Projected gradient descent for non-convex sparse spike estimation

Yann Traonmilin (1, 2) , Jean-François Aujol (2) , Arthur Leclaire (2)

1 CNRS - Centre National de la Recherche Scientifique
2 IMB - Institut de Mathématiques de Bordeaux

We propose a new algorithm for sparse spike estimation from Fourier measurements. Based on theoretical results on non-convex optimization techniques for off-the-grid sparse spike estimation, we present a projected gradient descent algorithm coupled with a spectral initialization procedure. Our algorithm permits to estimate the positions of large numbers of Diracs in 2d from random Fourier measurements. We present, along with the algorithm, theoretical qualitative insights explaining the success of our algorithm. This opens a new direction for practical off-the-grid spike estimation with theoretical guarantees in imaging applications.

Mots clés: non-convex optimization; projected gradient descent; Index Terms-spike super-resolution

Domaines: Traitement du signal et de l'image [eess.SP]

Yann Traonmilin, Jean-François Aujol, Arthur Leclaire. Projected gradient descent for non-convex sparse spike estimation. 2020. ⟨hal-02311624v2⟩