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Non-negative Super-resolution is Stable

Citation Author(s):
Armin Eftekhari, Jared Tanner, Andrew Thompson, Bogdan Toader, Hemant Tyagi
Submitted by:
Bogdan Toader
Last updated:
29 May 2018 - 7:34am
Document Type:
Poster
Document Year:
2018
Event:
Presenters:
Bogdan Toader
 

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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