The Doppler moment transform in Doppler tomography

Inverse Problems

Volumn 21, Issue 4, 2005, Pages 1249-1274

  Andersson, F ^a  

^a LUND UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

DATA ACQUISITION; DIFFERENTIAL EQUATIONS; DOPPLER EFFECT; INTEGRATION; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; VECTORS;

DOPPLER MOMENT TRANSFORM; DOPPLER TECHNIQUES; DOPPLER TOMOGRAPHY;

TOMOGRAPHY;

EID: 23244460962     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/21/4/004     Document Type: Article

References (25)

1. Akhiezer N I 1965 The Classical Moment Problem and Some Related Questions in Analysis transl. N Kemmer (New York: Hafner)
2. Andersson F and Beylkin G 2005 The fast Gauss transform with complex parameters J. Comput. Phys. 203 274-86
3. Arfken G B 1970 Mathematical Methods for Physicists 2nd edn (New York: Harcourt/Academic)
4. Boman J 1997 Unpublished manuscripts and personal communication
5. Boman J 2001 Injectivity for a weighted vectorial Radon transform Radon Transforms and Tomography (South Hadley, MA, 2000) (Contemp. Math. Am. Math. Soc. vol 278) (Providence, RI: American Mathematical Society) pp 87-95
6. Braun H and Hauk A 1991 Tomographic reconstrucion of vector fields IEEE Trans. Signal Process. 39 464-71
7. Caffarelli L A and Milman M 1999 Monge-Ampère Equation: Applications to Geometry and Optimization (Contemporary Mathematics vol 226) (Providence, RI: American Mathematical Society)
8. Golub G H and Van Loan C F 1989 Matrix Computations (Johns Hopkins Series in the Mathematical Sciences vol 3) 2nd edn (Baltimore, MD: Johns Hopkins University Press)
9. Goursat E 1896 Sur l'intégration des équations aux dérivées partielles (Paris: Herman)
10. Jansson T, Almqvist M, Eriksson R, Stråhlén K, Sparr G, Persson H W and Lindström K 1995 Ultrasonic Doppler tomography-a new method to measure blood flow vector fields Technical Report Department of Electrical Measurements, Lund Institute of Technology
11. Juhlin P 1992 Principles of Doppler tomography Technical Report Department of Mathematics, Lund Institute of Technology
12. Natterer F 1986 The Mathematics of Computerized Tomography (Stuttgart: Teubner)
13. Norton S J 1992 Unique tomographic reconstruction of vector fields using boundary data IEEE Trans. Image Process. 1 406-12
14. Rellich F 1933 Zur ersten randwertaufgabe bei Monge-Ampèreschen differentialgleichungen vom elliptischen typus: differentialgeometrische anwendungen Math. Ann. 107 505-13
15. Rieder A and Schuster T 2004 The approximate inverse in action: III. 3D-Doppler tomography Numer. Math. 97 353-78
16. Rudin W 1987 Real and Complex Analysis 3rd edn (New York: McGraw-Hill)
17. Schulz F 1990 Regularity Theory for Quasilinear Elliptic Systems and Monge-Ampère Equations in Two Dimensions (Lecture Notes in Mathematics vol 1445) (Berlin: Springer)
18. Schuster T 2001 An efficient mollifier method for three-dimensional vector tomography: convergence analysis and implementation Inverse Problems 17 739-66 (Special issue to celebrate Pierre Sabatier's 65th birthday (Montpellier, 2000))
19. Schuster T 2005 Defect correction in vector field tomography: detecting the potential part of a field using BEM and implementation of the method Inverse Problems 21 75-91
20. Sharafutdinov V 1994 Integral Geometry of Tensor Fields (Utrecht: VSP)
21. Sparr G and Stråhlén K 1997 Vector field tomography: an overview Technical Report Department of Mathematics, Lund Institute of Technology
22. Sparr G, Stråhlén K, Lindström K and Persson H 1995 Doppler tomography for vector fields Inverse Problems 11 1051-61
23. Stråhlén K 1999 Studies of vector tomography PhD Thesis Centre for Mathematical Sciences, Lund Institute of Technology
24. Wernsdörfer A 1993 Complete reconstruction of three-dimensional vector fields Proc. ECAPT93
25. Winters K B and Rouseff D 1993 Tomographic reconstruction of stratified fluid flow IEEE Trans. Ultrason. Ferroelectr. Freq. Control 40 26-33