2022
DOI: 10.1016/j.acha.2021.09.002
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A mathematical theory of the computational resolution limit in one dimension

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Cited by 19 publications
(13 citation statements)
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“…On the other hand, the resolution analysis in this paper also follows the line of the authors' previous researches on exploring the super-resolution capability for different imaging configurations [33][34][35][36]. Specifically, to analyze the resolution for recovering multiple point sources from a single measurement, in [34][35][36] the authors defined "computational resolution limits" which characterize the minimum required distance between point sources so that their number and locations can be stably resolved under certain noise level. Based on a new approximation theory in a so-called Vandermonde space, they derived bounds for the resolution limits of one-and multi-dimensional super-resolution problems [34][35][36].…”
Section: Related Workmentioning
confidence: 88%
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“…On the other hand, the resolution analysis in this paper also follows the line of the authors' previous researches on exploring the super-resolution capability for different imaging configurations [33][34][35][36]. Specifically, to analyze the resolution for recovering multiple point sources from a single measurement, in [34][35][36] the authors defined "computational resolution limits" which characterize the minimum required distance between point sources so that their number and locations can be stably resolved under certain noise level. Based on a new approximation theory in a so-called Vandermonde space, they derived bounds for the resolution limits of one-and multi-dimensional super-resolution problems [34][35][36].…”
Section: Related Workmentioning
confidence: 88%
“…Specifically, to analyze the resolution for recovering multiple point sources from a single measurement, in [34][35][36] the authors defined "computational resolution limits" which characterize the minimum required distance between point sources so that their number and locations can be stably resolved under certain noise level. Based on a new approximation theory in a so-called Vandermonde space, they derived bounds for the resolution limits of one-and multi-dimensional super-resolution problems [34][35][36]. In particular, they showed that the computational resolution limit for number and location recovery should be…”
Section: Related Workmentioning
confidence: 99%
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“…In this section, we present the main technique that is used in the proofs of the main results of the paper, namely the approximation theory in Vandermonde space. This theory was first introduced in [24,25]. Instead of considering the non-linear approximation problem there, we consider a different approximation problem, which is relevant to the stability analysis of (2.4).…”
Section: Non-linear Approximation Theory In Vandermonde Spacementioning
confidence: 99%
“…More recently, to analyze the resolution for recovering multiple point scatterers, in [23][24][25] the authors defined "computational resolution limits" which characterize the minimum required distance between point scatterers so that their number and locations can be stably resolved under certain noise level. By developing a non-linear approximation theory in a socalled Vandermonde space, they derived bounds for computational resolution limits for a deconvolution problem [25] and a line spectral problem [24] (equivalent to the super-resolution problem considered here). In particular, they showed in [24] that the computational resolution limit for number and location recovery should be respectively 2n−1 ), stably recovering the scatterer locations is impossible in the worst case.…”
Section: Introductionmentioning
confidence: 99%