@article{cb5d416854534fa4818c6068f15e4bd3,
title = "On the support of compressed modes",
abstract = "Compressed modes are solutions of the Laplace equation with a potential and a subgradient term. The subgradient term comes from addition of an L1 penalty in the corresponding variational principle. This paper presents an analysis of compressed modes, finding the minimizer of the variational principle, showing the spatial localization property of compressed modes, and establishing an upper bound on the volume of their support.",
keywords = "Compressed modes, Compressive sensing, L-regularization, PDE, Sparsity",
author = "Farzin Barekat and Russel Caflisch and Stanley Osher",
note = "Funding Information: ∗Received by the editors February 12, 2014; accepted for publication (in revised form) February 7, 2017; published electronically July 13, 2017. http://www.siam.org/journals/sima/49-4/95672.html Funding: The work of the first and second authors was partially supported by Department of Energy grant DOE-SC0010613. The work of the third author was partially supported by ONR N00014-11-1-719. †Mathematics Department, University of California at Los Angeles, Los Angeles, CA 90095-1555 (fbarekat@math.ucla.edu, caflisch@math.ucla.edu, sjo@math.ucla.edu). Publisher Copyright: {\textcopyright} 2017 Society for Industrial and Applied Mathematics.",
year = "2017",
doi = "10.1137/140956725",
language = "English (US)",
volume = "49",
pages = "2573--2590",
journal = "SIAM Journal on Mathematical Analysis",
issn = "0036-1410",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "4",
}