness of our approach.

In recent years, nonlinear unmixing of hyperspectral data has become an attractive topic in hyperspectral image analysis, because nonlinear models appear as more appropriate to represent photon interactions in real scenes. For this challenging problem, nonlinear methods operating in reproducing kernel Hilbert spaces have shown particular advantages. In this paper, we derive an efficient nonlinear unmixing algorithm based on a recently proposed linear mixture/ nonlinear fluctuation model. A multi-kernel learning support vector regressor is established to determine material abundances and nonlinear fluctuations. Moreover, a low complexity locally-spatial regularizer is incorporated to enhance the unmixing performance. Experiments with synthetic and real data illustrate the effectiveness of the proposed method.

Nonparametric Bayesian models are often preferred over parametric models due to their superior flexibility in interpreting data. A strong motivation for the use of these models is the desire of avoiding the assumptions that are necessary for parametric models. A prominent place in Bayesian nonparametrics is played by the Dirichlet process, which is defined by a base measure and a concentration parameter. In this paper, we propose the construction of models based on products of Dirichlet processes and corresponding mixture models. We show how these processes can be used for classification of data with shared features. The proposed processes are different from the recently introduced hierarchical Dirichlet processes. We show the use of the proposed model on classification of multivariate time series and demonstrate its performance with computer simulations.

We propose a method aimed at detecting weak, sparse signals in highly noisy three-dimensional (3D) data. 3D data sets usually combine two spatial directions x and y (e.g. image or video frame dimensions) with an additional direction λ (e.g. temporal, spectral or energy dimension). Such data most often suffer from information leakage caused by the acquisition system's point spread functions, which may be different and variable in the three dimensions. The proposed test is based on dedicated 3D dictionaries, and exploits both the sparsity of the data along the λ direction and the information spread in the three dimensions. Numerical results are shown in the context of astrophysical hyperspectral data, for which the proposed 3D model substantially improves over 1D detection approaches.

We consider the problem of detecting a target signature which is known (up to an amplitude factor) to belong to a (possibly very) large library of signatures. Thus we know how each signature to be detected looks like, but we do not know which one is activated under H1. We propose a minimax approach for this problem aimed at maximizing the worst detection performance. Optimization issues and connections with One-Class classifiers are discussed and illustrated geometrically. Numerical results comparing the proposed approach to the classical sparse-coding dictionary learning technique K-SVD are provided on astrophysical hyperspectral data.

While an exact stationarization of a process with a given spectrum magnitude can be obtained via a complete randomization of the spectrum phase ("surrogates" technique), we pro pose here a softened version in which the degree of stationarization can be controlled by a perturbation of the actual phase. A basic theory for such "transitional surrogates" is first discussed, with emphasis on two effective constructions based on either white Gaussian noise or random walks. Some typical examples are considered for illustration, and performance evaluations are provided for supporting the usefulness of the approach in the context of stationarity testing.

An operational framework is developed for testing stationarity relatively to an observation scale. The proposed method makes use of a family of stationary surrogates for defining the null hypothesis of stationarity. As a further contribution to the field, we demonstrate the strict-sense stationarity of surrogate signals and we exploit this property to derive the asymptotic distributions of their spectrogram and power spectral density. A statistical hypothesis testing framework is then proposed to check signal stationarity. Finally, some results are shown on a typical model of signals that can be thought of as stationary or nonstationary, depending on the observation scale used.

Direct imaging of exoplanets involves very low signal-to-noise ratio data, that need to be carefully acquired and processed. Multi-band devices enable the simultaneous record of images in different spectral bands. They can be used either for spectroscopy purposes or to improve detection capabilities. This work aims at detecting a potential source, when the source moves on a random background spatially and inter-spectrally correlated. A hierarchic Bayesian model is derived to take into account correlations and their randomness, and the high dynamic range involved in potentially low signal to noise ratio data. The point null hypothesis test is addressed using the posterior distribution of the likelihood ratio. Its percentiles are computed using a simple Markov Chain Monte Carlo method. This algorithm is illustrated using ID simulated data of a dual band signal.

With the current development of astronomical instruments able to detect the direct light of exoplanets, such as the very large telescope instrument SPHERE, statistical tools need to be developed in order to make precise detection and estimation assessments. We propose a detection algorithm that delivers an estimation of the position and the intensity of the potentially detected exoplanet. Because of the numerical constraints on the signal processing task, the detector- estimator is based on a simplified Gaussian model where we use a field-rotation effect as the main discriminating criterium between the planet and the speckles. However, for a given threshold on the statistics test, the probability of false alarm (PFA) and the probability of detection (PD) need to be accurate. For that purpose we use a more realistic model and the saddlepoint approximation to compute the PFA and PD. The performance of the approximation is evaluated on a ID data model.

This paper evaluates the potential interest of using bivariate gamma distributions for image registration and change detection. The first part of this paper studies estimators for the parameters of bivariate gamma distributions based on the maximum likelihood principle and the method of moments. The performance of both methods are compared in terms of estimated mean square errors and theoretical asymptotic variances. The mutual information is a classical similarity measure which can be used for image registration or change detection. The second part of the paper studies some properties of the mutual information for bivariate Gamma distributions. Image registration and change detection techniques based on bivariate gamma distributions are finally investigated. Simulation results conducted on synthetic and real data are very encouraging. Bivariate gamma distributions are good candidates allowing us to develop new image registration algorithms and new change detectors.

Estimating the parameters of multivariate distributions whose densities or masses cannot be expressed in tractable closed-form is a challenging problem. This paper concentrates on a family of such discrete distributions referred to as multivariate mixed Poisson distributions (MMPDs). These distributions are interesting for modeling correlations between adjacent pixels of active and astronomical images. Several estimators of MMPD parameters are investigated. These estimators include a composite likelihood estimator and a non-linear least squares estimator

This paper studies a measure of detection performance for testing binary hypotheses by using discrete test statistics. This measure is the area under the receiver operating characteristics. This theory is applied to the detection of changes in low-flux images with the Neyman Pearson detector. An approximation of this measure can be derived. It allows to define a specific signal to noise ratio for the low-flux detector.

The paper addresses the problem of detecting changes in the parameters of multivariate Poisson sequences. The Neyman Pearson Detector (NPD) and the, Generalized Likelihood Ratio Detector (GLRD) are easily derived for iid Poisson sequences. Unfortunately, the problem is more' complicated for correlated Poisson sequences. This paper studies the performance of the detectors obtained under the iid assumption, when the observed data are distributed according to multivariate correlated Poisson sequences. Theoretical expressions of the receiver operating characteristics are derived when the change location is known. These curves provide a reference to which other detectors can be compared. The more realistic situation of an unknown change location is finally considered.

The paper addresses the problem of determining the Cramer-Rao lower bounds for noise and abrupt change parameters, for steplike signals corrupted by multiplicative and/or additive noise. Closed-form expressions are derived for an ideal step with a known changepoint. For an unknown changepoint, the noise-free signal is modeled by a sigmoidal function parametrized by location and step rise parameters. The noise and step change CRLBs are then shown to be well approximated by the more tractable expressions derived for a known changepoint.

We present an algorithm for the detection of extra-solar planets by occultation on the satellite COROT. Under a high flux assumption, the signal is modeled as an autoregressive process having equal mean and variance. A transit of a planet in front of a star will produce an abrupt jump in the mean/variance of the process. The Neyman-Pearson detector is derived when the abrupt change parameters are known. The theoretical distribution of the test statistic is obtained allowing the computation of the ROC curves. The generalized likelihood ratio detector is then studied for the practical case were the change parameters are unknown. This detector requires the maximum likelihood estimates of the parameters. ROC curves are then determined using computer simulations.

This article tackles the problem of a Gaussian band-limited continuous signal with unknown characteristics sampled with jitter. Under this weak assumption, we demonstrate a relation linking the power spectral density of the continuous signal to the second and fourth order statistics of the measured samples. A fundamental point is that this relation does not require a knowledge of the jitter characteristics. This result can be exploited for the derivation of spectral estimation algorithms when the jitter is unknown or jitter detection tests when the sampled signal is unknown. A simulation of spectral estimation confirms the validity of the result.

The aim of this paper is Bayesian estimation of the parameters of a polynomial phase signal. This problem, encountered in radar systems for example, is usually solved using a time-frequency analysis or phase-only algorithms. A Bayesian approach using Markov chain Monte Carlo (MCMC) methods for estimating a posteriori densities of the polynomial parameters is proposed. The main advantage of this approach is that it gives a direct estimation of all polynomial coefficients, contrary to previously developed algorithms.

The paper treats the problem of ambiguity resolution using non-uniform sampling. This problem occurs for Doppler estimation in coherent pulsed Doppler radar. In the paper, the authors study the case where the duration between two samples is a linear function of time: quadratic sampling. Assuming that the continuous signal is stationary, the sampled signal will be non-stationary. The autocorrelation of this signal is derived and the Wigner distribution of the sampled signal related to the spectrum of the continuous signal. As a consequence, a time frequency relief of the signal will verify symmetries. These constraints, assuming an AR evolutive model for the sampled signal and band limitation for the continuous signal, allow the derivation of a particular time varying model for the samples. An associated estimation algorithm, leading to the unfolded spectrum is then proposed.

The paper deals with high-order moment-ergodic properties of a complex process composed of superimposed sinusoids. This is efficiently achieved using a state-space representation of the signal and Kronecker algebra. First, a simple formulation of the stationarity hypothesis is given, and finally, the moment-ergodic theorem for the associated moments is derived.>

The problem of the estimation of the fundamental frequency of a noisy complex sinusoidal signal with M harmonic related frequencies is addressed. This problem is studied by considering an extension of the MUSIC algorithm based on the minimization of the distance between two M-dimensional subspaces. An approach dual to the MUSIC algorithm is then proposed. This method leads to an optimized version with slight additional cost. Simulations are presented to illustrate the behavior of the estimators.>

The problem of estimating the frequencies of a complex sinusoidal signal corrupted by a correlated Gaussian noise is dealt with using the fourth order statistics. A definition of the complex fourth order statistics is introduced. A fourth order moments matrix, M4, and a fourth order cumulant matrix, C4, are defined. In the general case of a nonGaussian signal corrupted by a Gaussian noise, expressions of M4 and C4 in function of the second-order moment matrix of the noise and the fourth and second order moment matrices of the signal are given. With these expressions, the complex harmonic retrieval problem is solved and simulations are performed.>

The autoregressive principal component technique uses the singular value decomposition (SVD) of an augmented dimension estimated autocorrelation matrix R to provide an accurate identification of frequencies in white noise. To avoid the eigen-decomposition of the matrix R, S.M. Kay and A.K. Shaw (1988) have applied a transformation on the inverse of R that truncates the eigenvalues associated with the noise. However, this technique requires the inversion of R and of another matrix. Two transformations that are applied directly to the matrix R are proposed. One is based on the matrix exponential and the other on component matrices. Another transformation analog to the MUSIC method without calculus of the eigenvectors is also proposed.>