An explicit inversion formula for the exponential Radon transform using data from 180°
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 کاملAn inversion formula for the exponential radon transform in spatial domain with variable focal-length fan-beam collimation geometry.
Inverting the exponential Radon transform has a potential use for SPECT (single photon emission computed tomography) imaging in cases where a uniform attenuation can be approximated, such as in brain and abdominal imaging. Tretiak and Metz derived in the frequency domain an explicit inversion formula for the exponential Radon transform in two dimensions for parallel-beam collimator geometry. Pr...
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 کاملFast Inversion of the Exponential Radon Transform by Using Fast Laplace Transforms
Abstract. The Fourier slice theorem used for the standard Radon transform generalizes to a Laplace counterpart when considering the exponential Radon transform. We show how to use this fact in combination with using algorithms for unequally spaced fast Laplace transforms to construct fast and accurate methods for computing, both the forward exponential Radon transform and the corresponding back...
متن کاملThe inversion of the exponential Radon transform for quantitative brain SPECT.
The mathematical derivation for the inversion of the exponential Radon transform is presented and the implementation of the inversion is detailed. The inversion can be verified and implemented by the readers for practical applications, such as for quantitative reconstruction of brain SPECT (single-photon emission computed tomography).
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: Arkiv för Matematik
سال: 2004
ISSN: 0004-2080
DOI: 10.1007/bf02385485