  In this paper, we investigate the reconstruction error,
$N_\e^{\text{rec}}(x)$, when a linear, filtered back-projection (FBP) algorithm
is applied to noisy, discrete Radon transform data with sampling step size
$\epsilon$ in two-dimensions. Specifically, we analyze $N_\e^{\text{rec}}(x)$
for $x$ in small, $O(\e)$-sized neighborhoods around a generic fixed point,
$x_0$, in the plane, where the measurement noise values, $\eta_{k,j}$ (i.e.,
the errors in the sinogram space), are random variables. The latter are
independent, but not necessarily identically distributed. We show, under
suitable assumptions on the first three moments of the $\eta_{k,j}$, that the
following limit exists: $N^{\text{rec}}(\chx;x_0) =
\lim_{\e\to0}N_\e^{\text{rec}}(x_0+\e\chx)$, for $\check x$ in a bounded
domain. Here, $N_\e^{\text{rec}}$ and $ N^{\text{rec}}$ are viewed as
continuous random variables, and the limit is understood in the sense of
distributions. Once the limit is established, we prove that $N^{\text{rec}}$ is
a zero mean Gaussian random field and compute explicitly its covariance. In
addition, we validate our theory using numerical simulations and pseudo random
noise.
