arXiv subjects

Mohammed Nabil El Korso

Publications and source records attributed to Mohammed Nabil El Korso.

At least 19 recordsLinked to original sources

arXiv2026

Dimensionality Reduction for Hyperspectral Image Classification

This paper addresses the issue of supervised classification in the context of hyperspectral satellite images. It deals with two fundamental aspects: dimensionality reduction of data and the selection of appropriate supervised classification techniques. Firstly, we delve into dimensionality reduction, a critical step in simplifying the management of hyperspectral data. The reduction aims to decrease complexity in terms of memory and computing time. We examine two commonly used methods: Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA). Subsequently, we explore the selection of the most suitable supervised classification algorithms for hyperspectral images. We compare the performance of three methods: K-Nearest Neighbors (KNN), Support Vector Machines (SVM), and Random Forest (RF) using real hyperspectral data. The results highlight that the combination of PCA and RF yields the highest overall accuracy and Kappa coefficient.

cs.CV↗

arXiv2026

Stochastic Expectation Maximization for Robust State-Space Radio Interferometric Imaging

State--space models provide a flexible framework for analyzing dynamical systems, yet they often rely on Gaussian assumptions that fail to capture heavy-tailed or outlier-prone measurement noise. We propose a robust estimation scheme for linear state--space models subject to compound-Gaussian noise, as encountered for instance in radio interferometry affected by radio-frequency interference (RFI). The method relies on a Stochastic Approximation Expectation--Maximization (SAEM) algorithm in which the standard E-step is replaced by Monte Carlo sampling of the latent states and noise texture through closed-form Gibbs updates, enabling tractable inference despite the heavy-tailed likelihood. Numerical experiments show that the proposed method significantly improves reconstruction fidelity and robustness to RFI, outperforming a Gaussian EM algorithm and even an oracle RTS smoother. These results highlight the benefits of heavy-tailed state--space modeling and SAEM-based inference in interference-dominated imaging scenarios.

astro-ph.IM↗

arXiv2026

Amortized Variational Inference for Logistic Regression with Missing Covariates

Missing covariate data pose a significant challenge to statistical inference and machine learning, particularly for classification tasks like logistic regression. Classical iterative approaches (EM, multiple imputation) are often computationally intensive, sensitive to high missingness rates, and limited in uncertainty propagation. Recent deep generative models based on VAEs show promise but rely on complex latent representations. We propose Amortized Variational Inference for Logistic Regression (AV-LR), a unified end-to-end framework for binary logistic regression with missing covariates. AV-LR integrates a probabilistic generative model with a simple amortized inference network, trained jointly by maximizing the evidence lower bound. Unlike competing methods, AV-LR performs inference directly in the space of missing data without additional latent variables, using a single inference network and a linear layer that jointly estimate regression parameters and the missingness mechanism. AV-LR achieves estimation accuracy comparable to or better than state-of-the-art EM-like algorithms, with significantly lower computational cost. It naturally extends to missing-not-at-random settings by explicitly modeling the missingness mechanism. Empirical results on synthetic and real-world datasets confirm its effectiveness and efficiency across various missing-data scenarios.

cs.LG↗

arXiv2026

Missing Data in Signal Processing and Machine Learning: Models, Methods and Modern Approaches

This tutorial aims to provide signal processing (SP) and machine learning (ML) practitioners with vital tools, in an accessible way, to answer the question: How to deal with missing data? There are many strategies to handle incomplete signals. In this paper, we propose to group these strategies based on three common analytical tasks: i) missing-data imputation, ii) estimation with missing values and iii) prediction with missing values. We focus on methodological and experimental results through specific case studies on real-world applications. Promising and future research directions are also discussed. We hope that the proposed conceptual framework and the presentation of recent missing-data problems related will encourage researchers of the SP and ML communities to develop original methods and to efficiently deal with new applications involving missing data.

eess.SP↗

arXiv2025

Maximum Likelihood for Logistic Regression Model with Incomplete and Hybrid-Type Covariates

Logistic regression is a fundamental and widely used statistical method for modeling binary outcomes based on covariates. However, the presence of missing data, particularly in settings involving hybrid covariates (a mix of discrete and continuous variables), poses significant challenges. In this paper, we propose a novel Expectation-Maximization based algorithm tailored for parameter estimation in logistic regression models with missing hybrid covariates. The proposed method is specifically designed to handle these complexities, delivering efficient parameter estimates. Through comprehensive simulations and real-world application, we demonstrate that our approach consistently outperforms traditional methods, achieving superior accuracy and reliability.

stat.ME↗

arXiv2025

Sequential Covariance Fitting for InSAR Phase Linking

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.

stat.AP↗

arXiv2023

Multifrequency Array Calibration in Presence of Radio Frequency Interferences

Radio interferometers are phased arrays producing high-resolution images from the covariance matrix of measurements. Calibration of such instruments is necessary and is a critical task. This is how the estimation of instrumental errors is usually done thanks to the knowledge of referenced celestial sources. However, the use of high sensitive antennas in modern radio interferometers (LOFAR, SKA) brings a new challenge in radio astronomy because there are more sensitive to Radio Frequency Interferences (RFI). The presence of RFI during the calibration process generally induces biases in state-of-the-art solutions. The purpose of this paper is to propose an alternative to alleviate the effects of RFI. For that, we first propose a model to take into account the presence of RFI in the data across multiple frequency channels thanks to a low-rank structured noise. We then achieve maximum likelihood estimation of the calibration parameters with a Space Alternating Generalized Expectation-Maximization (SAGE) algorithm for which we derive originally two sets of complete data allowing close form expressions for the updates. Numerical simulations show a significant gain in performance for RFI corrupted data in comparison with some more classical methods.

astro-ph.IM↗

arXiv2021

Robust low-rank covariance matrix estimation with a general pattern of missing values

This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume unstructured signal models. The former can be inaccurate in real-world data sets in which heterogeneity causes heavy-tail distributions, while the latter does not profit from the usual low-rank structure of the signal. Taking advantage of both worlds, a covariance matrix estimation procedure is designed on a robust (mixture of scaled Gaussian) low-rank model by leveraging the observed-data likelihood function within an expectation-maximization algorithm. It is also designed to handle general pattern of missing values. The proposed procedure is first validated on simulated data sets. Then, its interest for classification and clustering applications is assessed on two real data sets with missing values, which include multispectral and hyperspectral time series.

stat.ME↗

arXiv2020

Multi-frequency calibration for DOA estimation with distributed sensors

In this work, we investigate direction finding in the presence of sensor gain uncertainties and directional perturbations for sensor array processing in a multi-frequency scenario. Specifically, we adopt a distributed optimization scheme in which coherence models are incorporated and local agents exchange information only between connected nodes in the network, i.e., without a fusion center. Numerical simulations highlight the advantages of the proposed parallel iterative technique in terms of statistical and computational efficiency.

eess.SP↗

arXiv2019

Asymptotic Performance of Complex M-estimators for Multivariate Location and Scatter Estimation

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 complex M-estimators for multivariate location and scatter matrix estimation.

eess.SP↗

arXiv2018

Iterative Marginal Maximum Likelihood DOD and DOA Estimation for MIMO Radar in the Presence of SIRP Clutter

The spherically invariant random process (SIRP) clutter model is commonly used in scenarios where the radar clutter cannot be correctly modeled as a Gaussian process. In this short communication, we devise a novel Maximum-Likelihood (ML)-based iterative estimator for direction-of-departure and direction-of-arrival estimation in the Multiple-input multiple-output (MIMO) radar context in the presence of SIRP clutter. The proposed estimator employs a stepwise numerical concentration approach w.r.t. the objective function related to the marginal likelihood of the observation data. Our estimator leads to superior performance, as our simulations show, w.r.t. to the existing likelihood based methods, namely, the conventional, the conditional and the joint likelihood based estimators, and w.r.t. the robust subspace decomposition based methods. Finally, interconnections and comparison between the Iterative Marginal ML Estimator (IMMLE), Iterative Joint ML Estimator (IJMLE) and Iterative Conditional ML Estimator (ICdMLE) are provided.

eess.SP↗

arXiv2018

Robust distributed calibration of radio interferometers with direction dependent distortions

In radio astronomy, accurate calibration is of crucial importance for the new generation of radio interferometers. More specifically, because of the potential presence of outliers which affect the measured data, robustness needs to be ensured. On the other hand, calibration is improved by taking advantage of these new instruments and exploiting the known structure of parameters of interest across frequency. Therefore, we propose in this paper an iterative robust multi-frequency calibration algorithm based on a distributed and consensus optimization scheme which aims to estimate the complex gains of the receivers and the directional perturbations caused by the ionosphere. Numerical simulations reveal that the proposed distributed calibration technique outperforms the conventional non-robust algorithm and per-channel calibration.

astro-ph.IM↗

arXiv2018

Robust Calibration of Radio Interferometers in Multi-Frequency Scenario

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.

stat.AP↗

arXiv2018

Bayesian Calibration using Different Prior Distributions: an Iterative Maximum A Posteriori Approach for Radio Interferometers

In this paper, we aim to design robust estimation techniques based on the compound-Gaussian (CG) process and adapted for calibration of radio interferometers. The motivation beyond this is due to the presence of outliers leading to an unrealistic traditional Gaussian noise assumption. Consequently, to achieve robustness, we adopt a maximum a posteriori (MAP) approach which exploits Bayesian statistics and follows a sequential updating procedure here. The proposed algorithm is applied in a multi-frequency scenario in order to enhance the estimation and correction of perturbation effects. Numerical simulations assess the performance of the proposed algorithm for different noise models, Student's t, K, Laplace, Cauchy and inverse-Gaussian compound-Gaussian distributions w.r.t. the classical non-robust Gaussian noise assumption.

stat.AP↗

arXiv2017

Robust Calibration of Radio Interferometers in Non-Gaussian Environment

The development of new phased array systems in radio astronomy, as the low frequency array (LOFAR) and the square kilometre array (SKA), formed of a large number of small and flexible elementary antennas, has led to significant challenges. Among them, model calibration is a crucial step in order to provide accurate and thus meaningful images and requires the estimation of all the perturbation effects introduced along the signal propagation path, for a specific source direction and antenna position. Usually, it is common to perform model calibration using the a priori knowledge regarding a small number of known strong calibrator sources but under the assumption of Gaussianity of the noise. Nevertheless, observations in the context of radio astronomy are known to be affected by the presence of outliers which are due to several causes, e.g., weak non-calibrator sources or man made radio frequency interferences. Consequently, the classical Gaussian noise assumption is violated leading to severe degradation in performances. In order to take into account the outlier effects, we assume that the noise follows a spherically invariant random distribution. Based on this modeling, a robust calibration algorithm is presented in this paper. More precisely, this new scheme is based on the design of an iterative relaxed concentrated maximum likelihood estimation procedure which allows to obtain closed-form expressions for the unknown parameters with a reasonable computational cost. This is of importance as the number of estimated parameters depends on the number of antenna elements, which is large for the new generation of radio interferometers. Numerical simulations reveal that the proposed algorithm outperforms the state-of-the-art calibration techniques.

stat.AP↗

arXiv2017

Bayesian Lower Bounds for Dense or Sparse (Outlier) Noise in the RMT Framework

Robust estimation is an important and timely research subject. In this paper, we investigate performance lower bounds on the mean-square-error (MSE) of any estimator for the Bayesian linear model, corrupted by a noise distributed according to an i.i.d. Student's t-distribution. This class of prior parametrized by its degree of freedom is relevant to modelize either dense or sparse (accounting for outliers) noise. Using the hierarchical Normal-Gamma representation of the Student's t-distribution, the Van Trees' Bayesian Cramér-Rao bound (BCRB) on the amplitude parameters is derived. Furthermore, the random matrix theory (RMT) framework is assumed, i.e., the number of measurements and the number of unknown parameters grow jointly to infinity with an asymptotic finite ratio. Using some powerful results from the RMT, closed-form expressions of the BCRB are derived and studied. Finally, we propose a framework to fairly compare two models corrupted by noises with different degrees of freedom for a fixed common target signal-to-noise ratio (SNR). In particular, we focus our effort on the comparison of the BCRBs associated with two models corrupted by a sparse noise promoting outliers and a dense (Gaussian) noise, respectively.

stat.ME↗

arXiv2017

Joint ML calibration and DOA estimation with separated arrays

This paper investigates parametric direction-of-arrival (DOA) estimation in a particular context: i) each sensor is characterized by an unknown complex gain and ii) the array consists of a collection of subarrays which are substantially separated from each other leading to a structured noise covariance matrix. We propose two iterative algorithms based on the maximum likelihood (ML) estimation method adapted to the context of joint array calibration and DOA estimation. Numerical simulations reveal that the two proposed schemes, the iterative ML (IML) and the modified iterative ML (MIML) algorithms for joint array calibration and DOA estimation, outperform the state of the art methods and the MIML algorithm reaches the Cramér-Rao bound for a low number of iterations.

stat.AP↗

arXiv2017

Relaxed concentrated MLE for robust calibration of radio interferometers

In this paper, we investigate the calibration of radio interferometers in which Jones matrices are considered to model the interaction between the incident electromagnetic field and the antennas of each station. Specifically, perturbation effects are introduced along the signal path, leading to the conversion of the plane wave into an electric voltage by the receptor. In order to design a robust estimator, the noise is assumed to follow a spherically invariant random process (SIRP). The derived algorithm is based on an iterative relaxed concentrated maximum likelihood estimator (MLE), for which closed-form expressions are obtained for most of the unknown parameters.

astro-ph.IM↗