Solution of the three-dimensional acoustic inverse scattering problem. The modified Novikov algorithm

Алексеенко, Н.А.; Burov, V. A.; Rumyantseva, O. D.

doi:10.1134/s1063771008030172

Cited by 41 publications

(74 citation statements)

References 2 publications

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“…The initial tail function was taken as in (6.14). Although Theorem 6.1 guarantees approximate global convergence only for the case of a small s− interval, our computational experience tells us that the interval s ∈ [1,12] is an optimal one. We attribute this to the well known fact that convergence estimates are rotinely much more pessimistic than computational results.…”

Section: Imaging Resultsmentioning

confidence: 93%

“…It was observed in computational simulations of [31] that the function ϕ (s) has the best sensitivity to the presence of inclusions for s ∈ [0.5, 1.2] . Nevertheless, we have observed that the larger interval s ∈ [1,12] provides better quality images for simulated data. The function ϕ (s) was computed accurately for the entire interval s ∈ [1,12] with the step size ∆s = 0.05 in the s−direction.…”

Section: Implies That It Is Not Necessary To Use the Condition Qmentioning

confidence: 79%

“…Nevertheless, we have observed that the larger interval s ∈ [1,12] provides better quality images for simulated data. The function ϕ (s) was computed accurately for the entire interval s ∈ [1,12] with the step size ∆s = 0.05 in the s−direction. However, because of their dependence on the derivative ϕ ′ (s) in (7.5), functions ψ 0 (s) = q (0, s) , ψ 1 (s) = q x (0, s) have oscillated for s ∈ [3,12].…”

Section: Implies That It Is Not Necessary To Use the Condition Qmentioning

confidence: 79%

“…and go to the step (n + 1) (1) . If n = N and k = m, then we set ε r,glob (x) := ε (N,m) r ∈ C α [0, 1] and stop the process.…”

Section: Integral Differential Equationmentioning

confidence: 99%

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Blind backscattering experimental data collected in the field and an approximately globally convergent inverse algorithm

et al. 2012

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Abstract.An approximately globally convergent numerical method for a 1-D Coefficient Inverse Problem for a hyperbolic PDE is applied to image dielectric constants of targets from blind experimental data. The data were collected in the field by the Forward Looking Radar of the US Army Research Laboratory. A posteriori analysis has revealed that computed and tabulated values of dielectric constants are in a good agreement. Convergence analysis is presented.1. Introduction. In this paper we test the 1-D version [31] of the numerical method of recent publications [5,6,7,8,9,10,11,12,27,28,32,48] for the case when the time resolved backscattering electric signal is measured experimentally in the field. Measurements were conducted by the Forward Looking Radar built in US Army Research Laboratory (ARL). All kinds of clutter were present at the site of data collection. The data are severely limited. The goal of this radar is to detect and possibly identify shallow explosive-like targets. Prior to this effort, the focus of the ARL team was on the image processing rather than on the target detection and identification [37]. The current data processing procedure of ARL delivers only the energy information. The algorithm of this paper computes values of dielectric constants of targets using those data. These values represent a new, surprising and quite useful dimension of information for the ARL team. A hope is that these values might be helpful in the target detection and identification process.The UNCC/ChalmersGU team has worked only with the most challenging case of blind experimental data. "Blind" means that first computations were made by the UNCC/ChalmersGU team without any knowledge of correct answers. Next, computational results were sent to the ARL team. The ARL team has compared a posteriori those results with the reality and then revealed correct answers to the UNCC/ChalmersGU team. The performance of the algorithm of above cited publications for transmitted blind experimental data was presented in [27], see Tables 5 and 6 there. Images of [27] were refined in the follow up publication [9] using the adaptivity technique of [3,4].In the above cited works a new numerical method was developed for some Multidimensional Coefficient Inverse Problems (MCIPs) for a hyperbolic PDE with single measurement data. "Single measurement" means that either only a single position of the point source or only a single direction of the incident plane wave is considered. Because of many dangers on the battlefield, the single measurement arrangement is the most suitable one for military applications. There were two goals of those publications: Goal 1. To develop such a numerical method, which would have a rigorous guarantee obtaining a good approximation for the exact solution of a CIP without using an advanced knowledge of neither a small neighborhood of that solution nor of the background medium in the domain of interest.Goal 2. This method should demonstrate a good performance on both computationally simulated and experimental data....

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Section: Imaging Resultsmentioning

confidence: 93%

Section: Implies That It Is Not Necessary To Use the Condition Qmentioning

confidence: 79%

Section: Implies That It Is Not Necessary To Use the Condition Qmentioning

confidence: 79%

“…and go to the step (n + 1) (1) . If n = N and k = m, then we set ε r,glob (x) := ε (N,m) r ∈ C α [0, 1] and stop the process.…”

Section: Integral Differential Equationmentioning

confidence: 99%

See 2 more Smart Citations

Blind backscattering experimental data collected in the field and an approximately globally convergent inverse algorithm

et al. 2012

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“…For more information on reconstruction methods for Problems 1.1 and 1.2 see [2], [9], [16], [17], [19], [23] and references therein. Problems 1.1 and 1.2 can be also considered as examples of ill-posed problems: see [15], [5] for an introduction to this theory.…”

Section: Introductionmentioning

confidence: 99%