Abstract
We investigate the exponential Radon transform on a certain function space of generalized functions. We establish certain space of generalized functions for the cited transform. The transform that is obtained is well defined. More properties of consistency, convolution, analyticity, continuity, and sufficient theorems have been established.
Highlights
The Radon transform of a sufficiently nice function f defined on Rn is given by (Rθf) (η) ≡ (Rf) (θ, η) ∫ θ⊥ f du, (1)
We investigate the exponential Radon transform on a certain function space of generalized functions
The attenuated Radon transform is defined in Mikusinski et al
Summary
The Radon transform of a sufficiently nice function f defined on Rn is given by (Rθf). More about the Radon transform is given in [5,6,7,8,9]. The discrete Radon transform is defined by [10, 11]. The attenuated Radon transform is defined in Mikusinski et al. For a uniform attenuation coefficient μ ∈ C, the exponential Radon transform of a compactly supported real valued function f, defined on R2, is given by Kurusa and Hertle [7, 8]: Teμ f (θ, t). If in addition μ is unknown, one first must find μ and find f For more information about the exponential Radon transform, we refer to [15, 16]
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