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.Comment: 34 pages, 6 figures (with a total of 30 subfigures); errors corrected
in Version 3, see Errata 1.1, 4.4, and 6.6 (v3 numbering) for more
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