Compressed sensing of data with a known distribution

Mateo Díaz, Mauricio Junca, Felipe Rincón, Mauricio Velasco

Producción científica: Contribución a una revistaArtículorevisión exhaustiva

4 Citas (Scopus)

Resumen

Compressed sensing is a technique for recovering an unknown sparse signal from a small number of linear measurements. When the measurement matrix is random, the number of measurements required for perfect recovery exhibits a phase transition: there is a threshold on the number of measurements after which the probability of exact recovery quickly goes from very small to very large. In this work we are able to reduce this threshold by incorporating statistical information about the data we wish to recover. Our algorithm works by minimizing a suitably weighted ℓ1-norm, where the weights are chosen so that the expected statistical dimension of the corresponding descent cone is minimized. We also provide new discrete-geometry-based Monte Carlo algorithms for computing intrinsic volumes of such descent cones, allowing us to bound the failure probability of our methods.

Idioma originalInglés
Páginas (desde-hasta)486-504
Número de páginas19
PublicaciónApplied and Computational Harmonic Analysis
Volumen45
N.º3
DOI
EstadoPublicada - nov. 2018
Publicado de forma externa

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