  We consider the problem of joint reconstruction of both attenuation $a$ and
source density $f$ in emission tomography in two dimensions. This is sometimes
called the Single Photon Emission Computed Tomography (SPECT) identification
problem, or referred to as attenuation correction in SPECT. Assuming that $a$
takes only finitely many values and $f \in C_c^1(\mathbb{R}^2)$ we are able to
characterise singularities appearing in the Attenuated Radon Transform $R_a f$,
which models emission tomography data. Using this characterisation we prove
that both $a$ and $f$ can be determined in some circumstances. We also propose
a numerical algorithm to jointly compute $a$ and $f$ from $R_af$ based on a
weakly convex regularizer when $a$ only takes values from a known finite list,
and show that this algorithm performs well on some synthetic examples.
