A bayesian-compressive-sampling-based inversion for imaging sparse scatterers

IEEE Transactions on Geoscience and Remote Sensing

Volumn 49, Issue 10 PART 2, 2011, Pages 3993-4006

  Oliveri, Giacomo ^a   Rocca, Paolo ^a   Massa, Andrea ^a  

^a UNIVERSITY OF TRENTO   (Italy)

Author keywords

Bayesian compressive sampling (BCS); contrast source formulation; inverse scattering; microwave imaging; relevance vector machine (RVM)

Indexed keywords

COMPRESSIVE SAMPLING; CONTRAST SOURCE FORMULATION; INVERSE SCATTERING; MICROWAVE IMAGING; RELEVANCE VECTOR MACHINE;

INVERSE PROBLEMS;

SCATTERING;

BAYESIAN ANALYSIS; DATA INVERSION; ERROR CORRECTION; HIERARCHICAL SYSTEM; IMAGE ANALYSIS; INVERSE PROBLEM; MICROWAVE IMAGERY; PROBABILITY; SAMPLING; SCATTERING; SIGNAL-TO-NOISE RATIO;

EID: 80053563269     PISSN: 01962892     EISSN: None     Source Type: Journal    
DOI: 10.1109/TGRS.2011.2128329     Document Type: Article

References (54)

1. D. Lesselier and T. Habashy, "Special issue on 'Electromagnetic imaging and inversion on the Earth's subsurface'," Inverse Probl., vol. 16, no. 5, Oct. 2000.
2. W. C. Chew and D. Lesseliser, "Special issue on 'Electromagnetic characterization of buried obstacles'," Inverse Probl., vol. 20, no. 6, pp. S1-S15, Dec. 2004.
3. J. A. Tropp and S. J. Wright, "Computational methods for sparse solution of linear inverse problems," Proc. IEEE, vol. 98, no. 6, pp. 948-958, Jun. 2010.
4. S. F. Cotter, B. D. Rao, K. Engan, and K. Kreutz-Delgado, "Sparse solutions to linear inverse problems with multiple measurement vectors," IEEE Trans. Signal Process., vol. 53, no. 7, pp. 2477-2488, Jul. 2005. (Pubitemid 41174440)
5. A. Abubakar, P. M. van den Berg, T. M. Habashy, and H. Braunisch, "A multiplicative regularization approach for deblurring problems," IEEE Trans. Image Process., vol. 13, no. 11, pp. 1524-1532, Nov. 2004.
6. C.-C. Chen, J. T. Johnson, M. Sato, and A. G. Yarovoy, "Special issue on 'Subsurface sensing using ground-penetrating radar'," IEEE Trans. Geosci. Remote Sens., vol. 44, no. 3, p. 751, Mar. 2006.
7. M. Pastorino, "Modern microwave: Inverse-scattering techniques for image reconstruction," IEEE Instrum. Meas. Mag., vol. 1, no. 4, pp. 20-25, Dec. 1998. (Pubitemid 128497887)
8. M. Pastorino, "Short-range microwave inverse scattering techniques for image reconstruction and applications," IEEE Trans. Instrum. Meas., vol. 47, no. 6, pp. 1419-1427, Dec. 1998. (Pubitemid 128738614)
9. M. Donelli, D. Franceschini, P. Rocca, and A.Massa, "Three- dimensional microwave imaging problems solved through an efficient multi-scaling particle swarm optimization," IEEE Trans. Geosci. Remote Sens., vol. 47, no. 5, pp. 1467-1481, May 2009.
10. M. Benedetti, D. Lesselier, M. Lambert, and A. Massa, "Multiple shapes reconstruction by means of multi-region level sets," IEEE Trans. Geosci. Remote Sens., vol. 48, no. 5, pp. 2330-2342, May 2010.
11. D. Lesselier and J. Bowler, "Special issue on 'Electromagnetic and ultrasonic nondestructive evaluation'," Inverse Probl., vol. 18, no. 6, pp. 1857-1871, Dec. 2002.
12. G. C. Giakos, M. Pastorino, F. Russo, S. Chowdhury, N. Shah, and W. Dawros, "Noninvasive imaging for the new century," IEEE Instrum. Meas. Mag., vol. 2, no. 2, pp. 32-35, Jun. 1999.
13. T. Lasri and R. Zoughi, "Special issue on "Advances and applications in microwave and millimeter wave nondestructive evaluation"," Subsurf. Sens. Technol. Appl., vol. 2, no. 4, pp. 435-451, Oct. 2001.
14. M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging. Bristol, U.K.: IOP, 1998.
15. P. Rocca, M. Donelli, G. L. Gragnani, and A. Massa, "Iterative multiresolution retrieval of non-measurable equivalent currents for the imaging of dielectric objects," Inverse Probl., vol. 25, no. 5, pp. 55 004-55 018, May 2009.
16. K. Agarwal, L. Pan, and X. Chen, "Subspace-based optimization method for reconstruction of 2-D complex anisotropic dielectric objects," IEEE Trans. Microw. Theory Techn., vol. 58, no. 4, pp. 1065-1074, Apr. 2010.
17. Y. Zhong, X. Chen, and K. Agarwal, "An improved subspace-based optimization method and its implementation in solving three-dimensional inverse problems," IEEE Trans. Geosci. Remote Sens., vol. 48, no. 10, pp. 3763-3768, Oct. 2010.
18. G. Bozza and M. Pastorino, "An inexact Newton-based approach to microwave imaging within the contrast source formulation," IEEE Trans. Antennas Propag., vol. 57, no. 4, pp. 1122-1132, Apr. 2009.
19. P. Lobel, L. Blanc-Feraud, C. Pichot, and M. Barlaud, "A new regularization scheme for inverse scattering," Inverse Probl., vol. 13, no. 2, pp. 403-410, Apr. 1997. (Pubitemid 127549973)
20. I. T. Rekanos, S. M. Panas, and T. D. Tsiboukis, "Microwave imaging using the finite-element method and a sensitivity analysis approach," IEEE Trans. Med. Imag., vol. 18, no. 11, pp. 1108-1114, Nov. 1999. (Pubitemid 30557284)
21. T. M. Habashy and A. Abubakar, "A general framework for constraint minimization for the inversion of electromagnetic measurements," Progr. Electromagn. Res., vol. 46, pp. 265-312, 2004.
22. P. M. van Den Berg and A. Abubakar, "Contrast source inversion method: State of the art," Progr. Electromagn. Res., vol. 34, pp. 189-218, 2001.
23. M. Pastorino, "Stochastic optimization methods applied to microwave imaging: A review," IEEE Trans. Antennas Propag., vol. 55, no. 3, pp. 538-548, Mar. 2007. (Pubitemid 46534656)
24. P. Rocca, M. Benedetti, M. Donelli, D. Franceschini, and A. Massa, "Evolutionary optimization as applied to inverse scattering problems," Inverse Probl., vol. 25, no. 12, p. 123 003, Dec. 2009.
25. E. J. Candes and M. B. Wakin, "An introduction to compressive sampling," IEEE Signal Process. Mag., vol. 25, no. 2, pp. 21-30, Mar. 2008.
26. R. G. Baraniuk, "Compressive sampling," IEEE Signal Process. Mag., vol. 24, no. 4, pp. 118-121, Jul. 2007.
27. L. C. Potter, E. Ertin, J. T. Parker, andM. Cetin, "Sparsity and compressed sensing in radar imaging," Proc. IEEE, vol. 98, no. 6, pp. 1006-1020, Jun. 2010.
28. M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, "Compressed sensing MRI," IEEE Signal Process. Mag., vol. 25, no. 2, pp. 72-82, Mar. 2008.
29. W. L. Chan, M. Moravec, R. Baraniuk, and D. Mittleman, "Terahertz imaging with compressed sensing and phase retrieval," Opt. Lett., vol. 33, no. 9, pp. 974-976, May 2008.
30. E. A. Marengo, R. D. Hernandez, Y. R. Citron, F. K. Gruber, M. Zambrano, and H. Lev-Ari, "Compressive sensing for inverse scattering," in Proc. XXIX URSI Gen. Assem., Chicago, IL, Aug. 7-16, 2008.
31. E. A. Marengo, "Compressive sensing and signal subspace methods for inverse scattering including multiple scattering," presented at the IEEE Geoscience Remote Sensing Symp., Boston, MA, Jul. 7-11, 2008, Paper WE1.101.2 .
32. E. A. Marengo, "Subspace and Bayesian compressive sensing methods in imaging," in Proc. Prog. Electromagn. Res. Symp., Cambridge, MA, Jul. 2-6, 2008, p. 366.
33. A. Fannjiang, P. Yan, and T. Strohmer, "Compressed remote sensing of sparse object," SIAM J. Imag. Sci., vol. 3, no. 3, pp. 595-618, 2009.
34. A. C. Fannjiang, "Compressive inverse scattering I. High frequency SIMO measurements," Inverse Probl., vol. 26, no. 3, p. 035 008, Mar. 2010.
35. A. C. Fannjiang, "Compressive inverse scattering II. SISO measurements with Born scatterers," Inverse Probl., vol. 26, no. 3, p. 35 009, Mar. 2010.
36. S. Ji, Y. Xue, and L. Carin, "Bayesian compressive sensing," IEEE Trans. Signal Process., vol. 56, no. 6, pp. 2346-2356, Jun. 2008. (Pubitemid 351795888)
37. A. C. Faul andM. E. Tipping, Advances in Neural Information Processing Systems (NIPS 14), T. G. Dietterich, S. Becker, and Z. Ghahramani, Eds. Cambridge, MA: MIT Press, 2002, pp. 383-389.
38. M. E. Tipping and A. C. Faul, "Fast marginal likelihood maximization for sparse Bayesian models," in Proc. 9th Int. Workshop Artif. Intell. Stat., C. M. Bishop and B. J. Frey, Eds., 2003, pp. 3-6.
39. M. E. Tipping, "Sparse Bayesian learning and the relevance vector machine," J. Mach. Learn. Res., vol. 1, pp. 211-244, Jun. 2001. (Pubitemid 33687203)
40. J. H. Richmond, "Scattering by a dielectric cylinder of arbitrary cross shape," IEEE Trans. Antennas Propag., vol. AP-13, no. 3, pp. 334-341, May 1965.
41. R. F. Harrington, Field Computation by Moment Methods. NewYork: IEEE Press, 1993.
42. J. Kaipio and E. Somersalo, "Statistical and computational inverse problems," in Applied Mathematical Sciences. New York: Springer Verlag, 2004.
43. O. M. Bucci and G. Franceschetti, "On the degrees of freedom of scattered fields," IEEE Trans. Antennas Propag., vol. 37, no. 7, pp. 918-926, Jul. 1989.
44. O. M. Bucci and T. Isernia, "Electromagnetic inverse scattering: Retrievable information and measurement strategies," Radio Sci., vol. 32, no. 6, pp. 2123-2137, 1997. (Pubitemid 127630831)
45. S. Ji, Y. Xue, and L. Carin, Bayesian Compressive Sensing Code2009. [Online]. Available: http://people.ee.duke.edu/~lihan/cs/
46. R. V. Kohn and A.McKenney, "Numerical implementation of a variational method for electrical impedance tomography," Inverse Probl., vol. 6, no. 3, pp. 389-414, Jun. 1990.
47. R. E. Kleinman and P. M. van den Berg, "A modified gradient method for two-dimensional problems in tomography," J. Comput. aAppl. Math., vol. 42, no. 1, pp. 17-35, Sep. 1992. (Pubitemid 23621062)
48. P. M. van den Berg and R. E. Kleinman, "A contrast source inversion method," Inverse Probl., vol. 13, no. 6, pp. 1607-1620, Dec. 1997.
49. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd ed. New York: Cambridge Univ. Press, 2007.
50. P. M. van den Berg, A. L. van Broekhoven, and A. Abubakar, "Extended contrast source inversion," Inverse Probl., vol. 15, no. 5, pp. 1325-1344, Oct. 1999. (Pubitemid 129618021)
51. P. M. van den Berg, A. Abubakar, and J. T. Fokkema, "Multiplicative regularization for contrast profile inversion," Radio Sci., vol. 38, no. 2, pp. VIC23/1-VIC23/10, Apr. 2003.
52. G. Oliveri and A. Massa, "Bayesian compressive sampling for pattern synthesis with maximally sparse non-uniform linear arrays," IEEE Trans. Antennas Propag., vol. 59, no. 2, pp. 467-481, Feb. 2011.
53. D. J. C. Mackay, "Bayesian interpolation," Neural Comput., vol. 4, no. 3, pp. 415-447, Mar. 1992.
54. W. M. Bolstad, Introduction to Bayesian Statistics. Hoboken, NJ:Wiley, 2007.