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

Authors:
Bastien Laville Laure Blanc-Féraud Gilles Aubert

J Imaging 2021 Dec 6;7(12). Epub 2021 Dec 6.

Université Côte d'Azur, CNRS, Inria, I3S, Morpheme Project, 06900 Sophia Antipolis, France.

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 (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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http://dx.doi.org/10.3390/jimaging7120266DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8707379PMC
December 2021

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