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Off-the-grid variational sparse spike recovery: methods and algorithms

Bastien Laville 1 Laure Blanc-Féraud 1 Gilles Aubert 2
1 MORPHEME - Morphologie et Images
CRISAM - Inria Sophia Antipolis - Méditerranée , IBV - Institut de Biologie Valrose : U1091, Laboratoire I3S - SIS - Signal, Images et Systèmes
Abstract : Gridless sparse spike reconstruction is a rather new research field with significant results for the super-resolution problem, where we want to retrieve fine-scale details from a noisy and filtered acquisition. To tackle this problem, we are interested in optimisation under some prior, typically the sparsity i.e., the source is composed of spikes. Following the seminal work on the generalised LASSO for measures called the Beurling-Lasso (BLASSO), we will give a review on the chief theoretical and numerical breakthrough of the off-the-grid inverse problem, as we illustrate its usefulness to the super-resolution problem in Single Molecule Localisation Microscopy (SMLM) through new reconstruction metrics and tests on synthetic and real SMLM data we performed for this review.
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Submitted on : Tuesday, December 7, 2021 - 10:21:08 AM
Last modification on : Sunday, May 1, 2022 - 3:17:35 AM

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Bastien Laville, Laure Blanc-Féraud, Gilles Aubert. Off-the-grid variational sparse spike recovery: methods and algorithms. Journal of Imaging, MDPI, 2021, 7 (12), pp.266. ⟨10.3390/jimaging7120266⟩. ⟨hal-03468412⟩

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