Mémoire

Abstract

Inverse methods are at the basis of the resolution of numerous applications, that notably take place in the context of signal processing. In particular, these techniques appear to be efficient for images-related problems, in which the analysed data are most of the time incomplete or at least perturbed by unwanted external contributions. These situations are commonly encountered when carrying out classical optical and remote sensing acquisitions, and it is therefore primordial to develop tools that will bring relevant solutions to these potential issues. On that purpose, series of numerical algorithms are currently tested and make use of both the so-called images sparsity property and the wavelet theory to recover the missing components of a broad variety of analysed images. This master thesis focuses on the development of some of these numerical algorithms, that are optimised in the present work through a succession of tests. First, an overall state of the art is provided and covers all the concepts of interest, including images properties, the selected inpainting technique that performs images completions, thanks to adequate images sampling and threshold-based method that are described as well, and image deconvolution involving a point spread function. An entire section is then dedicated to all the digital image processing steps that mainly rely on images produced by a compressive sensing imager designed at the Centre Spatial de Liège. The correlated methodologies, followed to produce satisfactory images reconstructions, are finally applied to some damaged scenes produced either in laboratory or during an existing space mission. The final selection of the mission of interest has been inclined, thanks to a bibliographic study, towards the Landsat 7 mission, for which one of its component's malfunction led to the production of incomplete scientific data.