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## Section: New Results

### A Characterization of the Non-Degenerate Source Condition in Super-Resolution

V. Duval

This article deals with the Basis Pursuit (or LASSO) for measures for for the super-resolution problem, i.e. retrieving the fine details of a signal or an image. If the signal is made of $M$ non-negative Dirac masses, under some assumptions on the measurement process, it is possible to exactly recover the signal from $2M$ observations, regardless of the minimum distance between the spikes. We study the stability to noise of such a reconstruction, and we propose a characterization of the Non-Degenerate Source Condition which is an almost necessary and sufficient for the stability of the support (the number and locations of the reconstructed spikes). The case of Laplace and Gaussian measurements are studied in detail.