Modern Signal Decomposition Methods

1. Empirical Mode Decomposition
o Definition of Intrinsic Mode Function
o Sifting process
o Stopping criteria
o Algorithm
o Application/Testing in presence of oscillations, ranking from high to low frequencies
o Jupyter Notebook provided for numerical experiments
o Q&A session

2. Variational Mode Decomposition (VMD): 
o Motivations: overcome the heuristic nature and limitations of EMD.  source mixing, noise
o Decomposition form
o Bandwidth measure
o Variational formulation
o Constrained optimization (ADMM)
o Sensitivity to hyperparameters
o Jupyter Notebook provided for numerical experiments
o Q&A session

3. Multivariate Variational Mode Decomposition (MVMD)
o Motivations: Extension to multivariate signals (e.g. brain recordings in MEG/EEG or fNIRS)
o MVMD jointly processes multiple channels to extract narrow-band modes
o Decomposition form
o Bandwidth measure
o Variational formulation
o Constrainted optimization (ADMM)
o Sensitivity to hyperparameters
o Jupyter Notebook provided for numerical experiments
o Benchmarking on simulations
o Q&A session

4. Application to real multivariate data (MEG or bring your own data)
o Single subject resting-state MEG data (exploration, 306 channels, 5min30s recordings, fs=250 Hz)
o Real data preprocessing: artifact removal
o Parameter tuning for each method
o Testing of each method
o Comparing the 3 methods (Jupyter notebooks provided)
o Using these approach as a preprocessing for further analysis. clustering modes by frequency

5. Scale invariance analysis

From spectral to fractal and multifractal analysis in presence of long-range correlation (or 1/f-shape power spectra)