An algorithm for non-convex off-the-grid sparse spike estimation with a minimum separation constraint

Yann Traonmilin, Jean-François Aujol, Arhur Leclaire

Theoretical results show that sparse off-the-grid spikes can be estimated from (possibly compressive) Fourier measurements under a minimum separation assumption. We propose a practical algorithm to minimize the corresponding non-convex functional based on a projected gradient descent coupled with an initialization procedure. We give qualitative insights on the theoretical foundations of the algorithm and provide experiments showing its potential for imaging problems.

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