Algorithms for magnetic tomography - On the role of a priori knowledge and constraints

Inverse Problems

Volumn 24, Issue 4, 2008, Pages

  Hauer, Karl Heinz ^a   Potthast, Roland ^b   Wannert, Martin ^c  

^a TomoScience GbR   (Germany)

^b UNIVERSITY OF READING   (United Kingdom)

^c FORSCHUNGSZENTRUM JÜLICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

DIAGNOSTIC RADIOGRAPHY; IMAGING TECHNIQUES; MAGNETIC FIELDS; MAGNETIC MATERIALS; MATHEMATICAL OPERATORS; MEDICAL IMAGING; THERMOGRAPHY (TEMPERATURE MEASUREMENT); TOMOGRAPHY;

A-PRIORI; INTEGRAL OPERATORS; MAGNETIC TOMOGRAPHY; PROJECTION METHODS; TIKHONOV REGULARIZATION;

INTEGRAL EQUATIONS;

EID: 49749143368     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/24/4/045008     Document Type: Article

References (17)

1. Colton D and Kress R 1998 Inverse Acoustic and Electromagnetic Scattering Theory (Applied Mathematical Sciences vol 93) 2nd edn (Berlin: Springer)
2. Del Gratta C, Pizzella V, Tecchio F and Romani G L 2001 Magnetoencephalography a noninvasive brain imaging method with 1 ms time resolution Rep. Prog. Phys. 64 1759-814
3. Engl H W, Hanke M and Neubauer A 1996 Regularization of Inverse Problems (Dordrecht: Kluwer)
4. Hämäläinen M, Hari R, Ilmoniemi R J, Knuutila J and Lounasmaa O V 1993 Magnetoencephalography-theory, instrumentation, and applications to noninvasive studies of the working human brain Rev. Mod. Phys. 65 413-97
5. Hauer K-H, Kühn L and Potthast R 2005 On uniqueness and non-uniqueness for current reconstruction from magnetic fields Inverse Problems 20 1-13
6. Hauer K-H, Potthast R, Stolten D and Wüster T 2005 Magnetotomography-a new method for analysing fuel cell performance and quality J. Power Sources 143 67-74
7. Potthast R and Wannert M Uniqueness of current reconstructions for magnetic tomography in multi-layer devices submitted
8. Kaipio J and Somersalo E 2005 Statistical and Computational Inverse Problems (Applied Mathematical Sciences vol 160) (Berlin: Springer)
9. Kirsch A 1996 An Introduction to the Mathematical Theory of Inverse Problems (Applied Mathematical Science vol 120) (Berlin: Springer)
10. Kress R 1999 Linear Integral Equations (Applied Mathematical Sciences vol 82) 2nd edn (Berlin: Springer)
11. Kühn L 2005 Magnetic tomography-on the nullspace of the Biot-Savart operator and point sources for field and domain reconstruction PhD Thesis University of Göttingen
12. Kühn L, Kre R and Potthast R 2002 The reconstruction of a current distribution from its magnetic fields Inverse Problems 18 1127-46
13. Kühn L and Potthast R 2003 On the convergence of the finite integration technique for the anisotropic boundary value problem of magnetic tomography Math. Methods Appl. Sci. 26 739-57
14. Lustfeld H, Reissel M, Schmidt U and Steffen B Reconstruction of electric currents in a fuel cell by magnetic field measurements J. Fuel Cell Sci. Technol. at press
15. Potthast R 2006 A survey on sampling and probe methods for inverse problems. Topical Review Inverse Problems 22 R1-47
16. Sarvas J 1987 Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem Phys. Med. Biol. 32 11-22
17. Tikhonov A N 1962 On the solution of incorrectly formulated problems and the regularization method Sov. Math.-Dokl. 4 1035-38 (Engl. Transl.)