منابع مشابه
Explicit inversion formulae for the spherical mean Radon transform
Abstract We derive explicit formulae for the reconstruction of a function from its integrals over a family of spheres, or for the inversion of the spherical mean Radon transform. Such formulae are important for problems of thermoand photo-acoustic tomography. A closed-form inversion formula of a filtrationbackprojection type is found for the case when the centres of the integration spheres lie ...
متن کاملRange descriptions for the spherical mean Radon transform ∗
The transform considered in the paper averages a function supported in a ball in Rn over all spheres centered at the boundary of the ball. This Radon type transform arises in several contemporary applications, e.g. in thermoacoustic tomography and sonar and radar imaging. Range descriptions for such transforms are important in all these areas, for instance when dealing with incomplete data, err...
متن کاملInversion algorithms for the spherical Radon and cosine transform
We consider two integral transforms which are frequently used in integral geometry and related fields, namely the cosine and the spherical Radon transform. Fast algorithms are developed which invert the respective transforms in a numerically stable way. So far, only theoretical inversion formulas or algorithms for atomic measures have been derived, which are not so important for applications. W...
متن کاملInverting the spherical Radon transform for physi- cally meaningful functions
Abstract In this paper we refer to the reconstruction formulas given in Andersson’s On the determination of a function from spherical averages, which are often used in applications such as SAR1 and SONAR2. We demonstrate that the first one of these formulas does not converge given physically reasonable assumptions. An alternative is proposed and it is shown that the second reconstruction formul...
متن کاملRadon transform and curvature
We interpret the setting for a Radon transform as a submanifold of the space of generalized functions, and compute its extrinsic curvature: it is the Hessian composed with the Radon transform. 1. The general setting. Let M and Σ be smooth finite dimensional manifolds. Let m = dim(M). A linear mapping R : C∞ c (M)→ C∞(Σ) is called a (generalized) Radon transform if it is given in the following w...
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ژورنال
عنوان ژورنال: Geophysical Journal International
سال: 1988
ISSN: 0956-540X,1365-246X
DOI: 10.1111/j.1365-246x.1988.tb00474.x