Spatial and temporal regularization to estimate COVID-19 reproduction number R(t): Promoting piecewise smoothness via convex optimization.

Among the different indicators that quantify the spread of an epidemic such as the on-going COVID-19, stands first the reproduction number which measures how many people can be contaminated by an infected person. In order to permit the monitoring of the evolution of this number, a new estimation procedure is proposed here, assuming a well-accepted model for current incidence data, based on past observations. The novelty of the proposed approach is twofold: 1) the estimation of the reproduction number is achieved by convex optimization within a proximal-based inverse problem formulation, with constraints aimed at promoting piecewise smoothness; 2) the approach is developed in a multivariate setting, allowing for the simultaneous handling of multiple time series attached to different geographical regions, together with a spatial (graph-based) regularization of their evolutions in time. The effectiveness of the approach is first supported by simulations, and two main applications to real COVID-19 data are then discussed. The first one refers to the comparative evolution of the reproduction number for a number of countries, while the second one focuses on French departments and their joint analysis, leading to dynamic maps revealing the temporal co-evolution of their reproduction numbers.

Adaptive multimode signal reconstruction from time-frequency representations.

This paper discusses methods for the adaptive reconstruction of the modes of multicomponent AM-FM signals by their time-frequency (TF) representation derived from their short-time Fourier transform (STFT). The STFT of an AM-FM component or mode spreads the information relative to that mode in the TF plane around curves commonly called ridges. An alternative view is to consider a mode as a particular TF domain termed a basin of attraction. Here we discuss two new approaches to mode reconstruction. The first determines the ridge associated with a mode by considering the location where the direction of the reassignment vector sharply changes, the technique used to determine the basin of attraction being directly derived from that used for ridge extraction. A second uses the fact that the STFT of a signal is fully characterized by its zeros (and then the particular distribution of these zeros for Gaussian noise) to deduce an algorithm to compute the mode domains. For both techniques, mode reconstruction is then carried out by simply integrating the information inside these basins of attraction or domains.

When Interpolation-Induced Reflection Artifact Meets Time-Frequency Analysis.

OBJECTIVE: While extracting the temporal dynamical features based on the time-frequency analyses, like the reassignment and synchrosqueezing transform, attracts more and more interest in biomedical data analysis, we should be careful about artifacts generated by interpolation schemes, in particular when the sampling rate is not significantly higher than the frequency of the oscillatory component we are interested in. METHODS: We formulate the problem called the reflection effect and provide a theoretical justification of the statement. We also show examples in the anesthetic depth analysis with clear but undesirable artifacts. RESULTS: The artifact associated with the reflection effect exists not only theoretically but practically as well. Its influence is pronounced when we apply the time-frequency analyses to extract the time-varying dynamics hidden inside the signal. CONCLUSION: We have to carefully deal with the artifact associated with the reflection effect by choosing a proper interpolation scheme.

2D Prony-Huang transform: a new tool for 2D spectral analysis.

This paper provides an extension of the 1D Hilbert Huang transform for the analysis of images using recent optimization techniques. The proposed method consists of: 1) adaptively decomposing an image into oscillating parts called intrinsic mode functions (IMFs) using a mode decomposition procedure and 2) providing a local spectral analysis of the obtained IMFs in order to get the local amplitudes, frequencies, and orientations. For the decomposition step, we propose two robust 2D mode decompositions based on nonsmooth convex optimization: 1) a genuine 2D approach, which constrains the local extrema of the IMFs and 2) a pseudo-2D approach, which separately constrains the extrema of lines, columns, and diagonals. The spectral analysis step is an optimization strategy based on Prony annihilation property and applied on small square patches of the IMFs. The resulting 2D Prony­Huang transform is validated on simulated and real data.

Characterization of dynamic interactions between cardiovascular signals by time-frequency coherence.

An assessment of the dynamic interactions between cardiovascular signals can provide valuable information to improve the understanding of cardiovascular control. In this study, two methodologies for the characterization of time-frequency (TF) coherence between cardiovascular signals are described. The methodologies are based on the smoothed pseudo-Wigner-Ville distribution (SPWVD) and multitaper spectrogram (MTSP), and include the automatic assessment of the significance level of coherence estimates. The capability to correctly localize TF regions, where signals are locally coupled, is assessed using computer-generated data, and data from healthy volunteers. The SPWVD allows for the localization of these regions with higher accuracy (AC > 96.9% for SNR ≥ 5 dB) than the MTSP (AC > 84.4% for SNR ≥ 5 dB). In 14 healthy subjects, TF coherence analysis was used to describe the changes, which a tilt table test provokes in the cardiovascular control. Orthostatic stress provoked an increase in the coupling between R-R variability (RRV) and systolic arterial pressure variability; it did not provoke any significant changes in the coupling between RRV and respiration. In HF band, it decreased the strength of the coupling between RRV and pulse interval variability estimated from arterial pressure signal.

Phase extraction in speckle interferometry by a circle fitting procedure in the complex plane.

In speckle interferometry (SI), temporal signals are amplitude- and frequency-modulated signals and exhibit a fluctuating background. Prior to phase computation, this background intensity must be eliminated. Here our approach is to build a complex signal from the raw one and to fit a circle through the points cloud representing its sampled values in the complex plane. The circle fit is computed from a set of points whose length is locally adapted to the signal. This procedure-new to our knowledge in SI-yields the background and the modulation depth and leads to the determination of the instantaneous frequency. The method, applied to simulated and experimental signals, is compared to empirical mode decomposition (EMD). It shows great robustness in the computation of the sought quantities in SI, especially with signals close to the critical sampling or, on the contrary, highly oversampled, situations where the background elimination by EMD is the most prone to errors.

Empirical mode decomposition to assess cardiovascular autonomic control in rats.

Heart beat rate and blood pressure, together with baroreflex sensitivity, have become important tools in assessing cardiac autonomic system control and in studying sympathovagal balance. These analyses are usually performed thanks to spectral indices computed from standard spectral analysis techniques. However, standard spectral analysis and its corresponding rigid band-pass filter formulation suffer from two major drawbacks. It can be significantly distorted by non-stationarity issues and it proves unable to adjust to natural intra- and inter-individual variability. Empirical mode decomposition (EMD), a tool recently introduced in the literature, provides us with a signal-adaptive decomposition that proves useful for the analysis of non-stationary data and shows a strong capability to precisely adjust to the spectral content of the analyzed data. It is based on the concept that any complicated set of data can be decomposed into a finite number of components, called intrinsic mode functions, associated with different spectral contributions. The aims of this study were twofold. First, we studied the changes in the sympathovagal balance induced by various pharmacological blockades (phentolamine, atropine and atenolol) of the autonomic nervous system in normotensive rats. Secondly, we assessed the use of EMD for the analysis of the cardiac sympathovagal balance after pharmacological injections. For this, we developed a new (EMD-based) low frequency vs. high frequency spectral decomposition of heart beat variability and systolic blood pressure, we define the corresponding EMD spectral indices and study their relevance to detect and analyze changes accurately in the sympathovagal balance without having recourse to any a priori fixed high-pass/low-pass filters.

Orthostatic tolerance and spontaneous baroreflex sensitivity in men versus women after 7 days of head-down bed rest.

Many factors are involved in the development of orthostatic intolerance after real or simulated weightlessness. The aim of our study was to compare the effects of 7-day head-down bed rest (HDBR) in eight women and eight men on the spontaneous baroreflex sensitivity (standard spectral method and new time-frequency algorithm) during lower body negative pressure (LBNP) tests. Results obtained before HDBR have shown in women, compared to men, higher heart rate, lower blood pressure, higher parasympathetic modulation at rest and greater decrease in baroreflex sensitivity with greater increase in sympathetic activity during LBNP. After HDBR, we observed in both men and women a dramatic decrease in orthostatic tolerance (7.0 min at R + 1 vs. 10.0 min, p<0.05, at BDC-1 in men; 5.4 vs. 9.0 min, p<0.05, in women) together with a decrease in plasma volume (-9.1 +/- 0.9% in men, -9.5 +/- 1.4% in women) and in spontaneous baroreflex sensitivity without gender effect. After HDBR, at the highest level of LBNP, diastolic blood pressure increased in men (+5.6 +/- 1.3 mm Hg) and decreased in women (-1.0 +/- 2.7 mm Hg) with a gender difference (p<0.05). This result suggests impaired vasoconstriction in women after HDBR. Neither endocrine response nor alterations to the cardiac baroreflex can explain gender differences in orthostatic tolerance after HDBR as reported by previous studies. Further studies need to be conducted in order to obtain a more precise analysis of gender difference in arteriolar vasoconstriction after HDBR. The time frequency method we developed to study changes in spontaneous baroreflex might be applied to the analysis of LBNP tests.