Momentum ray transforms | Sciact

Momentum ray transforms Full article

Journal

Inverse Problems and Imaging
ISSN: 1930-8337 , E-ISSN: 1930-8345

Output data

Year: 2019, Volume: 13, Number: 3, Pages: 679-701 Pages count : 23 DOI: 10.3934/ipi.2019031

Tags

Inverse problems; Ray transform; Reshetnyak formula; Stability estimates; Tensor analysis

Authors

Krishnan V.P. ¹ , Manna R. ¹ , Sahoo S.K. ¹ , Sharafutdinov V.A. ^2,3

Affiliations

1	TIFR Centre for Applicable Mathematics, Sharada Nagar, Chikkabommasandra, Yelahanka New Town, Bangalore, India
2	Sobolev Institute of Mathematics, 4 Koptyug Avenue, Novosibirsk, 630090, Russia
3	Novosibirsk State University, 2 Pirogov street 630090, Russia

The momentum ray transform I k integrates a rank m symmetric tensor field f over lines in R n with the weight t k : (I k f)(x,ξ)=∫ ∞ -∞ t k 〈 f(x+tξ),ξ m〉 dt. In particular, the ray transform I=I0 was studied by several authors since it had many tomographic applications. We present an algorithm for recovering f from the data (I 0 f,I 1 f,…,I m f). In the cases of m=1 and m=2, we derive the Reshetnyak formula that expresses ∥f∥Hst(ℝn) through some norm of (I 0 f,I 1 f,…,I m f). The Hst-norm is a modification of the Sobolev norm weighted differently at high and low frequencies. Using the Reshetnyak formula, we obtain a stability estimate.

Krishnan V.P. , Manna R. , Sahoo S.K. , Sharafutdinov V.A.
Momentum ray transforms
Inverse Problems and Imaging. 2019. V.13. N3. P.679-701. DOI: 10.3934/ipi.2019031 WOS Scopus OpenAlex

Web of science:	WOS:000461762200011
Scopus:	2-s2.0-85065743163
OpenAlex:	W2952893287

DB	Citing
Scopus	28
OpenAlex	32
Web of science	27