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This is a summary of the most important results presented in the author's PhD thesis. This thesis, written in French, was defended on 24 November 2004 and supervised by Marie-Christine Costa and Christophe Picouleau. This thesis consists in developing the study of discrete tomography problems. It aims at reconstructing discrete objects (matrices, images, discrete sets, etc) that are accessible only through few projections. A copy of the thesis is available on "http: //cedric.cnam.fr/AfficheArticle.php?id = 698".