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Sparsity regularization and graph-based representation in medical imaging

Abstract : Medical images have been used to depict the anatomy or function. Their high-dimensionality and their non-linearity nature makes their analysis a challenging problem. In this thesis, we address the medical image analysis from the viewpoint of statistical learning theory. First, we examine regularization methods for analyzing MRI data. In this direction, we introduce a novel regularization method, the k-support regularized Support Vector Machine. This algorithm extends the 1 regularized SVM to a mixed norm of both `1 and `2 norms. We evaluate our algorithm in a neuromuscular disease classification task. Second, we approach the problem of graph representation and comparison for analyzing medical images. Graphs are a technique to represent data with inherited structure. Despite the significant progress in graph kernels, existing graph kernels focus on either unlabeled or discretely labeled graphs, while efficient and expressive representation and comparison of graphs with continuous high-dimensional vector labels, remains an open research problem. We introduce a novel method, the pyramid quantized Weisfeiler-Lehman graph representation to tackle the graph comparison problem for continuous vector labeled graphs. Our algorithm considers statistics of subtree patterns based on the Weisfeiler-Lehman algorithm and uses a pyramid quantization strategy to determine a logarithmic number of discrete labelings. We evaluate our algorithm on two different tasks with real datasets. Overall, as graphs are fundamental mathematical objects and regularization methods are used to control ill-pose problems, both proposed algorithms are potentially applicable to a wide range of domains.
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Aikaterini Gkirtzou. Sparsity regularization and graph-based representation in medical imaging. Signal and Image processing. Ecole Centrale Paris, 2013. English. ⟨NNT : 2013ECAP0074⟩. ⟨tel-00960163v2⟩

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