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The main objective of this proposal is to explore and develop new methods and optimized algorithms for the analysis of high-dimensional data under the assumption of structured sparsity and low-rank conditions. Special attention will be paid to the impact of the numerical methods in statistical applications, especially in the domain of variable selection. We will investigate the benefits of structured sparse and low-rank models and their algorithms in relation to multiscale sparse decompositions, the regularization of inverse problems and in medical imaging. By linking these concepts to convex optimization problems, the planned research also contributes to turning these theoretical concepts into practical and efficient techniques for the solution of large scale inverse problems.
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