General formula of inversion of weighted spherical mean
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 ...
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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 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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ژورنال
عنوان ژورنال: Прикладная математика & Физика
سال: 2021
ISSN: 2687-0959
DOI: 10.52575/2687-0959-2021-53-1-13-30