2017/12/18 by Vincent Duval, Duval, Vincent
Engineering · Medicine · #FOS: Mathematics #Medical Imaging Techniques and Applications #Microwave Imaging and Scattering Analysis #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1712.06373
openalex publication_date 2017/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a recent article, Schiebinger et al. provided sufficient conditions for\nthe noiseless recovery of a signal made of M Dirac masses given 2M + 1\nobservations of, e.g. , its convolution with a Gaussian filter, using the Basis\nPursuit for measures. In the present work, we show that a variant of their\ncriterion provides a necessary and sufficient condition for the Non-Degenerate\nSource Condition (NDSC) which was introduced by Duval and Peyr 'e to ensure\nsupport stability in super-resolution. We provide sufficient conditions which,\nfor instance, hold unconditionally for the Laplace kernel provided one has at\nleast 2M measurements. For the Gaussian filter, we show that those conditions\nare fulfilled in two very different configurations: samples which approximate\nthe uniform Lebesgue measure or, more surprisingly, samples which are all\nconfined in a sufficiently small interval.\n