Multifractal analysis has become a reference tool for signal and image processing. Grounded in the quantification of local regularity fluctuations, it has proven useful in an increasing range of applications, yet so far involving only univariate data (scalar valued time series or single channel images). Recently the theoretical ground for multivariate multifractal analysis has been devised, showing potential for quantifying transient higher-order dependence beyond linear correlation among collections of data. However, the accurate estimation of the parameters associated with a multivariate multifractal model remains challenging, especially for small sample size data. This work studies an original Bayesian framework for multivariate multifractal estimation, combining a novel and generic multivariate statistical model, a Whittle-based likelihood approximation and a data augmentation strategy allowing parameter separability. This careful design enables efficient estimation procedures to be constructed for two relevant choices of priors using a Gibbs sampling strategy. Monte Carlo simulations, conducted on synthetic multivariate signals and images with various sample sizes and multifractal parameter settings, demonstrate significant performance improvements over the state of the art, at only moderately larger computational cost. Moreover, we show the relevance of the proposed framework for real-world data modeling in the important application of drowsiness detection from multichannel physiological signals.

Non-linear amplifiers distort signal constellations through their amplitude (AM/AM) and phase (AM/PM) curves versus input amplitude. This causes an increase in the average Error Vector Magnitude (EVM) of the amplified signal. Most commercial EVM simulation software and measurement devices display the ideal and distorted constellations. When computing separate EVMs for each value of ideal symbol power, it is possible to obtain a representation of the effect of AM/AM and AM/PM curves on the constellation. A new type of display, with the distorted constellation folded up on the real axis, is proposed to get a direct representation of the amplifier non-linearity. This can also be used for nonlinear equalization of the signal to improve the EVM.

This paper studies a new attention-based recurrent architecture, lighter and less computationally expensive than a global attention network. This type of architecture achieves better performance than commonly used recurrent networks for time series regression. An application to congestion control is considered, where the history of round trip times (RTT) evolution history is used to monitor congestion control. The performance of the proposed new congestion control strategy is evaluated with both synthetic and real traces, showing that it can be efficiently used to estimate the congestion state of a network.

Most modern congestion control algorithms, that aim to optimize delay and throughput, exploit more metrics than the sole packet loss congestion information. These additional metrics are mostly based on the round trip time evolution and allow congestion controls to reach better performance, in particular on wireless and cellular links as demonstrated by Copa, BBR, or REMY. Basically, these metrics allow congestion control to estimate the queuing level of the path and its evolution, to assess the presence of congestion. Actually, a good estimation of this level obviously prevents congestion losses, but also allows assessing a ratio of error link losses among the whole observed losses. The consistency and accuracy of these metrics are key to good congestion control performance, and this explains, for instance, the good performance of Copa currently in production at Facebook. However, these metrics remain challenging and the quest of an accurate and practical estimation seems complex. This paper investigates how a novel deep learning algorithm, known as Attention, can help in assessing queuing evolution and status on an end-to-end path. Among others, we focus on the evolution of the total time spent by packets in the buffers, which is the key metric of Copa. The results unequivocally demonstrate a better accuracy of this metric used by Copa.

As a multidimensional extension of matrices, tensors (≥3D) are a natural tool for representing and processing multidimensional data arrays. Capturing and recovering this multidimensional data is a long-term challenge in image processing and related fields. In particular, four-dimensional (4D) spectral videos contain highly redundant information across the spatial (2D), spectral (1D) and temporal (1D) axes which can be exploited through a data-learned sparse basis or dictionary. However, in compressive spectral video acquisition (where the data is compressed), tackling dictionary learning is time-consuming since it increases the computational complexity and presents drawbacks for real-time processing, where offline learning is required. In this talk, I will briefly introduce tensor representation and decomposition, and its application on spectral videos in a compressive sensing scenario. Then, I will present an approach to exploit tensor sparse representation for jointly learning the transform basis and the recovering from compressed measurements of a spectral video. I will show some results of the performance of the developed framework compared with matrix-based recovery approaches, including dictionary learning.

Dark Matter is a very active field of research in modern particle physics both on the theory and the experimental side. In this seminar, I will give a pedagogical introduction to particle Dark Matter physics and sketch the main challenges of this area of research. I will first present the astrophysical and cosmological evidence for Dark Matter and its general properties that can be inferred from observation. I will then move to the field of particle physics and discuss the general requirements of a viable Dark Matter model as well as the on-going experimental efforts to detect a potential Darl Matter particle. I will finish by showing a specific Dark Matter model, the supersymmetric WIMP, on which I have worked during my thesis.

Missing data is a recurrent problem in remote sensing, mainly due to cloud coverage for multispectral images and acquisition problems. This can be a critical issue for crop monitoring, especially for applications relying on machine learning techniques, which generally assume that the feature matrix does not have missing values. This paper proposes a Gaussian Mixture Model (GMM) for the reconstruction of parcel-level features extracted from multispectral images. A robust version of the GMM is also investigated, since datasets can be contaminated by inaccurate samples or features (e.g., wrong crop type reported, inaccurate boundaries, undetected clouds, etc). Additional features extracted from Synthetic Aperture Radar (SAR) images using Sentinel-1 data are also used to provide complementary information and improve the imputations. The robust GMM investigated in this work assigns reduced weights to the outliers during the estimation of the GMM parameters, which improves the final reconstruction. These weights are computed at each step of an Expectation-Maximization (EM) algorithm by using outlier scores provided by the isolation forest (IF) algorithm. Experimental validation is conducted on rapeseed and wheat parcels located in the Beauce region (France). Overall, we show that the GMM imputation method outperforms other reconstruction strategies. A mean absolute error (MAE) of 0.013 (resp. 0.019) is obtained for the imputation of the median Normalized Difference Index (NDVI) of the rapeseed (resp. wheat) parcels. Other indicators (e.g., Normalized Difference Water Index) and statistics (for instance the interquartile range, which captures heterogeneity among the parcel indicator) are reconstructed at the same time with good accuracy. In a dataset contaminated by irrelevant samples, using the robust GMM is recommended since the standard GMM imputation can lead to inaccurate imputed values. An application to the monitoring of anomalous crop development in the presence of missing data is finally considered. In this application, using the proposed method leads to the best detection results, especially when SAR data are used jointly with multispectral images. Exploiting the information contained in cloudy multispectral images instead of removing these images is beneficial for this application.

Satellite constellations have taken a new impetus in recent years with even more ambitious future rojects. The momentum has lasted long enough to raise the interest of the research community in addressing the adequacy of protocols mainly designed and used for terrestrial networks, to these satellite communications. There are thus versions of TCP specially designed for satellite networks [1]-[5]. Nevertheless, these previous works could turn out to be obsolete, in particular due to the recent versions of TCP based, for instance, on hybrid-type congestion control algorithms. The question we tackled in this thesis is : are the recent versions of TCP, such as CUBIC and BBR, able to meet the needs in such an environment ? We evaluated the differences between past and currently deployed TCP stacks. We gave an overview of the evolution of the use of protocols from a transport layer point of view of CUBIC and BBR. We identified the sources of delay variation in satellite constellations in order to study their impact and frequency. Modern variants of TCP accommodate this, especially for long flows. We then looked at the fairness between the flows with or without different variants. We highlighted some levels of unfairness in the heterogeneous contexts that are fairly consistent with those found in the terrestrial context. All of these studies were conducted through discrete event simulations but also emulations in order to obtain more realistic results.

Satellite constellations have taken a new impetus in recent years with even more ambitious future rojects. The momentum has lasted long enough to raise the interest of the research community in addressing the adequacy of protocols mainly designed and used for terrestrial networks, to these satellite communications. There are thus versions of TCP specially designed for satellite networks [1]-[5]. Nevertheless, these previous works could turn out to be obsolete, in particular due to the recent versions of TCP based, for instance, on hybrid-type congestion control algorithms. The question we tackled in this thesis is : are the recent versions of TCP, such as CUBIC and BBR, able to meet the needs in such an environment ? We evaluated the differences between past and currently deployed TCP stacks. We gave an overview of the evolution of the use of protocols from a transport layer point of view of CUBIC and BBR. We identified the sources of delay variation in satellite constellations in order to study their impact and frequency. Modern variants of TCP accommodate this, especially for long flows. We then looked at the fairness between the flows with or without different variants. We highlighted some levels of unfairness in the heterogeneous contexts that are fairly consistent with those found in the terrestrial context. All of these studies were conducted through discrete event simulations but also emulations in order to obtain more realistic results.