Karthik Ramaseshan University of Rochester

Given $f$ and $a$ in $C_0^{\infty} (\mathbf{R}^2)$, the attenuated Radon transform (ART) of $f$ with respect to the attenuation coefficient $a$ is the following function on the space of lines in $\mathbf{R}^2$:

$$R_a f(s, \omega) = \int_{x \cdot \omega^{\perp} = s} e^{-Da(x,\omega)} f(x) \; dx$$

where

$$Da(x, \omega) = \int_{\mathbf{R}} a(x+ t\omega) \; dt$$

is the divergent beam X-ray transform of $a$. The ART models data from Single Photon Emission Computed Tomography. We study the linearization of the ART with respect to the attenuation coefficient. Using microlocal techniques, we prove ellipticity of two normal operators associated to the linearized ART. This is joint work with Allan Greenleaf.