  We consider variations of the Rudin-Osher-Fatemi functional which are
particularly well-suited to denoising and deblurring of 2D bar codes. These
functionals consist of an anisotropic total variation favoring rectangles and a
fidelity term which measure the L^1 distance to the signal, both with and
without the presence of a deconvolution operator. Based upon the existence of a
certain associated vector field, we find necessary and sufficient conditions
for a function to be a minimizer. We apply these results to 2D bar codes to
find explicit regimes ---in terms of the fidelity parameter and smallest length
scale of the bar codes--- for which a perfect bar code is recoverable via
minimization of the functionals. Via a discretization reformulated as a linear
program, we perform numerical experiments for all functionals demonstrating
their denoising and deblurring capabilities.
