## Hi! I'm **Mohammed El Rhabi**, I am a researcher in applied mathematics.

You can find a resume of my scientific work here (work experience, phd students and scientifc publications).

I work at École des Ponts ParisTech. École des Ponts Paris Tech is present in international rankings, and is also in the top five in the french (national) rankings.

I am the academic director of the Computer Science and Applied Mathematics department.

email address: last_name@gmail.com

## Research interests

Applied Mathematics: P.D.E - numerical analysis, scientific computing, finite element method, spectral method. Non-conforming domain decomposition : the mortar element method. Electromagnetisme.

Signal processing: blind source separation. Independent Component Analysis (ICA). Applied Statistic- stochastic optimization. Application : diagnosis of the electromechanical systems.

Image processing: image restoration : blind deblurring, denoising, inpainting. Image segmentation. Document Image Analysis. Motion Estimation, Optical Flow, Egomotion. Application : cameraphone.

## Some research results

# Image processing: Image restoration

### Our embedded blind deblurring

# Image processing

### Our Camera-Based Motion Estimation : Motionized ; Interface Control (NB: Of course this phone has no accelerometer) ( Other test - Samsung instinct )

# Signal processing : blind source separation

### Upper figure : a mixing of 3 images and a gaussian noise given blindly to our algorithm. Bottom figure : the estimate separated sources

# Signal processing: blind source separation

### Upper figure : 3 images and a gaussian noise before the mixing (by a randomly chosen ill conditioned, non singular 4x4 matrix). Bottom figure : the estimate separated sources obtained by our algorithm

# Signal processing: blind source separation

# Application to electromechanical systems

### Benchmark: Motor 1 (left) has a bearing default at the frequency 207 Hz

### Upper figure: Measured frequencies of signals : a mixing of the information (motor 1 and 2) plus noise, given blindy to our algorithm

### Bottom figure: restored frequencies of signals : frequencies of Motor 1 plus bearing default (see frequency 207Hz) and Motor 2

# Numerical Analysis

### The mortar method (non-conforming domain decomposition method) for 3D Maxwell equations

the three components of the exact solution at the section y = 1/2 (left) and of the numerical one (right) at y = 1/2.