A Sampling Theorem for Deconvolution in Two Dimensions
Numerical Analysis
2020-08-05 v2 Information Theory
Numerical Analysis
math.IT
Optimization and Control
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 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.
Cite
@article{arxiv.2003.13784,
title = {A Sampling Theorem for Deconvolution in Two Dimensions},
author = {Joseph McDonald and Brett Bernstein and Carlos Fernandez-Granda},
journal= {arXiv preprint arXiv:2003.13784},
year = {2020}
}
Comments
41 pages, 18 figures; added references and additional comments and description throughout for clarity