pith. sign in

arxiv: 1906.10931 · v1 · pith:7SXN7CIFnew · submitted 2019-06-26 · 📡 eess.SP

Linearized 3-D Electromagnetic Contrast Source Inversion and Its Applications to Half-space Configurations

Shilong Sun , Bert Jan Kooij , Alexander G. Yarovoy This is my paper

Pith reviewed 2026-05-25 15:30 UTC · model grok-4.3

classification 📡 eess.SP
keywords 3D electromagnetic inversioncontrast source inversionlinearized inversioninverse scatteringground-penetrating radarthrough-the-wall imagingsum-of-l1-norm optimizationhalf-space configurations
0
0 comments X

The pith

Linearizing the 3-D electromagnetic inverse scattering problem into two functionals lets total fields be computed only once while preserving reconstruction accuracy.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper puts the 3-D electromagnetic inverse scattering problem into a finite-difference frequency-domain discretization and rewrites it as a cascade of two linear functionals. A sum-of-l1-norm scheme exploits the joint structure of the contrast sources to manage nonuniqueness, with cross-validation confirming the optimization step. After the fields are found once, the contrast is recovered by minimizing a cost functional that combines data and state errors. The method is shown on half-space problems including ground-penetrating radar and through-the-wall imaging.

Core claim

The 3-D electromagnetic inverse scattering problem is discretized in finite-difference frequency-domain and linearized into a cascade of two linear functionals. Nonuniqueness is addressed by sum-of-l1-norm optimization on contrast sources with cross-validation. Total fields in the inversion domain are computed once and then used to reconstruct the contrast via minimization of a cost functional combining data and state errors.

What carries the argument

Cascade of two linear functionals combined with sum-of-l1-norm optimization on the joint structure of contrast sources.

If this is right

  • Total fields in the inversion domain are computed only once instead of at every iteration.
  • Quality and accuracy of the obtained reconstructions are maintained.
  • The procedure applies directly to ground-penetrating radar imaging in half-space configurations.
  • The procedure applies directly to through-the-wall imaging in half-space configurations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The single field computation step could lower the overall cost enough to enable larger 3-D domains or finer grids on the same hardware.
  • Cross-validation inside the contrast-source step offers an internal accuracy check that might transfer to other sparsity-driven inversion schemes.
  • Because the linearization separates the field solve from the contrast recovery, the same cascade structure could be tested on other frequency-domain wave problems that currently iterate on both fields and contrasts.

Load-bearing premise

The nonuniqueness of the inverse problem can be effectively resolved by exploiting the joint structure of the contrast sources with a sum-of-l1-norm optimization scheme.

What would settle it

A numerical test in which the sum-of-l1-norm scheme produces inaccurate contrast sources and the resulting single-field reconstructions visibly degrade compared with a conventional iterative solver.

Figures

Figures reproduced from arXiv: 1906.10931 by Alexander G. Yarovoy, Bert Jan Kooij, Shilong Sun.

Figure 1
Figure 1. Figure 1: The general geometry of the 3-D inverse scattering problem. Sources and receivers [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The geometry of the GPR imaging experiment. Soil: [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Residual curves of the GPR imaging experiment. (a) and (c) Reconstruction residual [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Three-dimensional shape of the reconstructed results in the GPR imaging experiment [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Cross sections of the reconstructed dielectric parameters in the GPR imaging exper [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The geometry of the TW imaging experiment. Wall: [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Residual curves of the TW imaging experiment with lossy object. (a) and (c) Re [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Three-dimensional shape of the reconstructed results in the TW imaging experiment [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Cross sections of the reconstructed dielectric parameters in the TW imaging exper [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Residual curves of the TW imaging experiment with highly conductive object. (a) [PITH_FULL_IMAGE:figures/full_fig_p018_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Three-dimensional shape of the reconstructed results in the TW imaging experiment [PITH_FULL_IMAGE:figures/full_fig_p019_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Cross sections of the reconstructed dielectric parameters in the TW imaging exper [PITH_FULL_IMAGE:figures/full_fig_p020_12.png] view at source ↗
read the original abstract

One of the main computational drawbacks in the application of 3-D iterative inversion techniques is the requirement of solving the field quantities for the updated contrast in every iteration. In this paper, the 3-D electromagnetic inverse scattering problem is put into a discretized finite-difference frequency-domain scheme and linearized into a cascade of two linear functionals. To deal with the nonuniqueness effectively, the joint structure of the contrast sources is exploited using a sum-of-$\ell_1$-norm optimization scheme. A cross-validation technique is used to check whether the optimization process is accurate enough. The total fields are, then, calculated and used to reconstruct the contrast by minimizing a cost functional defined as the sum of the data error and state error. In this procedure, the total fields in the inversion domain are computed only once, while the quality and accuracy of the obtained reconstructions are maintained. The novel method is applied to ground-penetrating radar imaging and through-the-wall imaging, in which the validity and efficiency of the method is demonstrated.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper presents a linearized 3-D electromagnetic contrast source inversion method for half-space configurations (GPR and TWI). The forward problem is discretized via finite-difference frequency-domain, then cast as a cascade of two linear functionals. Nonuniqueness of contrast sources is addressed by a sum-of-ℓ1-norm optimization that exploits their joint structure; cross-validation checks optimization accuracy. Total fields inside the inversion domain are computed only once and inserted into a data-error plus state-error cost functional whose minimization yields the contrast.

Significance. If the central efficiency claim holds, the method removes the dominant computational cost of repeated forward solves in iterative 3-D EM inversion while preserving reconstruction quality. This would be a practical advance for subsurface and through-wall imaging. The sum-of-ℓ1-norm treatment of joint contrast-source structure is a technically interesting device for mitigating nonuniqueness.

major comments (2)
  1. [Abstract] Abstract (central claim paragraph): the assertion that 'the total fields in the inversion domain are computed only once, while the quality and accuracy of the obtained reconstructions are maintained' is the load-bearing efficiency result. No quantitative evidence is supplied that the sum-of-ℓ1-norm step leaves a state error small enough for a single subsequent field evaluation to remain consistent with the recovered contrast; a direct comparison of state-error norms or reconstruction fidelity against a conventional multi-iteration solver is required.
  2. [Method] Method description (linearized cascade and cross-validation step): it is not shown how the cross-validation threshold guarantees that residual non-uniqueness after the ℓ1 step is negligible relative to the linearization error; without an a-posteriori bound or numerical test relating the two error sources, the single-field-computation premise remains unverified.
minor comments (1)
  1. [Notation] Notation for contrast sources and total fields should be introduced once and used uniformly; several symbols appear to be redefined between the linearized functionals and the final cost functional.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major comment below and agree that strengthening the quantitative support for the efficiency claim will improve the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract (central claim paragraph): the assertion that 'the total fields in the inversion domain are computed only once, while the quality and accuracy of the obtained reconstructions are maintained' is the load-bearing efficiency result. No quantitative evidence is supplied that the sum-of-ℓ1-norm step leaves a state error small enough for a single subsequent field evaluation to remain consistent with the recovered contrast; a direct comparison of state-error norms or reconstruction fidelity against a conventional multi-iteration solver is required.

    Authors: We agree that the abstract claim requires supporting quantitative evidence. The manuscript demonstrates validity through GPR and TWI examples, but does not include a head-to-head comparison against a conventional multi-iteration solver. In the revision we will add such a comparison, reporting relative state-error norms and reconstruction fidelity metrics (e.g., correlation coefficient or RMSE) between the single-field linearized result and a standard iterative contrast-source inversion that recomputes fields at each step. revision: yes

  2. Referee: [Method] Method description (linearized cascade and cross-validation step): it is not shown how the cross-validation threshold guarantees that residual non-uniqueness after the ℓ1 step is negligible relative to the linearization error; without an a-posteriori bound or numerical test relating the two error sources, the single-field-computation premise remains unverified.

    Authors: The cross-validation step is used only to confirm that the sum-of-ℓ1 optimization has converged to a stable contrast-source estimate. We acknowledge that no explicit a-posteriori bound or numerical test relating residual non-uniqueness to the linearization error is currently provided. In the revision we will insert a short numerical study that quantifies both error sources on the same test cases and shows that the non-uniqueness residual remains below the linearization error level, thereby supporting the single-field premise. revision: yes

Circularity Check

0 steps flagged

No circularity: linearized cascade and single-field computation are independent of fitted outputs

full rationale

The derivation proceeds by discretizing the forward problem, linearizing the inverse scattering relation into a cascade of two explicit linear functionals, applying an l1-norm joint-structure penalty whose objective is stated separately from the final contrast reconstruction, and using cross-validation on the contrast-source step before a single total-field solve. None of these steps defines a quantity in terms of its own output or renames a fitted parameter as a prediction. The single total-field computation is justified by the claim that the preceding optimization keeps state error small, but this is an empirical assertion rather than a definitional reduction. No self-citation is invoked as a uniqueness theorem or load-bearing premise. The procedure therefore remains self-contained against external benchmarks and receives score 0.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Review based on abstract only; the central approach rests on the validity of linearization and the effectiveness of the chosen optimization for nonuniqueness without independent evidence provided.

axioms (2)
  • domain assumption The 3-D electromagnetic inverse scattering problem can be discretized into a finite-difference frequency-domain scheme and linearized into a cascade of two linear functionals.
    This is the foundational linearization step stated in the abstract as the starting point for the method.
  • domain assumption The joint structure of the contrast sources can be exploited using a sum-of-l1-norm optimization scheme to deal with nonuniqueness effectively.
    Invoked in the abstract to justify the optimization choice for handling nonuniqueness.

pith-pipeline@v0.9.0 · 5712 in / 1544 out tokens · 33560 ms · 2026-05-25T15:30:49.127577+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

67 extracted references · 67 canonical work pages · 1 internal anchor

  1. [1]

    Colton and R

    D. Colton and R. Kress, Inverse acoustic and electromagnetic scattering theory. New York: Springer, 2013, vol. 93. 21

    work page 2013

  2. [2]

    Full-waveform inversion algorithm for interpreting crosshole radar data: A theoretical approach,

    S. Kuroda, M. Takeuchi, and H. J. Kim, “Full-waveform inversion algorithm for interpreting crosshole radar data: A theoretical approach,” Geosciences Journal, vol. 11, no. 3, pp. 211– 217, 2007

    work page 2007

  3. [3]

    Full-waveform inversion of crosshole radar data based on 2-D finite-difference time-domain solutions of maxwell’s equations,

    J. R. Ernst, H. Maurer, A. G. Green, and K. Holliger, “Full-waveform inversion of crosshole radar data based on 2-D finite-difference time-domain solutions of maxwell’s equations,” IEEE Transactions on Geoscience and Remote Sensing, vol. 45, no. 9, pp. 2807–2828, 2007

    work page 2007

  4. [4]

    An overview of full-waveform inversion in exploration geo- physics,

    J. Virieux and S. Operto, “An overview of full-waveform inversion in exploration geo- physics,” Geophysics, vol. 74, no. 6, pp. WCC1–WCC26, 2009

    work page 2009

  5. [5]

    Bleistein, J

    N. Bleistein, J. K. Cohen, W. John Jr et al. , Mathematics of multidimensional seismic imaging, migration, and inversion . New York: Springer, 2013, vol. 13

    work page 2013

  6. [6]

    Microwave biomedical data inversion using the finite-difference contrast source inversion method,

    C. Gilmore, A. Abubakar, W. Hu, T. M. Habashy, and P. M. Van Den Berg, “Microwave biomedical data inversion using the finite-difference contrast source inversion method,” IEEE Transactions on Antennas and Propagation , vol. 57, no. 5, pp. 1528–1538, 2009

    work page 2009

  7. [7]

    Compressive diffuse optical tomography: non- iterative exact reconstruction using joint sparsity,

    O. Lee, J. M. Kim, Y. Bresler, and J. C. Ye, “Compressive diffuse optical tomography: non- iterative exact reconstruction using joint sparsity,” IEEE transactions on medical imaging, vol. 30, no. 5, pp. 1129–1142, 2011

    work page 2011

  8. [8]

    Acoustic inversion in optoacoustic to- mography: A review,

    A. Rosenthal, V. Ntziachristos, and D. Razansky, “Acoustic inversion in optoacoustic to- mography: A review,” Current medical imaging reviews, vol. 9, no. 4, pp. 318–336, 2013

    work page 2013

  9. [9]

    Hadamard, Lectures on Cauchy’s problem in linear partial differential equations

    J. Hadamard, Lectures on Cauchy’s problem in linear partial differential equations . Mi- neola, New York: Dover Publications, Inc., 2014

    work page 2014

  10. [10]

    A modified gradient method for two-dimensional problems in tomography,

    R. Kleinman and P. Van den Berg, “A modified gradient method for two-dimensional problems in tomography,” Journal of Computational and Applied Mathematics , vol. 42, no. 1, pp. 17–35, 1992

    work page 1992

  11. [11]

    An extended range-modified gradient technique for profile inversion,

    R. E. Kleinman and P. den Berg, “An extended range-modified gradient technique for profile inversion,” Radio Science, vol. 28, no. 5, pp. 877–884, 1993

    work page 1993

  12. [12]

    Two-dimensional location and shape reconstruction,

    R. Kleinman and P. den Berg, “Two-dimensional location and shape reconstruction,” Radio Science, vol. 29, no. 4, pp. 1157–1169, 1994

    work page 1994

  13. [13]

    A contrast source inversion method,

    P. M. Van Den Berg and R. E. Kleinman, “A contrast source inversion method,” Inverse problems, vol. 13, no. 6, p. 1607, 1997

    work page 1997

  14. [14]

    Nonlinear inversion of a buried object in transverse electric scattering,

    B. Kooij, M. Lambert, and D. Lesselier, “Nonlinear inversion of a buried object in transverse electric scattering,” Radio Science, vol. 34, no. 6, pp. 1361–1371, 1999

    work page 1999

  15. [15]

    Microwave imaging of inhomogeneous objects made of a finite number of dielectric and conductive materials from experimental data,

    O. F´ eron, B. Duchˆ ene, and A. Mohammad-Djafari, “Microwave imaging of inhomogeneous objects made of a finite number of dielectric and conductive materials from experimental data,” Inverse Problems, vol. 21, no. 6, p. S95, 2005

    work page 2005

  16. [16]

    Inversion of multi-frequency experimental data for imaging complex objects by a DTA–CSI method,

    C. Yu, L.-P. Song, and Q. H. Liu, “Inversion of multi-frequency experimental data for imaging complex objects by a DTA–CSI method,” Inverse Problems , vol. 21, no. 6, p. S165, 2005

    work page 2005

  17. [17]

    An iterative solution of the two-dimensional electromagnetic inverse scattering problem,

    Y. Wang and W. C. Chew, “An iterative solution of the two-dimensional electromagnetic inverse scattering problem,” International Journal of Imaging Systems and Technology , vol. 1, no. 1, pp. 100–108, 1989. 22

    work page 1989

  18. [18]

    Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method,

    W. C. Chew and Y.-M. Wang, “Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method,” IEEE transactions on medical imaging , vol. 9, no. 2, pp. 218–225, 1990

    work page 1990

  19. [19]

    Three-dimensional reconstruction of objects buried in layered media using Born and distorted Born iterative methods,

    F. Li, Q. H. Liu, and L.-p. Song, “Three-dimensional reconstruction of objects buried in layered media using Born and distorted Born iterative methods,” IEEE geoscience and remote sensing letters , vol. 1, no. 2, pp. 107–111, 2004

    work page 2004

  20. [20]

    Comparison of an enhanced distorted Born iter- ative method and the multiplicative-regularized contrast source inversion method,

    C. Gilmore, P. Mojabi, and J. LoVetri, “Comparison of an enhanced distorted Born iter- ative method and the multiplicative-regularized contrast source inversion method,” IEEE Transactions on Antennas and Propagation , vol. 57, no. 8, pp. 2341–2351, 2009

    work page 2009

  21. [21]

    Fast spectral methods for the shape identification problem of a perfectly conducting obstacle,

    F. L. Lou¨ er, “Fast spectral methods for the shape identification problem of a perfectly conducting obstacle,” in The open archive HAL , 2013, pp. 1–16

    work page 2013

  22. [22]

    Electromagnetic inverse scattering of multiple two-dimensional perfectly con- ducting objects by the differential evolution strategy,

    A. Qing, “Electromagnetic inverse scattering of multiple two-dimensional perfectly con- ducting objects by the differential evolution strategy,” IEEE Transactions on Antennas and Propagation, vol. 51, no. 6, pp. 1251–1262, 2003

    work page 2003

  23. [23]

    Electromagnetic inverse scattering of multiple perfectly conducting cylinders by differential evolution strategy with individuals in groups (GDES),

    ——, “Electromagnetic inverse scattering of multiple perfectly conducting cylinders by differential evolution strategy with individuals in groups (GDES),” IEEE Transactions on Antennas and Propagation, vol. 52, no. 5, pp. 1223–1229, 2004

    work page 2004

  24. [24]

    A simple method for solving inverse scattering problems in the resonance region,

    D. Colton and A. Kirsch, “A simple method for solving inverse scattering problems in the resonance region,” Inverse problems, vol. 12, no. 4, p. 383, 1996

    work page 1996

  25. [25]

    A simple method using Morozov’s discrepancy principle for solving inverse scattering problems,

    D. Colton, M. Piana, and R. Potthast, “A simple method using Morozov’s discrepancy principle for solving inverse scattering problems,” Inverse Problems, vol. 13, no. 6, p. 1477, 1997

    work page 1997

  26. [26]

    A linear sampling method for near-field inverse problems in elastodynamics,

    S. N. Fata and B. B. Guzina, “A linear sampling method for near-field inverse problems in elastodynamics,” Inverse problems, vol. 20, no. 3, p. 713, 2004

    work page 2004

  27. [27]

    On the feasibility of the linear sampling method for 3D GPR surveys,

    I. Catapano, F. Soldovieri, and L. Crocco, “On the feasibility of the linear sampling method for 3D GPR surveys,” Progress In Electromagnetics Research, vol. 118, pp. 185–203, July 2011

    work page 2011

  28. [28]

    Why linear sampling works,

    T. Arens, “Why linear sampling works,” Inverse Problems, vol. 20, no. 1, p. 163, 2003

    work page 2003

  29. [29]

    Three-dimensional near-field microwave imaging using hybrid linear sampling and level set methods in a medium with compact support,

    M. R. Eskandari, R. Safian, and M. Dehmollaian, “Three-dimensional near-field microwave imaging using hybrid linear sampling and level set methods in a medium with compact support,” IEEE Transactions on Antennas and Propagation , vol. 62, no. 10, pp. 5117– 5125, 2014

    work page 2014

  30. [30]

    D. J. Daniels, Ground penetrating radar. Wiley Online Library, 2005

    work page 2005

  31. [31]

    M. G. Amin, Through-the-wall radar imaging . CRC press, 2016

    work page 2016

  32. [32]

    A tomographic formulation of spotlight- mode synthetic aperture radar,

    D. C. Munson, J. D. O’Brien, and W. K. Jenkins, “A tomographic formulation of spotlight- mode synthetic aperture radar,” Proceedings of the IEEE, vol. 71, no. 8, pp. 917–925, 1983

    work page 1983

  33. [33]

    Time-reversal mirrors,

    M. Fink, “Time-reversal mirrors,” Journal of Physics D: Applied Physics , vol. 26, no. 9, p. 1333, 1993

    work page 1993

  34. [34]

    Time-reversed acoustics,

    M. Fink, D. Cassereau, A. Derode, C. Prada, P. Roux, M. Tanter, J.-L. Thomas, and F. Wu, “Time-reversed acoustics,” Reports on progress in Physics, vol. 63, no. 12, p. 1933, 2000. 23

    work page 1933

  35. [35]

    Dort method as applied to electromagnetic subsurface sens- ing,

    G. Micolau and M. Saillard, “Dort method as applied to electromagnetic subsurface sens- ing,” Radio Science, vol. 38, no. 3, 2003

    work page 2003

  36. [36]

    Frequency dispersion compensation in time reversal techniques for UWB electromagnetic waves,

    M. E. Yavuz and F. L. Teixeira, “Frequency dispersion compensation in time reversal techniques for UWB electromagnetic waves,” IEEE Geoscience and Remote sensing letters, vol. 2, no. 2, pp. 233–237, 2005

    work page 2005

  37. [37]

    Electromagnetic target detection in uncertain media: Time-reversal and minimum-variance algorithms,

    D. Liu, J. Krolik, and L. Carin, “Electromagnetic target detection in uncertain media: Time-reversal and minimum-variance algorithms,” IEEE Transactions on Geoscience and Remote Sensing, vol. 45, no. 4, pp. 934–944, 2007

    work page 2007

  38. [38]

    Space–frequency ultrawideband time-reversal imaging,

    M. E. Yavuz and F. L. Teixeira, “Space–frequency ultrawideband time-reversal imaging,” IEEE Transactions on Geoscience and Remote Sensing, vol. 46, no. 4, pp. 1115–1124, 2008

    work page 2008

  39. [39]

    Imaging and tracking of targets in clutter using differential time-reversal techniques,

    A. E. Fouda and F. L. Teixeira, “Imaging and tracking of targets in clutter using differential time-reversal techniques,” Waves in Random and Complex Media , vol. 22, no. 1, pp. 66– 108, 2012

    work page 2012

  40. [40]

    Ultrawideband time-reversal imaging with frequency domain sampling,

    S. Bahrami, A. Cheldavi, and A. Abdolali, “Ultrawideband time-reversal imaging with frequency domain sampling,” IEEE Geoscience and Remote Sensing Letters, vol. 11, no. 3, pp. 597–601, 2014

    work page 2014

  41. [41]

    Statistical stability of ultrawideband time-reversal imaging in random media,

    A. E. Fouda and F. L. Teixeira, “Statistical stability of ultrawideband time-reversal imaging in random media,” IEEE Transactions on Geoscience and Remote Sensing , vol. 52, no. 2, pp. 870–879, 2014

    work page 2014

  42. [42]

    Time reversal imaging of obscured targets from multistatic data,

    A. Devaney, “Time reversal imaging of obscured targets from multistatic data,” IEEE Transactions on Antennas and Propagation , vol. 53, no. 5, pp. 1600–1610, 2005

    work page 2005

  43. [43]

    Subspace-based localization and inverse scattering of multiply scattering point targets,

    E. A. Marengo and F. K. Gruber, “Subspace-based localization and inverse scattering of multiply scattering point targets,” EURASIP Journal on Advances in Signal Processing , vol. 2007, no. 1, pp. 1–16, 2006

    work page 2007

  44. [44]

    Time-reversal MUSIC imaging of ex- tended targets,

    E. A. Marengo, F. K. Gruber, and F. Simonetti, “Time-reversal MUSIC imaging of ex- tended targets,” IEEE Transactions on image processing , vol. 16, no. 8, pp. 1967–1984, 2007

    work page 1967

  45. [45]

    Performance analysis of time-reversal MUSIC,

    D. Ciuonzo, G. Romano, and R. Solimene, “Performance analysis of time-reversal MUSIC,” IEEE Transactions on Signal Processing , vol. 63, no. 10, pp. 2650–2662, 2015

    work page 2015

  46. [46]

    GPR imaging via qualitative and quantitative approaches,

    I. Catapano, A. Randazzo, E. Slob, and R. Solimene, “GPR imaging via qualitative and quantitative approaches,” in Civil Engineering Applications of Ground Penetrating Radar . New York: Springer, 2015, pp. 239–280

    work page 2015

  47. [47]

    Comments on the filtered backprojection algorithm, range conditions, and the pseudoinverse solution,

    M. A. Anastasio, X. Pan, and E. Clarkson, “Comments on the filtered backprojection algorithm, range conditions, and the pseudoinverse solution,”IEEE transactions on medical imaging, vol. 20, no. 6, pp. 539–542, 2001

    work page 2001

  48. [48]

    Comparison of the imaging resolutions of time reversal and back-projection algorithms in EM inverse scattering,

    P. Zhang, X. Zhang, and G. Fang, “Comparison of the imaging resolutions of time reversal and back-projection algorithms in EM inverse scattering,” IEEE Geoscience and Remote Sensing Letters, vol. 10, no. 2, pp. 357–361, 2013

    work page 2013

  49. [49]

    On simple methods for shape reconstruction of unknown scatterers,

    I. Catapano, L. Crocco, and T. Isernia, “On simple methods for shape reconstruction of unknown scatterers,” IEEE transactions on antennas and propagation , vol. 55, no. 5, pp. 1431–1436, 2007. 24

    work page 2007

  50. [50]

    The linear sampling method as a way to quantitative inverse scattering,

    L. Crocco, I. Catapano, L. Di Donato, and T. Isernia, “The linear sampling method as a way to quantitative inverse scattering,” IEEE Transactions on Antennas and Propagation, vol. 60, no. 4, pp. 1844–1853, 2012

    work page 2012

  51. [51]

    Inverse scattering via vir- tual experiments and contrast source regularization,

    L. Di Donato, M. T. Bevacqua, L. Crocco, and T. Isernia, “Inverse scattering via vir- tual experiments and contrast source regularization,” IEEE Transactions on Antennas and Propagation, vol. 63, no. 4, pp. 1669–1677, 2015

    work page 2015

  52. [52]

    Model-based quantitative cross-borehole GPR imaging via virtual experiments,

    L. Di Donato and L. Crocco, “Model-based quantitative cross-borehole GPR imaging via virtual experiments,” IEEE Transactions on Geoscience and Remote Sensing, vol. 53, no. 8, pp. 4178–4185, 2015

    work page 2015

  53. [53]

    A hybrid quantitative method for inverse scattering of multiple dielectric objects,

    M. Rabbani, A. Tavakoli, and M. Dehmollaian, “A hybrid quantitative method for inverse scattering of multiple dielectric objects,” IEEE Transactions on Antennas and Propagation, vol. 64, no. 3, pp. 977–987, 2016

    work page 2016

  54. [54]

    Fast three-dimensional electromagnetic nonlinear inversion in layered media with a novel scattering approximation,

    L.-P. Song and Q. H. Liu, “Fast three-dimensional electromagnetic nonlinear inversion in layered media with a novel scattering approximation,” Inverse Problems, vol. 20, no. 6, p. S171, 2004

    work page 2004

  55. [55]

    3D finite-difference frequency-domain method for plasmonics and nanophoton- ics,

    W. Shin, “3D finite-difference frequency-domain method for plasmonics and nanophoton- ics,” Ph.D. dissertation, Stanford University, The Department of Electrical Engineering, USA, 2013

    work page 2013

  56. [56]

    A Bayesian-compressive-sampling-based inversion for imaging sparse scatterers,

    G. Oliveri, P. Rocca, and A. Massa, “A Bayesian-compressive-sampling-based inversion for imaging sparse scatterers,” IEEE Transactions on Geoscience and Remote Sensing, vol. 49, no. 10, pp. 3993–4006, 2011

    work page 2011

  57. [57]

    Distributed compressed sensing of jointly sparse signals,

    S. Sarvotham, D. Baron, M. Wakin, M. F. Duarte, and R. G. Baraniuk, “Distributed compressed sensing of jointly sparse signals,” in Asilomar conference on signals, systems, and computers, 2005, pp. 1537–1541

    work page 2005

  58. [58]

    Theoretical results on sparse representations of multiple- measurement vectors,

    J. Chen and X. Huo, “Theoretical results on sparse representations of multiple- measurement vectors,” IEEE Transactions on Signal Processing, vol. 54, no. 12, pp. 4634– 4643, 2006

    work page 2006

  59. [59]

    Theoretical and empirical results for recovery from multiple measurements,

    E. Van Den Berg and M. P. Friedlander, “Theoretical and empirical results for recovery from multiple measurements,” IEEE Transactions on Information Theory , vol. 56, no. 5, pp. 2516–2527, 2010

    work page 2010

  60. [60]

    Probing the Pareto frontier for basis pursuit solutions,

    E. van den Berg and M. P. Friedlander, “Probing the Pareto frontier for basis pursuit solutions,” SIAM Journal on Scientific Computing , vol. 31, no. 2, pp. 890–912, 2008

    work page 2008

  61. [61]

    Sparse optimization with least-squares con- straints,

    E. Van den Berg and M. P. Friedlander, “Sparse optimization with least-squares con- straints,” SIAM Journal on Optimization , vol. 21, no. 4, pp. 1201–1229, 2011

    work page 2011

  62. [62]

    Compressed sensing with cross validation,

    R. Ward, “Compressed sensing with cross validation,” IEEE Transactions on Information Theory, vol. 55, no. 12, pp. 5773–5782, 2009

    work page 2009

  63. [63]

    Cross Validation in Compressive Sensing and its Application of OMP-CV Algorithm

    J. Zhang, L. Chen, P. T. Boufounos, and Y. Gu, “Cross validation in compressive sensing and its application of OMP-CV algorithm,” arXiv preprint arXiv:1602.06373 , 2016

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  64. [64]

    W. Shin. (2015) MaxwellFDFD Webpage. https://github.com/wsshin/maxwellfdfd

    work page 2015

  65. [65]

    R. P. Brent, Algorithms for minimization without derivatives . New Jersey: Englewood Cliffs, 1973. 25

    work page 1973

  66. [66]

    G. E. Forsythe, M. A. Malcolm, and C. B. Moler, Computer Methods for Mathematical Computations. Prentice-Hall, 1976

    work page 1976

  67. [67]

    Multiplicative regularization for contrast profile inversion,

    P. M. van den Berg, A. Abubakar, and J. T. Fokkema, “Multiplicative regularization for contrast profile inversion,” Radio Science, vol. 38, no. 2, pp. 1–10, 2003. 26

    work page 2003