= Solution
In <single-photon emission computed tomography>, the unknown is an emitting source, rather than the absorption coefficient reconstructed by transmission <computed tomography>. Photons emitted at different points on the same ray are weighted by their probability of surviving the path to the detector. If the known attenuation is $a$ and the detector is at the positive end of the ray, the data are an <attenuated Radon transform>
$$
R_af(\rho,\theta)=\int_{\mathbb R}f(\tau\boldsymbol d+\rho\boldsymbol n)
\exp\left[-\int_\tau^\infty a(s\boldsymbol d+\rho\boldsymbol n)ds\right]d\tau.
$$
The directional <transport equation> is $\boldsymbol d\cdot\nabla u+au=f$ with zero incoming intensity. An <integrating factor> derives this attenuation weight. The same complexification, boundary-value and jump strategy gives <spectral reconstruction of an attenuated Radon transform> when attenuation is known. \b[The unattenuated inverse from part (d) applies directly only when $a=0$]; for nonzero attenuation the weighted jump and inverse must be used. This distinction allows emission imaging of the source without confusing it with reconstruction of the absorbing medium.
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