A Numerical Method to Solve a Phaseless Coefficient Inverse Problem from a Single Measurement of Experimental Data

Klibanov, Michael V.; Koshev, Nikolay; Nguyen, Dinh-Liem; Nguyen, Loc H.; Brettin, Aaron; Astratov, Vasily N.

doi:10.1137/18m1179560

Cited by 24 publications

(17 citation statements)

References 74 publications

(136 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The difficulty in measuring phase is even more applicable at optical frequencies, where the phase often cannot be measured at all, and as such optical-frequency phaseless problems have received significant attention, e.g. [35]. The phaseless inversion problem is widely recognized as being more difficult to solve than its full-data counterpart.…”

Section: B Phaseless Inversion Algorithmsmentioning

confidence: 99%

Phaseless Parametric Inversion for System Calibration and Obtaining Prior Information

et al. 2019

View full text Add to dashboard Cite

Electromagnetic inversion systems require that the experimental data be calibrated to the computational inversion model being used. In addition, accurate prior information provided to the inversion algorithm leads to higher-quality images. For some applications of inversion, such as stored grain imaging or geophysical inversion, known (calibration) targets cannot be easily introduced into the imaging region and the ability to determine prior information can be limited. In an attempt to solve the problem of calibrating data from such field-inversion systems, we introduce a work flow where: (1) a simple parametric physical model of the scattering background is obtained via a phaseless (magnitude only data) inversion algorithm that works on phase-corrupted, uncalibrated total-field measurements, and (2) we then use this simple physical model to generate calibration and prior information for subsequent full-data (magnitude and phase) inversion. Using an example of in-bin stored grain imaging, the inverted parameters are the grain angle of repose, grain height, and the average bulk permittivity of the grain. Using uncalibrated total-field data, we show that the proposed work flow obtains the overall structure of the grain in a bin despite the use of this raw data. We then show that the simple physical model can be used as both a calibration data set as well as the prior information about the grain target in a full-data (magnitude and phase) inversion. The use of this phaseless algorithm means we are able to remotely calibrate imaging systems, and obtain critical prior information about the imaging region without introducing a calibration target or physically measuring the imaging region in other ways.INDEX TERMS Inverse problems, calibration, microwave tomography, inverse imaging.

show abstract

Section: B Phaseless Inversion Algorithmsmentioning

confidence: 99%

Phaseless Parametric Inversion for System Calibration and Obtaining Prior Information

et al. 2019

View full text Add to dashboard Cite

show abstract

“…This is also known as a coefficient inverse problem, if differential Maxwell's equations are considered as a forward model. [ 231 ] The necessary prior information is reflected mostly in the approximation used or in the knowledge of the RI value (then only the boundary is reconstructed). The main drawback of these methods is the enormous amount of required experimental data, severely limiting high‐throughput implementations.…”

Section: Characterization Methods and Inverse Problemsmentioning

confidence: 99%

Single‐Particle Characterization by Elastic Light Scattering

Romanov

Yurkin

2021

Laser & Photonics Reviews

View full text Add to dashboard Cite

The field of light‐scattering characterization of single particles has seen a rapid growth over the last 30 years largely due to the progress in measurement and simulation capabilities. In particular, several methods have been developed to reliably characterize various particles, described by a model with several characteristics, with geometric resolution significantly better than the diffraction limit. However, their development has been largely fragmentary, limited to specific experimental set‐ups. To fill this gap, these lines of development are reviewed within a unified framework. While focusing on characterization algorithms themselves, the experimental aspects related to the isolation and measurement of single particles are also discussed. The existing characterization methods are divided into three classes. The widest class is that of model‐driven methods based on solving parametric inverse light‐scattering problems, using a direct inversion of a low‐dimensional mapping, a nonlinear regression, or neural networks. Other classes include model‐free reconstruction methods and data‐driven classification methods. This review is designed to be extensive in including all relevant literature, but the discussion of semi‐quantitative imaging methods, such as tomography or holography‐based reconstruction, is deliberately omitted. Throughout the review the development of various characterization methods is described, they are critically compared, and promising directions of future research are highlighted.

show abstract

“…In addition to Problem 1, there are also other phaseless inverse problems for equation (1.1) and for related equations; see, for example, [3], [4], [7], [8], [10], [11], [12], [13], [14], [15], [21], [22], [23], [24], and references therein.…”

Section: Introductionmentioning

confidence: 99%

Approximate Lipschitz stability for phaseless inverse scattering with background information

Sivkin

2023

Journal of Inverse and Ill-Posed Problems

View full text Add to dashboard Cite

We prove approximate Lipschitz stability for monochromatic phaseless inverse scattering with background information in dimension d ≥ 2 {d\geq 2} . Moreover, these stability estimates are given in terms of non-overdetermined and incomplete data. Related results for reconstruction from phaseless Fourier transforms are also given. Prototypes of these estimates for the phased case were given in [R. G. Novikov, Approximate Lipschitz stability for non-overdetermined inverse scattering at fixed energy, J. Inverse Ill-Posed Probl. 21 2013, 6, 813–823].

show abstract

A Numerical Method to Solve a Phaseless Coefficient Inverse Problem from a Single Measurement of Experimental Data

Cited by 24 publications

References 74 publications

Phaseless Parametric Inversion for System Calibration and Obtaining Prior Information

Phaseless Parametric Inversion for System Calibration and Obtaining Prior Information

Single‐Particle Characterization by Elastic Light Scattering

Approximate Lipschitz stability for phaseless inverse scattering with background information

Contact Info

Product

Resources

About