arXiv subjects

Abdelhak M. Zoubir

Publications and source records attributed to Abdelhak M. Zoubir.

At least 37 records · Page 2Linked to original sources

arXiv2023

Robust Low-Rank Matrix Completion via a New Sparsity-Inducing Regularizer

This paper presents a novel loss function referred to as hybrid ordinary-Welsch (HOW) and a new sparsity-inducing regularizer associated with HOW. We theoretically show that the regularizer is quasiconvex and that the corresponding Moreau envelope is convex. Moreover, the closed-form solution to its Moreau envelope, namely, the proximity operator, is derived. Compared with nonconvex regularizers like the lp-norm with 0<p<1 that requires iterations to find the corresponding proximity operator, the developed regularizer has a closed-form proximity operator. We apply our regularizer to the robust matrix completion problem, and develop an efficient algorithm based on the alternating direction method of multipliers. The convergence of the suggested method is analyzed and we prove that any generated accumulation point is a stationary point. Finally, experimental results based on synthetic and real-world datasets demonstrate that our algorithm is superior to the state-of-the-art methods in terms of restoration performance.

eess.IV↗

arXiv2023

Radiation Hardness of MALTA2 Monolithic CMOS Sensors on Czochralski Substrates

MALTA2 is the latest full-scale prototype of the MALTA family of Depleted Monolithic Active Pixel Sensors (DMAPS) produced in Tower Semiconductor 180 nm CMOS technology. In order to comply with the requirements of High Energy Physics (HEP) experiments, various process modifications and front-end changes have been implemented to achieve low power consumption, reduce Random Telegraph Signal (RTS) noise, and optimise the charge collection geometry. Compared to its predecessors, MALTA2 targets the use of a high-resistivity, thick Czochralski (Cz) substrates in order to demonstrate radiation hardness in terms of detection efficiency and timing resolution up to 3E15 1 MeV neq/cm2 with backside metallisation to achieve good propagation of the bias voltage. This manuscript shows the results that were obtained with non-irradiated and irradiated MALTA2 samples on Cz substrates from the CERN SPS test beam campaign from 2021-2023 using the MALTA telescope.

physics.ins-det↗

arXiv2023

Identifying the Complete Correlation Structure in Large-Scale High-Dimensional Data Sets with Local False Discovery Rates

The identification of the dependent components in multiple data sets is a fundamental problem in many practical applications. The challenge in these applications is that often the data sets are high-dimensional with few observations or available samples and contain latent components with unknown probability distributions. A novel mathematical formulation of this problem is proposed, which enables the inference of the underlying correlation structure with strict false positive control. In particular, the false discovery rate is controlled at a pre-defined threshold on two levels simultaneously. The deployed test statistics originate in the sample coherence matrix. The required probability models are learned from the data using the bootstrap. Local false discovery rates are used to solve the multiple hypothesis testing problem. Compared to the existing techniques in the literature, the developed technique does not assume an a priori correlation structure and work well when the number of data sets is large while the number of observations is small. In addition, it can handle the presence of distributional uncertainties, heavy-tailed noise, and outliers.

stat.ME↗

arXiv2023

Attacks on Robust Distributed Learning Schemes via Sensitivity Curve Maximization

Distributed learning paradigms, such as federated or decentralized learning, allow a collection of agents to solve global learning and optimization problems through limited local interactions. Most such strategies rely on a mixture of local adaptation and aggregation steps, either among peers or at a central fusion center. Classically, aggregation in distributed learning is based on averaging, which is statistically efficient, but susceptible to attacks by even a small number of malicious agents. This observation has motivated a number of recent works, which develop robust aggregation schemes by employing robust variations of the mean. We present a new attack based on sensitivity curve maximization (SCM), and demonstrate that it is able to disrupt existing robust aggregation schemes by injecting small, but effective perturbations.

cs.LG↗

arXiv2023

Performance of the MALTA Telescope

MALTA is part of the Depleted Monolithic Active Pixel sensors designed in Tower 180nm CMOS imaging technology. A custom telescope with six MALTA planes has been developed for test beam campaigns at SPS, CERN, with the ability to host several devices under test. The telescope system has a dedicated custom readout, online monitoring integrated into DAQ with realtime hit map, time distribution and event hit multiplicity. It hosts a dedicated fully configurable trigger system enabling to trigger on coincidence between telescope planes and timing reference from a scintillator. The excellent time resolution performance allows for fast track reconstruction, due to the possibility to retain a low hit multiplicity per event which reduces the combinatorics. This paper reviews the architecture of the system and its performance during the 2021 and 2022 test beam campaign at the SPS North Area.

hep-ex↗

arXiv2023

Sparse Array Design for Dual-Function Radar-Communications System

The problem of sparse array design for dual-function radar-communications is investigated. Our goal is to design a sparse array which can simultaneously shape desired beam responses and serve multiple downlink users with the required signal-to-interference-plus-noise ratio levels. Besides, we also take into account the limitation of the radiated power by each antenna. The problem is formulated as a quadratically constrained quadratic program with a joint-sparsity-promoting regularization, which is NP-hard. The resulting problem is solved by the consensus alternating direction method of multipliers, which enjoys parallel implementation. Numerical simulations exhibit the effectiveness and superiority of the proposed method which leads to a more power-efficient solution.

eess.SY↗

arXiv2023

Convergence Analysis of Consensus-ADMM for General QCQP

We analyze the convergence properties of the consensus-alternating direction method of multipliers (ADMM) for solving general quadratically constrained quadratic programs. We prove that the augmented Lagrangian function value is monotonically non-increasing as long as the augmented Lagrangian parameter is chosen to be sufficiently large. Simulation results show that the augmented Lagrangian function is bounded from below when the matrix in the quadratic term of the objective function is positive definite. In such a case, the consensus-ADMM is convergent.

eess.SP↗

arXiv2022

Low-Rank and Row-Sparse Decomposition for Joint DOA Estimation and Distorted Sensor Detection

Distorted sensors could occur randomly and may lead to the breakdown of a sensor array system. We consider an array model within which a small number of sensors are distorted by unknown sensor gain and phase errors. With such an array model, the problem of joint direction-of-arrival (DOA) estimation and distorted sensor detection is investigated and the problem is formulated under the framework of low-rank and row-sparse decomposition. We derive an iteratively reweighted least squares (IRLS) algorithm to solve the resulting problem in both noiseless and noisy cases. The convergence property of the IRLS algorithm is analyzed by means of the monotonicity and boundedness of the objective function. Extensive simulations are conducted regarding parameter selection, convergence speed, computational complexity, and performances of DOA estimation as well as distorted sensor detection. Even though the IRLS algorithm is slightly worse than the alternating direction method of multipliers in detecting the distorted sensors, the results show that our approach outperforms several state-of-the-art techniques in terms of convergence speed, computational cost, and DOA estimation performance.

eess.SP↗

arXiv2022

Multiple Hypothesis Testing Framework for Spatial Signals

The problem of identifying regions of spatially interesting, different or adversarial behavior is inherent to many practical applications involving distributed multisensor systems. In this work, we develop a general framework stemming from multiple hypothesis testing to identify such regions. A discrete spatial grid is assumed for the monitored environment. The spatial grid points associated with different hypotheses are identified while controlling the false discovery rate at a pre-specified level. Measurements are acquired using a large-scale sensor network. We propose a novel, data-driven method to estimate local false discovery rates based on the spectral method of moments. Our method is agnostic to specific spatial propagation models of the underlying physical phenomenon. It relies on a broadly applicable density model for local summary statistics. In between sensors, locations are assigned to regions associated with different hypotheses based on interpolated local false discovery rates. The benefits of our method are illustrated by applications to spatially propagating radio waves.

eess.SP↗

arXiv2022

Robust and Efficient Aggregation for Distributed Learning

Distributed learning paradigms, such as federated and decentralized learning, allow for the coordination of models across a collection of agents, and without the need to exchange raw data. Instead, agents compute model updates locally based on their available data, and subsequently share the update model with a parameter server or their peers. This is followed by an aggregation step, which traditionally takes the form of a (weighted) average. Distributed learning schemes based on averaging are known to be susceptible to outliers. A single malicious agent is able to drive an averaging-based distributed learning algorithm to an arbitrarily poor model. This has motivated the development of robust aggregation schemes, which are based on variations of the median and trimmed mean. While such procedures ensure robustness to outliers and malicious behavior, they come at the cost of significantly reduced sample efficiency. This means that current robust aggregation schemes require significantly higher agent participation rates to achieve a given level of performance than their mean-based counterparts in non-contaminated settings. In this work we remedy this drawback by developing statistically efficient and robust aggregation schemes for distributed learning.

cs.LG↗

arXiv2022

Off-Grid Direction-of-Arrival Estimation Using Second-Order Taylor Approximation

The problem of off-grid direction-of-arrival (DOA) estimation is investigated. We develop a grid-based method to jointly estimate the closest spatial frequency (the sine of DOA) grids, and the gaps between the estimated grids and the corresponding frequencies. By using a second-order Taylor approximation, the data model under the framework of joint-sparse representation is formulated. We point out an important property of the signals of interest in the model, namely the proportionality relationship, which is empirically demonstrated to be useful in the sense that it increases the probability of the mixing matrix satisfying the block restricted isometry property. Simulation examples demonstrate the effectiveness and superiority of the proposed method against several state-of-the-art grid-based approaches.

eess.SP↗

arXiv2021

Minimax Robust Landmine Detection Using Forward-Looking Ground-Penetrating Radar

We propose a robust likelihood-ratio test (LRT) to detect landmines and unexploded ordnance using a forward-looking ground-penetrating radar. Instead of modeling the distributions of the target and clutter returns with parametric families, we construct a band of feasible probability densities under each hypothesis. The LRT is then devised based on the least favorable densities within the bands. This detector is designed to maximize the worst-case performance over all feasible density pairs and, hence, does not require strong assumptions about the clutter and noise distributions. The proposed technique is evaluated using electromagnetic field simulation data of shallow-buried targets. We show that, compared to detectors based on parametric models, robust detectors can lead to significantly reduced false alarm rates, particularly in cases where there is a mismatch between the assumed model and the true distributions.

eess.SP↗

arXiv2021

Robust Regularized Locality Preserving Indexing for Fiedler Vector Estimation

The Fiedler vector of a connected graph is the eigenvector associated with the algebraic connectivity of the graph Laplacian and it provides substantial information to learn the latent structure of a graph. In real-world applications, however, the data may be subject to heavy-tailed noise and outliers which results in deteriorations in the structure of the Fiedler vector estimate. We design a Robust Regularized Locality Preserving Indexing (RRLPI) method for Fiedler vector estimation that aims to approximate the nonlinear manifold structure of the Laplace Beltrami operator while minimizing the negative impact of outliers. First, an analysis of the effects of two fundamental outlier types on the eigen-decomposition for block affinity matrices which are essential in cluster analysis is conducted. Then, an error model is formulated and a robust Fiedler vector estimation algorithm is developed. An unsupervised penalty parameter selection algorithm is proposed that leverages the geometric structure of the projection space to perform robust regularized Fiedler estimation. The performance of RRLPI is benchmarked against existing competitors in terms of detection probability, partitioning quality, image segmentation capability, robustness and computation time using a large variety of synthetic and real data experiments.

eess.SP↗

arXiv2021

Minimax Robust Detection: Classic Results and Recent Advances

This paper provides an overview of results and concepts in minimax robust hypothesis testing for two and multiple hypotheses. It starts with an introduction to the subject, highlighting its connection to other areas of robust statistics and giving a brief recount of the most prominent developments. Subsequently, the minimax principle is introduced and its strengths and limitations are discussed. The first part of the paper focuses on the two-hypothesis case. After briefly reviewing the basics of statistical hypothesis testing, uncertainty sets are introduced as a generic way of modeling distributional uncertainty. The design of minimax detectors is then shown to reduce to the problem of determining a pair of least favorable distributions, and different criteria for their characterization are discussed. Explicit expressions are given for least favorable distributions under three types of uncertainty: $\varepsilon$-contamination, probability density bands, and $f$-divergence balls. Using examples, it is shown how the properties of these least favorable distributions translate to properties of the corresponding minimax detectors. The second part of the paper deals with the problem of robustly testing multiple hypotheses, starting with a discussion of why this is fundamentally different from the binary problem. Sequential detection is then introduced as a technique that enables the design of strictly minimax optimal tests in the multi-hypothesis case. Finally, the usefulness of robust detectors in practice is showcased using the example of ground penetrating radar. The paper concludes with an outlook on robust detection beyond the minimax principle and a brief summary of the presented material.

cs.IT↗

arXiv2021

Bayesian Sequential Joint Detection and Estimation under Multiple Hypotheses

We consider the problem of jointly testing multiple hypotheses and estimating a random parameter of the underlying distribution. This problem is investigated in a sequential setup under mild assumptions on the underlying random process. The optimal method minimizes the expected number of samples while ensuring that the average detection/estimation errors do not exceed a certain level. After converting the constrained problem to an unconstrained one, we characterize the general solution by a non-linear Bellman equation, which is parametrized by a set of cost coefficients. A strong connection between the derivatives of the cost function with respect to the coefficients and the detection/estimation errors of the sequential procedure is derived. Based on this fundamental property, we further show that for suitably chosen cost coefficients the solutions of the constrained and the unconstrained problem coincide. We present two approaches to finding the optimal coefficients. For the first approach, the final optimization problem is converted into a linear program, whereas the second approach solves it with a projected gradient ascent. To illustrate the theoretical results, we consider two problems for which the optimal schemes are designed numerically. Using Monte Carlo simulations, it is validated that the numerical results agree with the theory.

eess.SP↗

arXiv2020

Sparsity-aware Robust Community Detection(SPARCODE)

Community detection refers to finding densely connected groups of nodes in graphs. In important applications, such as cluster analysis and network modelling, the graph is sparse but outliers and heavy-tailed noise may obscure its structure. We propose a new method for Sparsity-aware Robust Community Detection (SPARCODE). Starting from a densely connected and outlier-corrupted graph, we first extract a preliminary sparsity improved graph model where we optimize the level of sparsity by mapping the coordinates from different clusters such that the distance of their embedding is maximal. Then, undesired edges are removed and the graph is constructed robustly by detecting the outliers using the connectivity of nodes in the improved graph model. Finally, fast spectral partitioning is performed on the resulting robust sparse graph model. The number of communities is estimated using modularity optimization on the partitioning results. We compare the performance to popular graph and cluster-based community detection approaches on a variety of benchmark network and cluster analysis data sets. Comprehensive experiments demonstrate that our method consistently finds the correct number of communities and outperforms existing methods in terms of detection performance, robustness and modularity score while requiring a reasonable computation time.

eess.SP↗

arXiv2020

Minimax Optimal Sequential Hypothesis Tests for Markov Processes

Under mild Markov assumptions, sufficient conditions for strict minimax optimality of sequential tests for multiple hypotheses under distributional uncertainty are derived. First, the design of optimal sequential tests for simple hypotheses is revisited and it is shown that the partial derivatives of the corresponding cost function are closely related to the performance metrics of the underlying sequential test. Second, an implicit characterization of the least favorable distributions for a given testing policy is stated. By combining the results on optimal sequential tests and least favorable distributions, sufficient conditions for a sequential test to be minimax optimal under general distributional uncertainties are obtained. The cost function of the minimax optimal test is further identified as a generalized $f$-dissimilarity and the least favorable distributions as those that are most similar with respect to this dissimilarity. Numerical examples for minimax optimal sequential tests under different uncertainties illustrate the theoretical results.

math.ST↗

arXiv2020

Doppler Radar for the Extraction of Biomechanical Parameters in Gait Analysis

The applicability of Doppler radar for gait analysis is investigated by quantitatively comparing the measured biomechanical parameters to those obtained using motion capturing and ground reaction forces. Nineteen individuals walked on a treadmill at two different speeds, where a radar system was positioned in front of or behind the subject. The right knee angle was confined by an adjustable orthosis in five different degrees. Eleven gait parameters are extracted from radar micro-Doppler signatures. Here, new methods for obtaining the velocities of individual lower limb joints are proposed. Further, a new method to extract individual leg flight times from radar data is introduced. Based on radar data, five spatiotemporal parameters related to rhythm and pace could reliably be extracted. Further, for most of the considered conditions, three kinematic parameters could accurately be measured. The radar-based stance and flight time measurements rely on the correct detection of the time instant of maximal knee velocity during the gait cycle. This time instant is reliably detected when the radar has a back view, but is underestimated when the radar is positioned in front of the subject. The results validate the applicability of Doppler radar to accurately measure a variety of medically relevant gait parameters. Radar has the potential to unobtrusively diagnose changes in gait, e.g., to design training in prevention and rehabilitation. As contact-less and privacy-preserving sensor, radar presents a viable technology to supplement existing gait analysis tools for long-term in-home examinations.

eess.SP↗