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Non-negative Super-resolution is Stable

Abstract: 

We consider the problem of localizing point sources on an interval from possibly noisy measurements. In the absence of noise, we show that measurements from Chebyshev sys- tems are an injective map for non-negative sparse measures, and therefore non-negativity is sufficient to ensure unique- ness for sparse measures. Moreover, we characterize non- negative solutions from inexact measurements and show that any non-negative solution consistent with the measurements is proportionally close to the solution of the system with ex- act measurements. Our results substantially simplify, extend, and generalize the prior work by De Castro et al. [1] and Schiebinger et al. [2], which relies upon sparsifying penal- ties, by showing that it is the non-negativity constraint, rather than any particular algorithm, that imposes uniqueness of the sparse non-negative measure, and by extending the results to inexact samples.

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Paper Details

Authors:
Armin Eftekhari, Jared Tanner, Andrew Thompson, Bogdan Toader, Hemant Tyagi
Submitted On:
29 May 2018 - 7:34am
Short Link:
Type:
Poster
Event:
Presenter's Name:
Bogdan Toader
Document Year:
2018
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[1] Armin Eftekhari, Jared Tanner, Andrew Thompson, Bogdan Toader, Hemant Tyagi, "Non-negative Super-resolution is Stable", IEEE SigPort, 2018. [Online]. Available: http://sigport.org/3212. Accessed: Aug. 21, 2018.
@article{3212-18,
url = {http://sigport.org/3212},
author = {Armin Eftekhari; Jared Tanner; Andrew Thompson; Bogdan Toader; Hemant Tyagi },
publisher = {IEEE SigPort},
title = {Non-negative Super-resolution is Stable},
year = {2018} }
TY - EJOUR
T1 - Non-negative Super-resolution is Stable
AU - Armin Eftekhari; Jared Tanner; Andrew Thompson; Bogdan Toader; Hemant Tyagi
PY - 2018
PB - IEEE SigPort
UR - http://sigport.org/3212
ER -
Armin Eftekhari, Jared Tanner, Andrew Thompson, Bogdan Toader, Hemant Tyagi. (2018). Non-negative Super-resolution is Stable. IEEE SigPort. http://sigport.org/3212
Armin Eftekhari, Jared Tanner, Andrew Thompson, Bogdan Toader, Hemant Tyagi, 2018. Non-negative Super-resolution is Stable. Available at: http://sigport.org/3212.
Armin Eftekhari, Jared Tanner, Andrew Thompson, Bogdan Toader, Hemant Tyagi. (2018). "Non-negative Super-resolution is Stable." Web.
1. Armin Eftekhari, Jared Tanner, Andrew Thompson, Bogdan Toader, Hemant Tyagi. Non-negative Super-resolution is Stable [Internet]. IEEE SigPort; 2018. Available from : http://sigport.org/3212