Geodesic
Sparse recovery under weak moment assumptions
Journal of the European Mathematical Society, Tome 19 (2017) no. 3, pp. 881-904

Voir la notice de l'article provenant de la source EMS Press

We prove that iid random vectors that satisfy a rather weak moment assumption can be used as measurement vectors in Compressed Sensing, and the number of measurements required for exact reconstruction is the same as the best possible estimate – exhibited by a random Gaussian matrix. We also prove that this moment condition is necessary, up to a log log factor. In addition, we explore the Compatibility Condition and the Restricted Eigenvalue Condition in the noisy setup, as well as properties of neighbourly random polytopes.
DOI : 10.4171/jems/682
Classification : 62-XX, 60-XX
Keywords: Compressed sensing, empirical processes, statistics, high dimensions 
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     author = {Guillaume Lecu\'e and Shahar Mendelson},
     title = {Sparse recovery under weak moment assumptions},
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     year = {2017},
     doi = {10.4171/jems/682},
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Guillaume Lecué; Shahar Mendelson. Sparse recovery under weak moment assumptions. Journal of the European Mathematical Society, Tome 19 (2017) no. 3, pp. 881-904. doi: 10.4171/jems/682

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