The approach to the study of vector and 2-tensor tomography problems on the plane is presented. The new orthogonal polynomial bases of vector and symmetrical 2-tensor solenoidal fields were built with the help of bivariate Chebyshev ridge polynomials. These bases are useful not only in tomography, but also have potential applications in fluid mechanics, electromagnetism and image processing problems. This approach can be generalized for the m-tensor tomography of arbitrary rank m. The numerical results of novel inversion algorithm for vector and tensor Radon transforms are presented.
Editor-in-Chief: Kabanikhin, Sergey I.
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The Chebyshev ridge polynomials in 2D tensor tomography
∗Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, Acad. Koptyug prosp., 4, Novosibirsk, 630090, Russia. E-mail: kazan@math.nsc.ru
†Schlumberger, Aslakveien 14A, 0753 Oslo, Norway. E-mail: ABoukhgueim@slb.com
Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 14, Issue 2, Pages 157–188, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: 10.1515/156939406777571094,
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