منابع مشابه
The Radon-gauss Transform
Gaussian measure is constructed for any given hyperplane in an infinite dimensional Hilbert space, and this is used to define a generalization of the Radon transform to the infinite dimensional setting, using Gauss measure instead of Lebesgue measure. An inversion formula is obtained and a support theorem proved.
متن کاملSingularities of the Radon Transform
Singularities of the Radon transform of a piecewise smooth function f(x), x e R" , n > 2, are calculated. If the singularities of the Radon transform are known, then the equations of the surfaces of discontinuity of f(x) are calculated by applying the Legendre transform to the functions, which appear in the equations of the discontinuity surfaces of the Radon transform of f(x) ; examples are gi...
متن کاملThe Radon Transform on Z *
where S + x denotes the setf-s + x i s e S ) . Thus, the Radon transform can be thought of as a way of replacing/by a "smeared out" version of /. This form of the transform represents a simplified model of the kind of averaging which occurs in certain applied settings, such as various types of tomography and recent statistical averaging techniques. A fundamental question which arises in connect...
متن کاملThe Radon Transform on Zn
The Radon transform on Zn averages a function over its values on a translate of a fixed subset S in Zn. We discuss invertibility conditions and computer inverse formulas based on the Moore-Penrose inverse and on linear algorithms. We expect the results to be of use in directional and toroidal time series.
متن کاملThe Radon Transform on Z
The Radon transform on Zn averages a function over its values on a translate of a fixed subset S in Zn. We discuss invertibility conditions and computer inverse formulas based on the Moore–Penrose inverse and on linear algorithms. We expect the results to be of use in directional and toroidal time series.
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2009
ISSN: 0035-7596
DOI: 10.1216/rmj-2009-39-3-927