The image resolution, i.e. the pixel density in a given surface, is an important characteristic that influences the representation of details. If the resolution has a minor impact on natural images, it is absolutely important to document images for which the loss of details can make a text unreadable by human and unable to recognize it by OCR (Optical Character Recognition) systems. The need for high-resolution images continues to enlarge in various computer vision applications in order to achieve better performance in pattern recognition and image analysis. However, high resolution images are not always available due for example to the quality of scanners used in the ancient digitization projects.
Research works of this thesis fit in the context of resolution enhancement of texts in low-resolution images and videos. The main objective of this thesis is to reconstruct a high-resolution image from one or more observed low-resolution images. Generic and unsupervised methods cannot reconstruct the complex shapes of characters in a scanned textual document. So, we chose to orient ourselves to the supervised methods based on the learning on a significant number of character images. Among the existing supervised methods, we chose the sparse analysis that offers a rigorous methodological framework in mathematics for many applications of image processing and restoration. This approach is adapted to the particular specificities that distinguish textual images from natural ones. In perspective, we will extend the sparse analysis to other applications such as the reconstruction of degraded characters, reducing blur, character segmentation in noisy images...