Inversion of the Weighted Spherical Mean
نویسندگان
چکیده
The paper contains the inversion formula for weighted spherical mean. interest to reconstruction a function by its integral sphere grews tremendously in last six decades, stimulated spectrum of new problems and methods image reconstruction. We consider generalization classical mean inverse case when generalized translation acts instead regular. As particular this problem includes action means on radially symmetric functions.
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 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 کاملSome weighted operator geometric mean inequalities
In this paper, using the extended Holder- -McCarthy inequality, several inequalities involving the α-weighted geometric mean (0<α<1) of two positive operators are established. In particular, it is proved that if A,B,X,Y∈B(H) such that A and B are two positive invertible operators, then for all r ≥1, ‖X^* (A⋕_α B)Y‖^r≤‖〖(X〗^* AX)^r ‖^((1-α)/2) ‖〖(Y〗^* AY)^r ‖^((1-α)/2) ‖〖(X〗^* BX)^r ‖^(α/2) ‖〖(Y...
متن کاملInversion of spherical means using geometric inversion and Radon transforms
We consider the problem of reconstmcting a continuous function on R" from certain values of its spherical means. A novel aspect of our approach is the use of geometric inversion to recast the inverse spherical mean problem as an inverse Radon transform problem. W define WO spherical mean inverse problems the entire problem and the causal problem. We then present a dual filtered backprojection a...
متن کاملThe effect of inversion times on the minimum signal intensity of the contrast agent concentration using inversion recovery t1-weighted fast imaging sequence
Background :Inversion recovery (IR) pulse sequences can generate T1-weighted images with a different range of inversion time (TI) to suppress or null the signal intensity (SI) for a specified tissue. In this study, we aimed to investigate the effect of TI values on the concentration of the contrast agent, which leads to a minimum signal intensity, using an inversion recovery T1-weighted 3-dim...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Springer proceedings in mathematics & statistics
سال: 2021
ISSN: ['2194-1009', '2194-1017']
DOI: https://doi.org/10.1007/978-3-030-77493-6_30