Regularized factorization method for a perturbed positive compact operator applied to inverse scattering

Harris, Isaac

doi:10.1088/1361-6420/acfd59

Cited by 3 publications

(2 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Different methods can be categorized into qualitative and quantitative approaches for solving inverse scattering problems. Qualitative methods, such as linear sampling [23], factorization [24], and singular sources methods [25] aim to determine the approximate shape and location of objects, providing limited information about their material properties or the surrounding medium . On the other hand, quantitative methods define an objective function related to the desired characteristics of scattering objects.…”

Section: Introductionmentioning

confidence: 99%

Revealing the Invisible: Imaging Through Non-radiating Subspace

Siampour,

Nezhad

2024

JOPR

View full text Add to dashboard Cite

This paper presents a novel modification to the subspace optimization method (SOM) for solving inverse scattering problems in diverse background media. By incorporating sequential quadratic programming (SQP), a fast and accurate optimization technique, our approach aims to improve the reconstruction of dielectric objects buried in complex environments. We investigate the influence of non-radiating (NR) subspace reconstruction on imaging quality by analyzing the induced current-exterior field mapping operator's singular values. The scattering formulation of direct problems is performed through numerical methods such as coupled dipole method, finite elements-boundary integral, and electric field integral equations. Radiating and non-radiating objective functions are defined and minimized using SQP to evaluate the effectiveness of the proposed method. Numerical experiments demonstrate significant enhancements in imaging quality, robustness, and computational efficiency compared to existing techniques. This modified SOM offers a promising avenue for precise and reliable reconstruction of electromagnetic scattering objects, with potential applications in various fields including medical imaging, remote sensing, and non-destructive evaluation.

show abstract

Section: Introductionmentioning

confidence: 99%

Revealing the Invisible: Imaging Through Non-radiating Subspace

Siampour,

Nezhad

2024

JOPR

View full text Add to dashboard Cite

show abstract

“…This regularized variant of the factorization method was initially studied in [26] for a similar problem coming from diffuse optical tomography. See [28] for stability. This method is based on the analysis in [1,2,20,31].…”

mentioning

confidence: 99%

Reconstruction of extended regions in EIT with a generalized Robin transmission condition

Granados,

Harris,

Lee

2023

CAC

View full text Add to dashboard Cite

In this paper, we consider an inverse shape problem coming from electrical impedance tomography (EIT) with a generalized Robin transmission condition. We will derive an algorithm in order to detect whether two materials that should be in contact are separated or delaminated. More precisely, we assume that the undamaged material or background state is known and shares an interface or boundary with the damaged subregion. The Robin transmission condition on this boundary asymptotically models delamination. We assume that the Dirichlet-to-Neumann (DtN) operator is given from measuring the current on the surface of the material from an imposed voltage. We show that this mapping uniquely recovers the boundary parameters. Furthermore, using this electrostatic Cauchy data as physical measurements, we can determine if all of the coefficients from the Robin transmission condition are real-valued or complex-valued. We study these two cases separately and show that the regularized factorization method can be used to detect whether delamination has occurred and recover the damaged subregion. Numerical examples will be presented for both cases in two dimensions in the unit circle.

show abstract

Analysis of the monotonicity method for an anisotropic scatterer with a conductive boundary

Harris,

Hughes,

Lee

2024

Inverse Problems

View full text Add to dashboard Cite

In this paper, we consider the inverse scattering problem associated with an anisotropic medium with a conductive boundary. We will assume that the corresponding far-field pattern is known/measured and we consider two inverse problems. First, we show that the far-field data uniquely determines the boundary coefficient. Next, since it is known that anisotropic coefficients are not uniquely determined by this data we will develop a qualitative method to recover the scatterer. To this end, we study the so-called monotonicity method applied to this inverse shape problem. This method has recently been applied to some inverse scattering problems but this is the first time it has been applied to an anisotropic scatterer. This method allows one to recover the scatterer by considering the eigenvalues of an operator associated with the far-field operator. We present some simple numerical reconstructions to illustrate our theory in two dimensions. For our reconstructions, we need to compute the adjoint of the Herglotz wave function as an operator mapping into $H^1$ of a small ball. 

show abstract

Regularized factorization method for a perturbed positive compact operator applied to inverse scattering

Cited by 3 publications

References 34 publications

Revealing the Invisible: Imaging Through Non-radiating Subspace

Revealing the Invisible: Imaging Through Non-radiating Subspace

Reconstruction of extended regions in EIT with a generalized Robin transmission condition

Analysis of the monotonicity method for an anisotropic scatterer with a conductive boundary

Contact Info

Product

Resources

About