Inversion of Higher Dimensional Radon Transforms of Seismic-Type
نویسندگان
چکیده
منابع مشابه
Inversion of spherical means using geometric inversion and Radon transforms
We consider the problem of reconstmcting a continuous function on R" from certain values of its spherical means. A novel aspect of our approach is the use of geometric inversion to recast the inverse spherical mean problem as an inverse Radon transform problem. W define WO spherical mean inverse problems the entire problem and the causal problem. We then present a dual filtered backprojection a...
متن کاملRadon Transforms and Finite Type Conditions
The purpose of this paper is to study averaging operators of Radon transform type. We shall formulate suitable finite type conditions and prove L-Sobolev and L → L estimates. The results will be essentially sharp for operators associated with families of curves in the plane. Let X and Y be smooth manifolds, dimX = nL, dim Y = nR, and let M be a submanifold in X×Y with conormal bundle N∗M; we de...
متن کاملInversion of the two dimensional Radon transformation by diagonalisation
Based on an explicit diagonalisation of Abel’s integral operator, we give an inversion of the plane Radon transformation R(f)(p, θ) = ∫ {x cos(θ)+y sin(θ)=p} f(x, y) ds by diagonalising explicitly R̃(f)(r, φ) = R(f(r, φ)/r). We calculate the spectrum and the kernel of R̃.
متن کاملGeneralized Transforms of Radon Type and Their Applications
These notes represent an extended version of the contents of the third lecture delivered at the AMS Short Course “Radon Transform and Applications to Inverse Problems” in Atlanta in January 2005. They contain a brief description of properties of some generalized Radon transforms arising in inverse problems. Here by generalized Radon transforms we mean transforms that involve integrations over c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Vietnam Journal of Mathematics
سال: 2020
ISSN: 2305-221X,2305-2228
DOI: 10.1007/s10013-020-00446-8