An explicit inversion formula for the exponential Radon transform using data from \(180^\circ\)
The exponential Radon transform on the plane is defined by \[ R\mu f(\theta,s)=\int_{-\infty}^{\infty} f (s \theta +t\theta^{\perp}) e^{\mu t} \,dt, \quad (\theta,s) \in S^1 \times {\mathbb R}, \tag{1} \] \(\mu\) being a real number. The author obtains an explicit inversion formula provided that \(R\mu f(\theta,s)\) is known only for \(\theta\) belonging to the right half of the unit circle. Comment: Explicit inversion formulas for the more general exponential transform associated to \(k\)-dimensional planes in \( {\mathbb R}^n\) and \(\mu \in {\mathbb C}^k\), where obtained by \textit{B. Rubin} [J. Fourier Anal. Appl. 6, No. 2, 185--205 (2000; Zbl 0973.44001)].
scientific article; zbMATH DE number 2103854