57 citations · 60 across the 6 of their papers we have counts for
9 papers
Adjoint Method in PDE-based Image Compression
Zakaria Belhachmi, Thomas Jacumin
We consider a shape optimization based method for finding the best interpolation data in the compression of images with noise. The aim is to reconstruct missing regions by means of…
Iterative Approach to Image Compression with Noise : Optimizing Spatial and Tonal Data
Zakaria Belhachmi, Thomas Jacumin
We consider some iterative methods for finding the best interpolation data in the images compression with noise. The interpolation data consists of the set of pixels and their grey…
Optimal Interpolation Data for PDE-based Compression of Images with Noise
Zakaria Belhachmi, Thomas Jacumin
We introduce and discuss shape-based models for finding the best interpolation data in the compression of images with noise. The aim is to reconstruct missing regions by means of m…
Choosing The Best Interpolation Data in Images with Noise
Zakaria Belhachmi, Thomas Jacumin
We introduce and discuss shape based models for finding the best interpolation data in compression of images with noise. The aim is to reconstruct missing regions by means of minim…
The bidomain problem as a gradient system
Zakaria Belhachmi, Ralph Chill
We consider a general, nonlinear version of the bidomain system. Using the gradient structure of this system, but also the notion of -subgradient, we prove wellposedness of the…
Photoacoustic Tomography With Spatially Varying Compressibility and Density
Zakaria Belhachmi, Thomas Glatz, Otmar Scherzer
This paper investigates photoacoustic tomography with two spatially varying acoustic parameters, the compressibility and the density. We consider the reconstruction of the absorpti…
A massively parallel multi-level approach to a domain decomposition method for the optical flow estimation with varying illumination
Diane Gilliocq-Hirtz, Zakaria Belhachmi
We consider a variational method to solve the optical flow problem with varying illumination. We apply an adaptive control of the regularization parameter which allows us to preser…
A Direct Method for Photoacoustic Tomography with Inhomogeneous Sound Speed
Zakaria Belhachmi, Thomas Glatz, Otmar Scherzer
The standard approach for photoacoustic imaging with variable speed of sound is time reversal, which consists in solving a well-posed final-boundary value problem for the wave equa…
Application of the -subgradient in a problem of electropermeabilisation
Ralph Chill, Zakaria Belhachmi
We study a coupled elliptic-parabolic Poincaré-Steklov system arising in electrical cell activity in biological tissues. By using the notion of -subgradient, we show that this s…