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

2020/09/18 by Traonmilin, Yann, Jean-Francois Aujol, Aujol, Jean-François +1 · 1 citation
Earth and Planetary Sciences · Engineering · Computer Science · #Seismic Imaging and Inversion Techniques #Ultrasonics and Acoustic Wave Propagation #Image and Signal Denoising Methods

paper · pdf · doi:10.48550/arxiv.2009.08670

Abstract

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

Citations

• Proximal alternating linearized minimization for nonconvex and nonsmooth problems
• Local Minima and Convergence in Low-Rank Semidefinite Programming

Cited by

• A convergence framework for energy minimisation of linear self-adjoint elliptic PDEs in nonlinear approximation spaces

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