@article{1f38185fdc264c879afca37edca1028c,
title = "A sampling theorem for deconvolution in two dimensions",
abstract = "This work studies the problem of estimating a two-dimensional superposition of point sources or spikes from samples of their convolution with a Gaussian kernel. Our results show that minimizing a continuous counterpart of the ℓ1-norm exactly recovers the true spikes if they are sufficiently separated, and the samples are sufficiently dense. In addition, we provide numerical evidence that our results extend to non-Gaussian kernels relevant to microscopy and telescopy.",
keywords = "Convex optimization, Deconvolution, Dual certificate, Gaussian convolution, Sampling theory, Sparsity, Super-resolution",
author = "Joseph McDonald and Brett Bernstein and Carlos Fernandez-Granda",
note = "Funding Information: The work of the second author was supported by the MacCracken Fellowship and the Isaac Barkey and Ernesto Yhap Fellowship. The work of the third author was supported by the National Science Foundation grant DMS-1616340. †Joint first authors. ‡Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 USA (mcdonald@ cims.nyu.edu, brettb@cims.nyu.edu). §Center for Data Science, New York University, New York, NY 10012 USA (cfgranda@cims.nyu.edu). Funding Information: ∗Received by the editors April 7, 2020; accepted for publication (in revised form) July 15, 2020; published electronically October 22, 2020. https://doi.org/10.1137/20M1329615 Funding: The work of the authors was supported by the National Science Foundation grant NRT-HDR 1922658. Publisher Copyright: {\textcopyright} 2020 Society for Industrial and Applied Mathematics.",
year = "2020",
doi = "10.1137/20M1329615",
language = "English (US)",
volume = "13",
pages = "1754--1780",
journal = "SIAM Journal on Imaging Sciences",
issn = "1936-4954",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "4",
}