Analysis and Separation of Complex signals: Exploiting the Time-frequency structure – ASCETE

Our goal is to develop new approaches for the study of multicomponent signals with synchrosqueezing transform. We are also improving signal representations using data-driven and machine learning approaches, and seek to combine non negative matrix factorization and SST for the purpose of improving source separation. Another aspect of our research will be on the topic of phase retrieval from the modulus of the synchrosqueezing transform.

In this first part of the project, we have already obtained interesting results on the construction of a new ridge detector on the time-frequency representation of noisy multicomponent signals [R1]. Furthermore, we have proposed new techniques for reconstructing the modes of such signals [R3], an adaptive approach for ridge detection[R2], and an in depth comparison of the mode reconstruction techniques using either the downsampled short time Fourier transform or the synchrosqueezing technique.

In another direction, synchrosqueezing techniques along the time axis were developed [R5] and Bayesian approach for ridge detection were also introduced. Comparisons are being carried out with deterministic approaches in this regard.

We think that we are rapidly going to be able to define reassignment operators robust to noise and that behave well in the presence of interference. We are currently developing new tools using neural networks to improve reassignment results when the mathematical analysis fails.
Furthermore, we are going to study in details the relations between amplitude and phase in synchrosqueezing transforms so as to propose new algorithms for phase retrieval. In terms of applications, we plan to tacckle source separation problems in music sounds and in fetal ECG recordings.

journal

[R1] N. Laurent and S. Meignen, «A Novel Ridge Detector for Non stationary Multicomponent Signals: Development and Application to Robust Mode Retrieval«, IEEE Transactions on Signal Processing, vol. 69, pp. 3325-3336, may 2021.
[R2] M. Colominas, S. Meignen and D-H. Pham, «Fully Adaptive Ridge Detection Based on STFT Phase Information«, IEEE Signal Processing Letters, vol. 27, no. 1, pp. 620-624, 2020.
[R3] N. Laurent, S. Meignen, «A Novel Time-Frequency Technique for Mode Retrieval Based on Linear Chirp Approximation«, vol. 27, pp. 935-939, IEEE Signal Processing Letters, 2020.
[R4] S. Meignen, D-H. Pham and Marcelo Colominas, «On the use of Short-Time Fourier Transform and Synchrosqueezing Based Demodulation for the Retrieval of the Modes of Multicomponent Signals«, Signal Processing, 100760, vol. 178, january 2021
R5] S. Houidi, D. Fourer and F. Auger, «On the Use of Concentrated Time-Frequency Representations as Input to a Deep Convolutional Neural Network: Application to Non Intrusive Load Monitoring, MDPI, vol. 22, issue: 9.

conference

[C1] N. Laurent, S.Meignen, J. Fontecave-Jallon, B. Rivet, «A Novel Algorithm for Heart Rate Estimation Based on SynchrosqueezingTransform«, EUSIPCO 2021.
[C2] N. Singh, S. Meignen, T. Oberlin «Source Separation Based on Non-Negative Matrix Factorization of the Synchrosqueezing Transform«, EUSIPCO 2021.
[C3] Q. Legros, D. Fourer,«A novel Pseudo-Bayesian Approoach for Robust Multi-Ridge Detection and Mode Retrieval«, EUSIPCO 2021.
[C4] S. Meignen, M. Colominas, and D-H Pham, «On the Use of Rényi Entropy for Optimal Window Size Computation in the Short-Time Fourier Transform«, ICASSP 2020.
[C5] D. Fourer and Francois Auger, «Second-Order Horizontal
Synchrosqueezing of the S-Transform: A Specific Wavelet Case
Study«, EUSIPCO 2020.
[C6] Karol Abratkiewicz, Piotr Samczynski and Dominique Fourer. A Comparison of the Recursive and FFT-based Reassignment Methods in micro-Doppler Analysis. Proc. IEEE radar conf 2020. Florence, Italy.
[C7] D. Fourer and F. Auger. Second-order Time-Reassigned Synchrosqueezing Transform: Application to Draupner Wave
Analysis. EUSIPCO 2019, Coruna, Spain.

Multicomponent signals (MCSs) are ubiquitous in real life signals: for instance, audio (music, speech), medical (electrocardiogram ECG, phonocardiogram PCG electroencephalogram EEG), astronomical (gravitational waves) or echolocation (bats, marine mammals) signals can be modeled as the superimposition of amplitude/frequency modulated (AM/FM) modes. Identifying and separating these constituent modes are challenging tasks due to the variety of MCSs encountered. In this regard, the ANR-ASTRES project focused on the design of advanced, data adaptive, signal and image processing techniques to decompose complex non stationary signals into physically meaningful modes. To this aim, several techniques were investigated based either on a revisit of the reallocation principles through the concept of synchrosqueezing transform (SST), optimization techniques in relation with the notion of sparsity or empirical mode decomposition.

Different extensions of the reassignment techniques, mainly based on a finer analysis of the reassignment operators, were beneficial to improve the original SST by adapting it to modes with strong frequency modulation or fast oscillating phases. Demodulation algorithms were also used in conjunction with SST to improve mode retrieval and extension of these approaches will be discussed in the present project.

In spite of these achievements, the behavior of the synchrosqueezing operators in a noisy environment still needs to be better understood. Furthermore, the extension of SST to bivariate signals will be discussed in the present project, putting the emphasis on noisy cases, and connections will be established between monovariate and bivariate cases.

Moreover, SST even in its most recent variants contains several intrinsic limitations: it assumes first the modes of the MCS to be separated in the time-frequency (TF) plane, and second that they have regular instantaneous phase and amplitude, which precludes the study of modes with finite duration. We propose to try and circumvent these issues in the present project.

In addition to this, if SST is used for mode retrieval, the recovery process relies on a basic ridge extractor which has seldom been discussed, and which we propose to revisit in the present project. As we will see, mode retrieval in that context is also greatly influenced by the time and frequency resolutions, and we will investigate how to perform the reconstruction of the modes from downsampled SST.

Another way to deal with intrinsic limitations of SST such as its robustness to noise and how to deal with overlapping components is to use machine learning approaches like deep neural networks (DNN). We will also investigate how to optimize the filter parameters and the resolution in TF representations as well as how to extract components of an MCS using DNN.

The study of MCS can be seen from another angle which relates to the concept of source separation, for which non negative matrix factorization (NMF) has been extensively used. In the present project, we propose to investigate how NMF can be used in conjunction with SST to improve mode extraction. Since NMF is performed on the magnitude of a TF, the recovery of the mode will also imply that we investigate phase retrieval ; this will be done in the present project.

Finally, we will also address the study of specific applications of SST. In particular, we will study how it applies to the context of audio source separation and how recent extensions of SST to the multivariate setting can be used on EEG recordings for the study of emotional states, and then on ECG and PCG signals for the monitoring of foetal cardiac activity. Note that, in all the developed applications and in term of programming, we will try to be in line with the ASTRES-Toolbox.