Deblurring of One Dimensional Bar Codes via Total Variation Energy Minimization
Using total variation-based energy minimization we address the recovery of a blurred (convoluted) one dimensional (1D) bar code. We consider functionals defined over all possible bar codes with fidelity to a convoluted signal of a bar code and regularized by total variation. Our fidelity terms consist of the L(2) distance either directly to the measured signal or preceded by deconvolution. Key length scales and parameters are the X-dimension of the underlying bar code, the size of the supports of the convolution and deconvolution kernels, and the fidelity parameter. For all functionals, we establish parameter regimes (sufficient conditions) wherein the underlying bar code is the unique minimizer. We also present some numerical experiments suggesting that these sufficient conditions are not optimal and the energy methods are quite robust for significant blurring.
deblurring bar code total variation energy minimization