# Homepage of Rémy Abergel

## About me

I am a young researcher, in Applied Mathematics and Image Processing, working as a post-doctorate fellow at the IMAGES department of Telecom ParisTech.

My Ph.D was hosted at MAP5 Laboratory under the supervision of Lionel Moisan. I have been teaching Mathematics to first year and second year students (level L1 and L2) at I.U.T of Paris Descartes (department of Informatics) from 2013 to 2016.

## Research topics

- Image analysis, modelling, and processing
- Total Variation based methods
- Convex and nonsmooth optimization
- Continuous and discrete Fourier analysis
- Shannon Sampling Theory
- Subpixel image processing
- Poisson noise
- A contrario methodology
- Floating-point arithmetic, numerical calculus
- SAR image processing (target detection, sidelobes supression, sampling)

## Source codes and examples

- The Shannon total variation, software in C , in Matlab (version >= 2013) , published version SharedIt / revised preprint .
- Fast and accurate evaluation of a generalized incomplete gamma function (software in C language , preprint )
- ASTRE/CUTASTRE A contrario point tracking algorithms (C langage)

## Tutorials about total variation based image processing (Scilab)

- Basic tools for manipulating the total variation (Legendre-Fenchel-Rockafellar duality)
- Restoration of images corrupted with Gaussian noise (the Rudin, Osher and Fatemi model)
- Inverse problems with quadratic data fidelity (deconvolution, zoom, spectrum extrapolation)
- Minimizing the total variation under affine constraints (inpainting, zoom, spectrum extrapolation)
- Restoration of images corrupted with Poisson noise
- Inverse problems with Poisson data fidelity