Explicit inversion formulae for the spherical mean Radon transform
نویسندگان
چکیده
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 on a sphere in R surrounding the support of the unknown function.
منابع مشابه
A 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...
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An explicit series solution is proposed for the inversion of the spherical mean Radon transform. Such an inversion is required in problems of thermo-and photo-acoustic tomography. Closed-form inversion formulae are currently known only for the case when the centers of the integration spheres lie on a sphere surrounding the support of the unknown function, or on certain unbounded surfaces. Our a...
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