Multifractal analysis provides the theoretical and practical tools for describing the fluctuations of pointwise regularity in data and has led to many successful applications in signal and image processing. Originally limited to the analysis of single time series or images, a definition of multivariate multifractal analysis, i.e., the joint multifractal analysis of several data components, was recently proposed and was shown to effectively quantify local or transient dependencies in data regularity, beyond linear correlation. However, the accurate estimation of the associated matrix-valued joint multifractality parameters is notoriously difficult, thus limiting its practical usefulness. Leveraging a recent statistical model for bivariate multifractality, the goal of this work is to define and study Bayesian estimators designed to bypass this difficulty. Specifically, we study the original use of two different priors, combined with two different averages (arithmetic and Karcher means), for bivariate multifractal analysis. Monte Carlo simulations with synthetic data allow us to appreciate their relative performance and to conclude that our novel and original estimator based on a scaled inverse Wishart prior and the Karcher mean yields particularly favorable results with up to 5 times smaller rootmean-squared error than previous formulations.

This paper studies a new expectation maximization (EM) algorithm to estimate the centers and radii of multiple hyperspheres. The proposed method introduces latent variables indicating to which hypersphere each vector from the dataset belongs to, in addition to random latent vectors having an a priori von Mises-Fisher distribution characterizing the location of each vector on the different hyperspheres. This statistical model allows a complete data likelihood to be derived, whose expected value conditioned on the observed data has a known distribution. This property leads to a simple and efficient EM algorithm whose performance is evaluated for the estimation of hypersphere mixtures yielding promising results.

This paper proposes a novel framework for multipath prediction in Global Navigation Satellite System (GNSS) signals. The method extends from dataset generation to deep learning inference through Convolutional Neural Network (CNN). The process starts at the output of the correlation stage of the GNSS receiver. Correlations of the received signal with a local replica over a (Doppler shift, propagation delay)-grid are mapped into grey scale 2D images. They depict the received information possibly contaminated by multipath propagation. The images feed a CNN for automatic feature construction and multipath pattern detection. The issue of unavailability of a large amount of supervised data required for CNN training has been overcome by the development of a synthetic data generator. It implements a well-established and documented theoretical model. A comparison of synthetic data with real samples is proposed. The complete framework is tested for various signal characteristics and algorithm parameters. The prediction accuracy does not fall below 93% for C/N0 ratio as low as 36 dBHz, corresponding to poor receiving conditions. In addition, the model turns out to be robust to the reduction of image resolution. Its performance is also measured and compared with an alternative Support Vector Machines (SVM) technique. The results show the undeniable superiority of the proposed CNN algorithm over the SVM benchmark.

The popular Discrete Fourier Transform (DFT) is known to be a sub‐optimal frequency estimation technique for a finite transform length. In order to approach the Cramer‐Rao Lower Bound (CRLB), many refinement techniques have been considered, but little considering both zero padding or tapering, also known as windowing or apodisation. In this paper, a frequency estimator with closed‐form combination of three DFT samples is generalized to zero padding and tapered data within the class of cosine windowing. Root Mean Squared Error (RMSE) is shown to approach the CRLB in the case of a single tone signal with additive white Gaussian noise. Compared to state‐of‐the‐art techniques, the proposed algorithm improves the frequency RMSE up to 1 dB when using significant zero‐padding lengths (K ≥ 2 N) and for small to moderate SNR, which is the most challenging case for practical radar applications.

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.