Anisotropic Total Variation Regularized L^1-Approximation and Denoising/Deblurring of 2D Bar Codes

TL;DR

This paper introduces anisotropic total variation regularized L^1-approximation models tailored for denoising and deblurring 2D bar codes, providing theoretical conditions for perfect recovery and validating through numerical experiments.

Contribution

It develops new variational models with explicit recovery conditions for 2D bar codes and demonstrates their effectiveness via numerical linear programming approaches.

Findings

Explicit regimes for perfect bar code recovery identified.

Models effectively denoise and deblur 2D bar codes.

Numerical experiments confirm theoretical results.

Abstract

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.