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The Chebyshev ridge polynomials in 2D tensor tomography

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.