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Article Dans Une Revue Information and Inference Année : 2022

The basins of attraction of the global minimizers of non-convex inverse problems with low-dimensional models in infinite dimension

Yann Traonmilin
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Jean-François Aujol
Arthur Leclaire

Résumé

Non-convex methods for linear inverse problems with low-dimensional models have emerged as an alternative to convex techniques. We propose a theoretical framework where both finite dimensional and infinite dimensional linear inverse problems can be studied. We show how the size of the the basins of attraction of the minimizers of such problems is linked with the number of available measurements. This framework recovers known results about low-rank matrix estimation and off-the-grid sparse spike estimation, and it provides new results for Gaussian mixture estimation from linear measurements. keywords: low-dimensional models, non-convex methods, low-rank matrix recovery, off-the-grid sparse recovery, Gaussian mixture model estimation from linear measurements.
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Dates et versions

hal-02941814 , version 1 (17-09-2020)
hal-02941814 , version 2 (18-02-2022)

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Yann Traonmilin, Jean-François Aujol, Arthur Leclaire. The basins of attraction of the global minimizers of non-convex inverse problems with low-dimensional models in infinite dimension. Information and Inference, 2022. ⟨hal-02941814v2⟩

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