  For a point of the projective space $\PG(n,q)$, its R\'edei factor is the
linear polynomial in $n+1$ variables, whose coefficients are the point
coordinates. The power sum polynomial of a subset $S$ of $\PG(n,q)$ is the sum
of the $(q-1)$-th powers of the R\'edei factors of the points of $S$. The fact
that many subsets may share the same power sum polynomial offers a natural
connection to discrete tomography. In this paper we deal with the
two-dimensional case and show that the notion of ghost, whose employment
enables to find all solutions of the tomographic problem, can be rephrased in
the finite geometry context, where subsets with null power sum polynomial are
called ghosts as well. In the latter case, one can add ghosts still preserving
the power sum polynomial by means of the multiset sum (modulo the field
characteristic). We prove some general results on ghosts in $\PG(2,q)$ and
compute their number in case $q$ is a prime.
