Exact reconstruction formula for the spherical mean Radon transform on ellipsoids
نویسندگان
چکیده
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 کاملA series solution and a fast algorithm for the inversion of the spherical mean Radon transform
An explicit series solution is proposed for the inversion of the spherical mean Radon transform. Such an inversion is required in problems of thermoand photo-acoustic tomography. Closed-form inversion formulae are currently known only for the case when the centres of the integration spheres lie on a sphere surrounding the support of the unknown function, or on certain unbounded surfaces. Our ap...
متن کاملRange Descriptions for the Spherical Mean Radon Transform. I. Functions Supported in A
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 کاملJu l 2 00 6 Range 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...
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ژورنال
عنوان ژورنال: Inverse Problems
سال: 2014
ISSN: 0266-5611,1361-6420
DOI: 10.1088/0266-5611/30/10/105006