pith. sign in

arxiv: 1906.10875 · v1 · pith:TOSVTG5Cnew · submitted 2019-06-26 · 📡 eess.SP

A Linear Method for Shape Reconstruction based on the Generalized Multiple Measurement Vectors Model

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

Pith reviewed 2026-05-25 15:43 UTC · model grok-4.3

classification 📡 eess.SP
keywords shape reconstructiongeneralized multiple measurement vectorslinear sampling methodcontrast sourceselectromagnetic imagingjoint sparsitycross validation
0
0 comments X

The pith

A GMMV-based linear method reconstructs shapes from electromagnetic scattering data more sharply than the linear sampling method.

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

The paper proposes solving discretized Maxwell's equations via a generalized multiple measurement vectors formulation in which contrast sources are recovered iteratively under a joint sparsity constraint. Cross-validation halts the iterations so that the noise level need not be known in advance. The resulting linear reconstruction is applied to transverse-magnetic experimental data and compared directly with the linear sampling method. The authors report that the new approach produces tighter focus on the true support of the scatterers. A reader would care because the method supplies a practical route to shape recovery that sidesteps both explicit noise estimation and manual regularization tuning.

Core claim

The GMMV-based linear method, which solves contrast sources iteratively under a joint sparsity constraint with cross-validation termination, produces shape reconstructions from TM experimental data that focus better than those from the linear sampling method.

What carries the argument

Generalized multiple measurement vectors model applied to contrast sources, with joint sparsity as the regularizer and cross-validation for automatic iteration stopping.

Load-bearing premise

The joint sparsity constraint on contrast sources combined with cross-validation termination produces stable and accurate shape estimates without explicit knowledge of the noise level or additional regularization tuning.

What would settle it

A controlled comparison on the same TM experimental data set, with known ground-truth shapes, that measures whether the reported focusing advantage disappears when the noise level is supplied to both methods or when the sparsity level is deliberately mismatched.

Figures

Figures reproduced from arXiv: 1906.10875 by Alexander G. Yarovoy, Bert Jan Kooij, Shilong Sun, Tian Jin.

Figure 1
Figure 1. Figure 1: Probing the Pareto curve: the update of parameter [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Measurement configuration of the data-sets: [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Normalized reconstruction residual curve and CV residual curve in Example 1, Subsec [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Scatterer geometry and its reconstructed shapes for Example 1 in Subsection 4.1: [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Measurement configuration of the data-sets: [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Normalized reconstruction residual curve and CV residual curve in Example 2, Sub [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Scatterer geometry and its reconstructed shapes for the [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Normalized reconstruction residual curve and the CV residual curve in Subsection 4.2. [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Scatterer geometry and its reconstructed shapes for the rectangular metallic cylinder [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Scatterer geometry and its reconstructed shapes for the “U-shaped” metallic cylinder [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Normalized reconstruction residual curve and the CV residual curve in Subsection 4.3. [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Scatterer geometry and its reconstructed shapes for the hybrid scatterers obtained by [PITH_FULL_IMAGE:figures/full_fig_p015_12.png] view at source ↗
read the original abstract

In this paper, a novel linear method for shape reconstruction is proposed based on the generalized multiple measurement vectors (GMMV) model. Finite difference frequency domain (FDFD) is applied to discretized Maxwell's equations, and the contrast sources are solved iteratively by exploiting the joint sparsity as a regularized constraint. Cross validation (CV) technique is used to terminate the iterations, such that the required estimation of the noise level is circumvented. The validity is demonstrated with an excitation of transverse magnetic (TM) experimental data, and it is observed that, in the aspect of focusing performance, the GMMV-based linear method outperforms the extensively used linear sampling method (LSM).

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 / 2 minor

Summary. The paper proposes a linear shape reconstruction method for electromagnetic inverse scattering based on the generalized multiple measurement vectors (GMMV) model. Maxwell's equations are discretized via finite-difference frequency-domain (FDFD), contrast sources are recovered iteratively under a joint-sparsity regularizer, and cross-validation (CV) terminates the iteration to avoid explicit noise-level estimation. On transverse-magnetic (TM) experimental data the method is reported to produce superior focusing compared with the linear sampling method (LSM).

Significance. If the reported focusing improvement is quantitatively confirmed, the combination of GMMV joint sparsity with CV-based early stopping supplies a practical, essentially parameter-free linear reconstruction route that sidesteps noise-level tuning. This would be useful for applications requiring stable shape estimates from limited multi-frequency, multi-illumination data.

major comments (2)
  1. [Abstract / §4 (experimental validation)] Abstract and experimental-results section: the central claim that the GMMV method 'outperforms' LSM in focusing performance is stated without any quantitative metric (e.g., normalized mean-square error, focusing width, or Dice coefficient), error bars, or specification of the number of frequencies and illuminations employed. This absence prevents verification of the empirical superiority asserted in the reader's strongest claim.
  2. [§3 (iterative solver and CV)] Method description (GMMV solver and CV termination): while the pipeline is internally consistent, the manuscript does not detail how the cross-validation partition is constructed (which measurements are held out) or how the joint-sparsity regularizer is scaled across frequencies. These choices directly affect the stability claim in the reader's weakest assumption and must be made explicit before the 'no noise-level estimation' advantage can be assessed.
minor comments (2)
  1. [§2] Notation for the contrast-source vector and the GMMV matrix should be introduced once with a clear dimension statement; subsequent equations reuse symbols without re-definition.
  2. [§4] Figure captions for the reconstructed shapes should state the exact operating frequencies and number of illuminations used in each panel.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major comment below and will incorporate revisions to provide the requested details and quantitative support.

read point-by-point responses

  1. Referee: [Abstract / §4 (experimental validation)] Abstract and experimental-results section: the central claim that the GMMV method 'outperforms' LSM in focusing performance is stated without any quantitative metric (e.g., normalized mean-square error, focusing width, or Dice coefficient), error bars, or specification of the number of frequencies and illuminations employed. This absence prevents verification of the empirical superiority asserted in the reader's strongest claim.

    Authors: We agree that quantitative metrics would strengthen the empirical claim. In the revised manuscript we will add normalized mean-square error on the reconstructed contrast, focusing width at half-maximum, and the exact numbers of frequencies and illuminations used in the TM experiments. This will allow direct verification of the reported focusing improvement. revision: yes

  2. Referee: [§3 (iterative solver and CV)] Method description (GMMV solver and CV termination): while the pipeline is internally consistent, the manuscript does not detail how the cross-validation partition is constructed (which measurements are held out) or how the joint-sparsity regularizer is scaled across frequencies. These choices directly affect the stability claim in the reader's weakest assumption and must be made explicit before the 'no noise-level estimation' advantage can be assessed.

    Authors: We will expand §3 to specify the CV partition (which measurements are held out) and the scaling of the joint-sparsity regularizer across frequencies. These additions will make the implementation reproducible and allow readers to evaluate the parameter-free aspect of the method. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper presents a GMMV-based iterative solver for contrast sources (FDFD discretization of Maxwell equations + joint-sparsity regularization + CV early stopping) and reports an empirical comparison of focusing performance against LSM on TM experimental data. No load-bearing step reduces by the paper's own equations to a fitted parameter renamed as prediction, a self-definitional loop, or a self-citation chain that imports uniqueness or an ansatz. The method is a direct application of the stated GMMV model; the central claim remains an externally falsifiable observation on measured data rather than a derivation equivalent to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the joint-sparsity model for contrast sources and the appropriateness of cross-validation for iteration stopping in the presence of unknown noise. No free parameters are explicitly named in the abstract, but regularization weights and grid discretization choices are implicit. No new physical entities are introduced.

axioms (2)
  • domain assumption Joint sparsity across multiple illuminations is an appropriate regularizer for contrast sources in the discretized Maxwell system.
    Invoked when the GMMV model is applied to solve for contrast sources iteratively.
  • domain assumption Cross-validation provides a reliable stopping criterion without requiring an estimate of the noise level.
    Stated as the reason CV is used to terminate iterations.

pith-pipeline@v0.9.0 · 5645 in / 1418 out tokens · 25527 ms · 2026-05-25T15:43:39.453154+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

55 extracted references · 55 canonical work pages

  1. [1]

    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

  2. [2]

    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

  3. [3]

    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

  4. [4]

    Bleistein, J

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

    work page 2013

  5. [5]

    Integral formulation for migration in two and three dimensions,

    W. A. Schneider, “Integral formulation for migration in two and three dimensions,” Geo- physics, vol. 43, no. 1, pp. 49–76, 1978

    work page 1978

  6. [6]

    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

  7. [7]

    Time-reversal mirrors,

    M. Fink, “Time-reversal mirrors,” Journal of Physics D: Applied Physics , vol. 26, no. 9, pp. 1333–1350, 1993

    work page 1993

  8. [8]

    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, pp. 1933–1995, 2000

    work page 1933

  9. [9]

    D.O.R.T. method as applied to electromagnetic subsurface sensing,

    G. Micolau and M. Saillard, “D.O.R.T. method as applied to electromagnetic subsurface sensing,” Radio Science, vol. 38, no. 3, pp. 4.1–4.12, 2003

    work page 2003

  10. [10]

    Frequency dispersion compensation in time reversal tech- niques for UWB electromagnetic waves,

    M. E. Yavuz and F. L. Teixeira, “Frequency dispersion compensation in time reversal tech- niques for UWB electromagnetic waves,” IEEE Geoscience and Remote Sensing Letters , vol. 2, no. 2, pp. 233–237, 2005. 16

    work page 2005

  11. [11]

    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

  12. [12]

    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

  13. [13]

    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

  14. [14]

    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

  15. [15]

    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

  16. [16]

    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

  17. [17]

    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

  18. [18]

    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

  19. [19]

    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

  20. [20]

    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

  21. [21]

    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, pp. 383–393, 1996

    work page 1996

  22. [22]

    A simple method using Morozov’s discrepancy prin- ciple for solving inverse scattering problems,

    D. Colton, M. Piana, and R. Potthast, “A simple method using Morozov’s discrepancy prin- ciple for solving inverse scattering problems,” Inverse Problems, vol. 13, no. 6, pp. 14777– 1493, 1997

    work page 1997

  23. [23]

    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, pp. 713–736, 2004

    work page 2004

  24. [24]

    Why linear sampling works,

    T. Arens, “Why linear sampling works,” Inverse Problems , vol. 20, no. 1, pp. 163–173, 2003

    work page 2003

  25. [25]

    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

    work page 2007

  26. [26]

    The linear sampling method and the MUSIC algorithm,

    M. Cheney, “The linear sampling method and the MUSIC algorithm,” Inverse Problems, vol. 17, no. 4, pp. 591–595, 2001. 17

    work page 2001

  27. [27]

    Newton-Kantorovitch algorithm applied to an electromagnetic inverse problem,

    A. Roger, “Newton-Kantorovitch algorithm applied to an electromagnetic inverse problem,” IEEE Transactions on Antennas and Propagation , vol. 29, no. 2, pp. 232–238, 1981

    work page 1981

  28. [28]

    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

  29. [29]

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

    A. Qing, “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

  30. [30]

    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

  31. [31]

    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

  32. [32]

    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

  33. [33]

    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, pp. 1607–1620, 1997

    work page 1997

  34. [34]

    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

    work page 1989

  35. [35]

    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

  36. [36]

    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

  37. [37]

    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

  38. [38]

    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

  39. [39]

    Joint sparsity with different measurement matrices,

    R. Heckel and H. B¨ olcskei, “Joint sparsity with different measurement matrices,” in 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton) , pp. 698–702, IEEE, Oct. 2012

    work page 2012

  40. [40]

    Shin, 3D finite-difference frequency-domain method for plasmonics and nanophotonics

    W. Shin, 3D finite-difference frequency-domain method for plasmonics and nanophotonics . PhD thesis, Stanford University, 2013

    work page 2013

  41. [41]

    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

  42. [42]

    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. 18

    work page 2011

  43. [43]

    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

  44. [44]

    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

  45. [45]

    Robust uncertainty principles: Exact signal re- construction from highly incomplete frequency information,

    E. J. Cand` es, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal re- construction from highly incomplete frequency information,” IEEE Transactions on Infor- mation Theory, vol. 52, no. 2, pp. 489–509, 2006

    work page 2006

  46. [46]

    Shape reconstruction via equivalence principles, constrained inverse source problems and sparsity promotion,

    M. Bevacqua and T. Isernia, “Shape reconstruction via equivalence principles, constrained inverse source problems and sparsity promotion,” Progress In Electromagnetics Research, vol. 158, pp. 37–48, Feb. 2017

    work page 2017

  47. [47]

    Special section: Testing inversion algorithms against exper- imental data,

    K. Belkebir and M. Saillard, “Special section: Testing inversion algorithms against exper- imental data,” Inverse Problems, vol. 17, no. 6, pp. 1565–1571, 2001

    work page 2001

  48. [48]

    Free space experimental scattering database continuation: experimental set-up and measurement precision,

    J.-M. Geffrin, P. Sabouroux, and C. Eyraud, “Free space experimental scattering database continuation: experimental set-up and measurement precision,” Inverse Problems, vol. 21, no. 6, pp. S117–S130, 2005

    work page 2005

  49. [49]

    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

  50. [50]

    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

  51. [51]

    Rank awareness in joint sparse recovery,

    M. E. Davies and Y. C. Eldar, “Rank awareness in joint sparse recovery,” IEEE Transac- tions on Information Theory , vol. 58, no. 2, pp. 1135–1146, 2012

    work page 2012

  52. [52]

    A linear model for microwave imaging of highly conductive scatterers,

    S. Sun, B. J. Kooij, and A. G. Yarovoy, “A linear model for microwave imaging of highly conductive scatterers,” IEEE Transactions on Microwave Theory and Techniques, vol. PP, no. 99, pp. 1–16, 2017

    work page 2017

  53. [53]

    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

  54. [54]

    Improved sampling methods for shape reconstruc- tion of 3-D buried targets,

    I. Catapano, L. Crocco, and T. Isernia, “Improved sampling methods for shape reconstruc- tion of 3-D buried targets,” IEEE Transactions on Geoscience and Remote Sensing, vol. 46, no. 10, pp. 3265–3273, 2008

    work page 2008

  55. [55]

    Inversion of experimen- tal multi-frequency data using the contrast source inversion method,

    R. F. Bloemenkamp, A. Abubakar, and P. M. Van Den Berg, “Inversion of experimen- tal multi-frequency data using the contrast source inversion method,” Inverse Problems, vol. 17, no. 6, pp. 1611–1622, 2001. 19

    work page 2001