Regularization approach for inverting the exponential Radon transforms (ERT) (Q1002310)

The exponential Radon transform is defined as \[ R_\mu f= \int^\infty_{-\infty} f(p\omega+ t\omega^\perp)\,e^{\mu t}\,dt, \] where \(\mu\) is a constant, \(\omega\) is a unit vector in \(\mathbb{R}^2\), \((x_1,x_2)^\perp= (-x_2, x_1)\) and \(f(.)\) is a continuous function with compact support in \(\mathbb{R}^2\). In this paper, the authors use the Tikhonov regularization approach to define and construct approximate solutions for the inversion problem of the exponential Radon transform for non-exact and hence often non-smooth data. They establish estimates for the Radon transform in Sobolev spaces to prove their main theorem.