In this thesis, we will propose mathematical models and methods based on partial
differential equations to compress images and videos. In the first part, we will propose a …

This thesis investigates image compression with partial differential equations (PDEs) based
on edges and optimal data. It first presents a lossy compression method for cartoon-like …

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 …

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 …

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 …

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 …

We present here a new image inpainting algorithm based on the Sobolev gradient method
in conjunction with the Navier–Stokes model. The original model of Bertalmío, Bertozzi, and …

We implement a video codec with a decompression scheme based on image inpainting
using different kinds of diffusion models. The arising PDEs are solved by an efficient …

While methods based on partial differential equations (PDEs) and variational techniques are
powerful tools for denoising and inpainting digital images, their use for image compression …

This paper describes the coding of video data and presents a variational approach to
decompress the data. For encoding we select an adapted sub selection of all points in the …