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Review

Off-The-Grid Variational Sparse Spike Recovery: Methods and Algorithms

1
Université Côte d’Azur, CNRS, Inria, I3S, Morpheme Project, 06900 Sophia Antipolis, France
2
Université Côte d’Azur, CNRS, LJAD, 06000 Nice, France
*
Authors to whom correspondence should be addressed.
Academic Editors: Fabiana Zama and Elena Loli Piccolomini
J. Imaging 2021, 7(12), 266; https://doi.org/10.3390/jimaging7120266
Received: 21 October 2021 / Revised: 24 November 2021 / Accepted: 28 November 2021 / Published: 6 December 2021
(This article belongs to the Special Issue Inverse Problems and Imaging)
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. View Full-Text
Keywords: off-the-grid optimisation review; inverse problems; sparse spike localisation; super-resolution; fluorescence microscopy; SMLM; functional analysis off-the-grid optimisation review; inverse problems; sparse spike localisation; super-resolution; fluorescence microscopy; SMLM; functional analysis
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MDPI and ACS Style

Laville, B.; Blanc-Féraud, L.; Aubert, G. Off-The-Grid Variational Sparse Spike Recovery: Methods and Algorithms. J. Imaging 2021, 7, 266. https://doi.org/10.3390/jimaging7120266

AMA Style

Laville B, Blanc-Féraud L, Aubert G. Off-The-Grid Variational Sparse Spike Recovery: Methods and Algorithms. Journal of Imaging. 2021; 7(12):266. https://doi.org/10.3390/jimaging7120266

Chicago/Turabian Style

Laville, Bastien, Laure Blanc-Féraud, and Gilles Aubert. 2021. "Off-The-Grid Variational Sparse Spike Recovery: Methods and Algorithms" Journal of Imaging 7, no. 12: 266. https://doi.org/10.3390/jimaging7120266

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