Schrödinger filtering is a new signal processing technique based on semi-classical signal analysis (SCSA) (https://doi.org/10.1007/s00498-012-0091-1), which treats an input signal as an attractive potential in the one-dimensional semi-classical Schrödinger operator. The discrete spectrum of the operator is used for the signal's analysis. The basis functions of this eigenvalue decomposition are localized and pulse-shaped. Individually, these components naturally suit needs such as peak detection or removal. Together, they reconstruct the input with a preference for energy-dense input peaks. Based on the value of a single decomposition parameter, the user has control over how much of the energy-sparse parts of the input (e.g., noise) are captured in the reconstruction. Schrödinger filtering is the term describing any filtering use of SCSA.
Here, Schrödinger filtering has been used for gradient artifact spike removal from EEG data acquired in the presence of fMRI. Schrödinger filtering handles the data after processing by average artifact subtraction (https://doi.org/10.1006/nimg.2000.0599), which contains residual artifact with time-domain spikes.
All code in this repository was written in MATLAB by Gabriel Benigno except where stated otherwise.
Please cite the following article if you use this repository's code in any capacity:
Benigno GB, Menon RS, Serrai H. 2020. Schrödinger filtering: a precise EEG despiking technique for EEG-fMRI gradient artifact. NeuroImage. https://doi.org/10.1016/j.neuroimage.2020.117525.
The data used in the Schrödinger filtering paper comprises a freely available online dataset available at https://fsl.fmrib.ox.ac.uk/eeglab/fmribplugin/#tutorial, a dataset for which permission is required (https://doi.org/10.1101/253047), and simulated data. The code used to generate the simulated data is within the figures folder.
Feedback is welcome: [email protected].