Celebratio Mathematica — Daubechies

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S. Voronin and I. Daubechies: “An iteratively reweighted least squares algorithm for sparse regularization,” pp. 391–411 in Functional analysis, harmonic analysis, and image processing: A collection of papers in honor of Björn Jawerth. Edited by M. Cwikel and M. Milman. Contemporary Mathematics 693. American Mathematical Society (Providence, RI), 2017. MR 3682621 Zbl 1392.65074 ArXiv 1511.08970 incollection

We present a new algorithm and the corresponding convergence analysis for the regularization of linear inverse problems with sparsity constraints, applied to a new generalized sparsity promoting functional. The algorithm is based on the idea of iteratively reweighted least squares, reducing the minimization at every iteration step to that of a functional including only \( \ell_2 \)-norms. This amounts to smoothing of the absolute value function that appears in the generalized sparsity promoting penalty we consider, with the smoothing becoming iteratively less pronounced. We demonstrate that the sequence of iterates of our algorithm converges to a limit that minimizes the original functional.

Björn David Jawerth	Related
Michael Ćwikel	Related
Mario Marcos Milman	Related
Sergey Voronin	Related