Defect Detection from Multi-frequency Limited Data via Topological Sensitivity

Funes, José Félix; Perales, José Manuel Perales; Rapún, María-Luisa; Vega, José M.

doi:10.1007/s10851-015-0611-y

Cited by 38 publications

(42 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…E n and P n being forward and adjoint fields with object Ω n , governed by systems (22) and (23) respectively. The positive constants C n+1 , c n+1 in (25) are ultimately chosen to ensure decrease of the cost functional, i.e., J(R 3 \ Ω n+1 ) < J(R 3 \ Ω n ). Initially, we may set C n+1 = C n and c n+1 = c n .…”

Section: Topological Derivative Based Reconstruction Algorithmmentioning

confidence: 99%

“…Other negative regions outside are an artifact associated to the spurious points included in Ω 0 . We can propose a new approximation Ω 1 using either the peak of the topological energy (20) or the strategy (25) for the topological derivative. The computation of updated topological energies and derivatives in both cases does not yield a clear improvement.…”

Section: Shape Correctionsmentioning

confidence: 99%

“…In our imaging setting, considering multiple frequencies in the visible light range does not seem to produce significative improvements over working with one, as deduced from the numerical simulations we have performed so far. On the contrary, averaging information from multiple frequencies has been shown to enhance precision in 3D microwave imaging [52] and 2D acoustic applications [25,40]. Let us emphasize that, in holography, light detectors are placed past the objects, whereas in underground acoustic imaging, for instance, emitters and receptors are usually placed on the same surface.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Noninvasive Imaging of Three-Dimensional Micro and Nanostructures by Topological Methods

Carpio¹,

Dimiduk²,

Rapún³

et al. 2016

SIAM J. Imaging Sci.

View full text Add to dashboard Cite

We present topological derivative and energy based procedures for the imaging of micro and nanostructures using one beam of visible light of a single wavelength. Objects with diameters as small as 10 nm can be located, and their position tracked with nanometer precision. Multiple objects distributed either on planes perpendicular to the incidence direction or along axial lines in the incidence direction are distinguishable. More precisely, the shape and size of plane sections perpendicular to the incidence direction can be clearly determined, even for asymmetric and non-convex scatterers. Axial resolution improves as the size of the objects decreases. Initial reconstructions may proceed by glueing together 2D horizontal slices between axial peaks or by locating objects at 3D peaks of topological energies, depending on the effective wavenumber. Below a threshold size, topological derivative based iterative schemes improve initial predictions of the location, size and shape of objects by postprocessing fixed measured data. For larger sizes, tracking the peaks of topological energy fields that average information from additional incident light beams seems to be more effective.

show abstract

Section: Topological Derivative Based Reconstruction Algorithmmentioning

confidence: 99%

Section: Shape Correctionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Noninvasive Imaging of Three-Dimensional Micro and Nanostructures by Topological Methods

Carpio¹,

Dimiduk²,

Rapún³

et al. 2016

SIAM J. Imaging Sci.

View full text Add to dashboard Cite

show abstract

“…The main advantages of this method are: (i) it is a one-step method, (ii) it does not require any a priori information about the number, size, shape or location of the defects, (iii) it has a very small computational cost. Topological derivatives have been successfully used for solving a wide variety of problems related with defect identification in many fields, like in acoustics [6,9,19], electromagnetism [37,42], elasticity [4,25,41], and electrical impedance tomography problems [2,8,11], to mention a few. Related work dealing with thermal problems was published in [7,10], where a two dimensional unsteady thermal propagation problem in an unbounded media was studied.…”

Section: Introductionmentioning

confidence: 99%

Application of the topological derivative to post-processing infrared time-harmonic thermograms for defect detection

Peña

Rapún

2020

J.Math.Industry

Self Cite

View full text Add to dashboard Cite

This paper deals with active time-harmonic infrared thermography applied to the detection of defects inside thin plates. We propose a method to post-process raw thermograms based on the computation of topological derivatives which will produce much sharper images (namely, where contrast is highly enhanced) than the original thermograms. The reconstruction algorithm does not need information about the number of defects, nor the size or position. A collection of numerical experiments illustrates that the algorithm is highly robust against measurement errors in the thermograms, giving a good approximation of the shape, position and number of defects without the need of an iterative process.

show abstract

“…6 Special attention has been devoted to the topological derivative associated with the Helmholtz problem, 7 which has been successfully applied for imaging small acoustic anomalies. [8][9][10][11][12][13] See also an experimental validation of the topological derivative method in the context of elastic-wave imaging. 14 The stability and resolution analysis for a topological-derivative-based imaging functional has been presented in Ammari et al, 15 showing why it works so well in the context of inverse scattering.…”

Section: Introductionmentioning

confidence: 99%

A noniterative reconstruction method for the inverse potential problem with partial boundary measurements

Fernandez

Novotny

Prakash

2019

Math Methods in App Sciences

View full text Add to dashboard Cite

In this paper, a noniterative reconstruction method for solving the inverse potential problem is proposed. The forward problem is governed by a modified Helmholtz equation. The inverse problem consists in the reconstruction of a set of anomalies embedded into a geometrical domain from partial or total boundary measurements of the associated potential. Since the inverse problem is written in the form of an ill‐posed boundary value problem, the idea is to rewrite it as a topology optimization problem. In particular, a shape functional measuring the misfit between the solution obtained from the model and the data taken from the boundary measurements is minimized with respect to a set of ball‐shaped anomalies by using the concept of topological derivatives. It means that the shape functional is expanded asymptotically and then truncated up to the desired order term. The resulting truncated expansion is trivially minimized with respect to the parameters under consideration that leads to a noniterative second order reconstruction algorithm. As a result, the reconstruction process becomes very robust with respect to the noisy data and independent of any initial guess. Finally, some numerical experiments are presented showing the capability of the proposed method in reconstructing multiple anomalies of different sizes and shapes by taking into account complete or partial boundary measurements.

show abstract

Defect Detection from Multi-frequency Limited Data via Topological Sensitivity

Cited by 38 publications

References 36 publications

Noninvasive Imaging of Three-Dimensional Micro and Nanostructures by Topological Methods

Noninvasive Imaging of Three-Dimensional Micro and Nanostructures by Topological Methods

Application of the topological derivative to post-processing infrared time-harmonic thermograms for defect detection

A noniterative reconstruction method for the inverse potential problem with partial boundary measurements

Contact Info

Product

Resources

About