Anisotropic Total Variation Regularized L^1-Approximation and Denoising-Deblurring of 2D Bar Codes - Mathematics > Optimization and ControlReportar como inadecuado




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Abstract: We consider variations of the Rudin-Osher-Fatemi functional which areparticularly well-suited to denoising and deblurring of 2D bar codes. Thesefunctionals consist of an anisotropic total variation favoring rectangles and afidelity term which measure the L^1 distance to the signal, both with andwithout the presence of a deconvolution operator. Based upon the existence of acertain associated vector field, we find necessary and sufficient conditionsfor a function to be a minimizer. We apply these results to 2D bar codes tofind explicit regimes -in terms of the fidelity parameter and smallest lengthscale of the bar codes- for which a perfect bar code is recoverable viaminimization of the functionals. Via a discretization reformulated as a linearprogram, we perform numerical experiments for all functionals demonstratingtheir denoising and deblurring capabilities.



Autor: Rustum Choksi, Yves van Gennip, Adam Oberman

Fuente: https://arxiv.org/







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