A systematic approach to robust preconditioning for gradient-based inverse scattering algorithms

Inverse Problems

Volumn 24, Issue 2, 2008, Pages

  Nordebo, Sven ^a   Fhager, Andreas ^b   Gustafsson, Mats ^c   Persson, Mikael ^b  

^a LINNAEUS UNIVERSITY   (Sweden)

^b CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

^c LUND UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

CONJUGATE GRADIENT METHOD; INVERSE PROBLEMS; PERMITTIVITY; TWO DIMENSIONAL;

FDTD-ELECTROMAGNETIC SOLVERS; INVERSION ALGORITHMS; ROBUST PRECONDITIONING;

ALGORITHMS;

EID: 42549158861     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/24/2/025027     Document Type: Article

References (39)

1. Bertero M 1989 Linear inverse and ill-posed problems Adv. Electron. Electr. Phys. 75 1-120
2. Boström A, Kristensson G and Ström S 1991 Transformation properties of plane, spherical and cylindrical scalar and vector wave functions Field Representations and Introduction to Scattering ed V V Varadan, A Lakhtakia and V K Varadan (Amsterdam: Elsevier) chapter 4 pp 165-210 (Acoustic, Electromagnetic and Elastic Wave Scattering)
3. Bucci O M, Crocco L, Isernia T and Pascazio V 2001 Subsurface inverse scattering problems: quantifying qualifying and achieving the available information IEEE Trans. Geosci. Remote Sens. 39 2527-38
4. Cheney M and Isaacson D 1995 Issues in electrical impedance imaging IEEE Comput. Sci. Eng. 53-62
5. Cohen-Bacrice C, Goussard Y and Guardo R 1997 Regularized reconstruction in electrical impedance tomography using a variance uniformization constraint IEEE Trans. Med. Imaging 16 562-71
6. Collier S L 2005 Fisher information for a complex Gaussian random variable: beamforming applications for wave propagation in a random medium IEEE Trans. Signal Process. 53 4236-48
7. Devaney A J and Tsihirintzis G A 1991 Maximum likelihood estimation of object location in diffraction tomography IEEE Trans. Signal Process. 39 672-82
8. Dogandzic A and Nehorai A 2001 Cramér-Rao bounds for estimating range, velocity, and direction with an active array IEEE Trans. Signal Process. 49 1122-37
9. Fear E and Stuchly M A 2000 Microwave detection of breast cancer IEEE Trans. Microwave Theory Tech. 48 1854-63
10. Fhager A, Hashemzadeh P and Persson M 2006 Reconstruction quality and spectral content of an electromagnetic time-domain inversion algorithm IEEE Trans. Biomed. Eng. 53 1594-604
11. Fhager A and Persson M 2005 Comparison of two image reconstruction algorithms for microwave tomography Radio Sci. 40
12. Fletcher R 1987 Practical Methods of Optimization (Chichester: Wiley)
13. Gilliam D S, Lund J R and Vogel C R 1990 Quantifying information content for ill-posed problems Inverse Problems 6 725-36
14. Greenbaum A 1997 Iterative Methods for Solving Linear Systems (Philadelphia: SIAM)
15. Gustafsson M and Nordebo S 2006 Bandwidth, Q-factor, and resonance models of antennas Prog. Electromagn. Res. 62 1-20
16. Gustafsson M 2000 Wave splitting in direct and inverse scattering problems PhD Thesis Lund Institute of Technology, Department of Electromagnetic Theory, Lund, Sweden (http://www.es.lth.se/home/mats)
17. Gustafsson M and He S 2000 An optimization approach to two-dimensional time domain electromagnetic inverse problems Radio Sci. 35 525-36
18. Habashy T M and Abubakar A 2004 A general framework for constraint minimization for the inversion of electromagnetic measurements Prog. Electromagn. Res. 46 265-312
19. Hashemzadeh P, Fhager A and Persson M 2006 Experimental investigation of an optimization approach to microwave tomography Electromagn. Biol. Med. 25 1-12
20. Kaipio J and Somersalo E 2005 Statistical and Computational Inverse Problems (New York: Springer)
21. Kay S M 1993 Fundamentals of Statistical Signal Processing, Estimation Theory (Englewood Cliffs, NJ: Prentice-Hall)
22. Kelley C T 1995 Iterative Methods for Linear and Nonlinear Equations (Philadelphia: SIAM)
23. Kleinman R, Kress R and Martensen E (ed) 1991 Direct and Inverse Boundary Value Problems. Methoden und Verfahren der Mathematischen Physik, Band 37. Peter Lang, Frankfurt am Main
24. Kosmas P and Rappaport C 2006 A FDTD-based time reversal for microwave breast cancer detection-localization in three dimensions IEEE Trans. Microwave Theory Tech. 54 1921-7
25. Lesselier D 1982 Optimization techniques and inverse problems: reconstruction of conductivity profiles in the time domain IEEE Trans. Antennas Propagat. 30 59-65
26. Meaney P M, Fanning M W, Raynolds T, Fox C J, Fang Q Q, Kogel C A, Poplack S P and Paulsen K D 2007 Initial clinical experience with microwave breast imaging in women with normal mammography Acad. Radiol. 14 207-18
27. Miller K S 1974 Complex Stochastic Processes (Reading, MA: Addison-Wesley)
28. Naidu P S and Buvaneswari A 1999 A study of Cramér-Rao bounds on object shape parameters from scattered field IEEE Trans. Signal Process. 47 1478-81
29. Nordebo S, Gustafsson M and Nilsson B 2007 Fisher information analysis for two-dimensional microwave tomography Inverse Problems 23 859-77
30. Pierri R and Soldovieri F 1998 On the information content of the radiated fields in the near zone over bounded domains Inverse Problems 14 321-37
31. Proakis J G 1995 Digital Communications 3rd edn (New York: McGraw-Hill)
32. Saad Y 1996 Iterative Methods for Sparse Linear Systems (Boston: PWS Publishing Company)
33. Seidman T I and Vogel C R 1989 Well posedness and convergence of some regularisation methods for non-linear ill posed problems Inverse Problems 5 227-38
34. Sill J M and Fear E C 2005 Tissue sensing adaptive radar for breast cancer detection-experimental investigation of simple tumor models IEEE Trans. Microwave Theory Tech. 53 3312-9
35. Smith S T 2005 Statistical resolution limits and the complexified Cramér-Rao bound IEEE Trans. Signal Process. 53 1597-609
36. Taflove A and Hagness S C 2000 Computational Electrodynamics: The Finite-Difference Time-Domain Method (Boston, MA: Artech House Publishers)
37. Tarantola A 2005 Inverse Problem Theory and Methods for Model Parameter Estimation (Philadelphia: SIAM)
38. Tsihirintzis G A and Devaney A J 1991 Maximum likelihood estimation of object location in diffraction tomography: Part II. Strongly scattering objects IEEE Trans. Signal Process. 39 1466-70
39. van den Berg P and Kleinman R E 1988 The conjugate gradient spectral iterative technique for planar structures IEEE Trans. Antennas Propagat. 36 1418-23