A unified radon inversion formula
نویسندگان
چکیده
منابع مشابه
Novikov ’ s Inversion Formula for the Attenuated Radon Transform — A New Approach
We study the inversion of weighted Radon transforms in two dimensions,Rρf (L) = ∫ L f (·) ρ(L, ·) ds, where the weight function ρ(L, x), L a line and x ∈ L, has a special form. It was an important breakthrough when R.G. Novikov recently gave an explicit formula for the inverse of Rρ when ρ has the form (1.2); in this case Rρ is called the attenuated Radon transform. Here we prove similar result...
متن کاملLocal Inversion of the Radon
We use the theory of the continuous wavelet transform to derive inversion formulas for the Radon transform on L 1 \L 2 (R d). These inversion formulas turn out to be local in even dimensions in the following sense. In order to recover a function f from its Radon transform in a ball of radius R > 0 about a point x to within error , we can nd () > 0 such that this can be accomplished by knowing t...
متن کاملInversion 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 کاملA Fourier Inversion Formula for Evolutionary Trees
We establish a pair of identities, which will provide a useful tool in the reconstruction of evolutionary trees in Kimura's 3-parameter model. The starting point of this paper was an attempt for a better understanding and generalization of an Hadamard inverse pair of formulae, which was used in statistics by Cooper [l], in image processing by Andrews [2, Chapters 6,7], and in information theory...
متن کاملRadon Inversion Formulas over Local Fields
Let F be a local field and n ≥ 2 an integer. We study the Radon transform as an operator M : C+ → C− from the space of smooth K-finite functions on Fn \ {0} with bounded support to the space of smooth K-finite functions on Fn \{0} supported away from a neighborhood of 0. These spaces naturally arise in the theory of automorphic forms. We prove that M is an isomorphism and provide formulas for M...
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: Journal of Mathematical Physics
سال: 1978
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.523592