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Keywords = sparse spike localisation

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33 pages, 3286 KB  
Review
Off-The-Grid Variational Sparse Spike Recovery: Methods and Algorithms
by Bastien Laville, Laure Blanc-Féraud and Gilles Aubert
J. Imaging 2021, 7(12), 266; https://doi.org/10.3390/jimaging7120266 - 6 Dec 2021
Cited by 9 | Viewed by 4477
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Inverse Problems and Imaging)
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