I defended my thesis the 9th of July 2014.
Download my thesis :
« Relations entre le modèle d’image et le nombre de mesures pour une super-résolution fidèle »
Multi-image super-resolution produces a high resolution image from several low resolution acquisitions of a scene. This inverse problem can be ill-posed. We then need to use a regularity model on the scene to be able to produce a realistic image. However, modelling errors limit the performance of such methods. Consequently, finding conditions where the problem is well-posed is necessary to be able to limit the amount of regularization when possible, and maximize the fidelity of the result. We ask ourselves the following questions : For noises with finite energy or outliers, how many images permit the reconstruction of a high resolution image close to the real scene ? How can we maximize fidelity of regularized methods when the number of images is too small ? For observation noise, an asymptotic study of the conditioning guarantees that it is possible to use an unregularized method if enough images are available. In cases closes to the critical inversible case, which are not well-posed, we propose and validate a local estimator of the conditioning, which we use to limit the amount of regularization. For outliers, we use the equivalence between the sparse recovery problem and the robustness to outliers to calculate bounds for the robustness of super-resolution. We also study the regularized case and show conditions which increase the robustness of the problem. All these results are validated by experiments.
Keywords : super-resolution, regularization interpolation, outliers, robustness, sparse models