PhD Position F/M Signal processing-based on the squared eigenfunctions of the Schrodinger operator. Application to EEG signals

The Inria Saclay-Île-de-France Research Centre was established in 2008. It has developed as part of the Saclay site in partnership with Paris-Saclay University and with the Institut Polytechnique de Paris .

The centre has 39 project teams , 27 of which operate jointly with Paris-Saclay University and the Institut Polytechnique de Paris; Its activities occupy over 600 people, scientists and research and innovation support staff, including 44 different nationalities.

Biomedical signals are usually characterized by the presence of peaks that provide direct or indirect information on the physiological and metabolic state. Usually, these pulse-shaped signals require preprocessing such as denoising and artifact removals. Further analysis and processing might be required in some specific situations to allow for the extraction of pertinent information from these signals. Despite the fact that the literature abounds with signal processing methods, there are still challenges that need to be overcome and further improvements can be achieved for processing pulse-shaped signals. In this context, a quantum-based signal processing method has been proposed in 1. This method called the semi‐classical signal analysis (SCSA) method decomposes the signal into a set of functions given by the squared eigenfunctions of the Schrödinger operator associated with its negative eigenvalues 1. Thus, and unlike traditional signal decomposition tools, the SCSA expresses the signal through a set of functions that are signal dependent, that is, these functions are not fixed and known in advance but are computed by solving the spectral problem of the Schrödinger operator whose potential is the signal to be analyzed. Accordingly, these eigenfunctions capture more details about the signal and its morphological variations 2. The SCSA has been successfully applied in many applications for signal representation, denoising, post‐processing, and feature extraction. For example, it has been used for arterial blood pressure waveform analysis in 3,4 and for magnetic resonance spectroscopy (MRS) denoising 5, for MRS water suppression 6, and for MRS lipid suppression 7. It has been also used for feature extraction in epileptic seizure detection 8 and for the characterization of PPG signals and blood pressure signals for non-invasive estimation of central pressure and arterial stiffness respectively 9. Recent work on the characterization of EEG signals for epileptic seizure detection and seizure onset zone location has shown promising results 10, 11.

The objective of this research project is to study the mathematical properties of the SCSA and compare the approach qualitatively and quantitatively to state-of-the-art methods such as Wavelets and empirical mode decomposition methods. A parallel between quantum and signal processing properties will be studied. In particular, the student will use some quantum properties of the operator to propose new criteria for the selection of the semi-classical parameter a key design parameter of the method for both denoising and signal characterization. Numerical properties of the algorithm will be also analyzed, with a focus on the optimization of the current codes. Applications to biomedical signals will be investigated with a particular focus on EEG signals for epileptic seizure detection and prediction and for monitoring the mental health of athletes.

We seek a student with strong background and expertise in signal processing and mathematics.

Knowledge in biomedical signals and learning algorithms is a plus.

• Subsidized meals
• Partial reimbursement of public transport costs
• Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
• Possibility of teleworking and flexible organization of working hours
• Professional equipment available (videoconferencing, loan of computer equipment, etc.)
• Social, cultural and sports events and activities
• Access to vocational training
• Social security coverage

• 1st and 2nd year : 2051€ gross/month
• 3rd year : 2158€ gross/month