Inversion of spherical means using geometric inversion and Radon transforms
نویسندگان
چکیده
منابع مشابه
Inversion 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 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 کاملExplicit 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 کاملRadon Transform Inversion using the Shearlet Representation
The inversion of the Radon transform is a classical ill-posed inverse problem where some method of regularization must be applied in order to accurately recover the objects of interest from the observable data. A well-known consequence of the traditional regularization methods is that some important features to be recovered are lost, as evident in imaging applications where the regularized reco...
متن کاملLagrange Inversion via Transforms
In [3] we described a technique for solving certain linear operator equations by studying the operator power series de ned by the system. Essential for obtaining explicit solutions is a Lagrange inversion formula for power series with coe¢ cients in an integral domain K. Such a formula can be found in Recursive Matrices and Umbral Calculusby Barnabei, Brini and Nicoletti [1]. J. F. Freemans ...
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: Inverse Problems
سال: 1992
ISSN: 0266-5611,1361-6420
DOI: 10.1088/0266-5611/8/6/010