2023
DOI: 10.1553/etna_vol59s24
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Deautoconvolution in the two-dimensional case

Abstract: There is extensive mathematical literature on the inverse problem of deautoconvolution for a function with support in the unit interval [0, 1] ⊂ R, but little is known about the multidimensional situation. This article tries to fill this gap with analytical and numerical studies on the reconstruction of a real function of two real variables over the unit square from observations of its autoconvolution on [0, 2] 2 ⊂ R 2 (full data case) or on [0, 1] 2 (limited data case). In an L 2 -setting, twofoldness and uni… Show more

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Cited by 1 publication
(3 citation statements)
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“…We are going to extend, with respect to the reconstruction of real functions with n real variables, assertions on uniqueness, ambiguity and ill-posedness that previously had been proven in the one-dimensional case. We also complement and generalize findings of our recent paper [10], where such results have been stated for the two-dimensional case. Our focus is on the reconstruction of a square integrable real function x = x(t) with t = (t 1 , t 2 , .…”
Section: Introductionsupporting
confidence: 85%
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“…We are going to extend, with respect to the reconstruction of real functions with n real variables, assertions on uniqueness, ambiguity and ill-posedness that previously had been proven in the one-dimensional case. We also complement and generalize findings of our recent paper [10], where such results have been stated for the two-dimensional case. Our focus is on the reconstruction of a square integrable real function x = x(t) with t = (t 1 , t 2 , .…”
Section: Introductionsupporting
confidence: 85%
“…The discretization is achieved via the composite midpoint rule, and the corresponding discretized nonlinear optimization problem (5.1) is solved by using a damped Newton method. More details and a conceptional algorithm can be found in [10].…”
Section: A Glimpse Of Rate Results For Regularized Solutionsmentioning
confidence: 99%
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