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Accelerating sparse inverse problems using structured approximations

Abstract : As the quantity and size of available data grow, the existing algorithms for solving sparse inverse problems can become computationally intractable. In this work, we explore two main strategies for accelerating such algorithms. First, we study the use of structured dictionaries which are fast to operate with. A particular family of dictionaries, written as a sum of Kronecker products, is proposed. Then, we develop stable screening tests, which can safely identify and discard useless atoms (columns of the dictionary matrix which do not correspond to the solution support), despite manipulating approximate dictionaries.
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Cássio Fraga Dantas. Accelerating sparse inverse problems using structured approximations. Machine Learning [cs.LG]. Université Rennes 1, 2019. English. ⟨NNT : 2019REN1S065⟩. ⟨tel-02494569v2⟩

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