Deblurring of One Dimensional Bar Codes via Total Variation Energy Minimization

Using total variation based energy minimisation 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 regularised by total variation. Our fidelity terms consist of the L 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 minimiser. We also present some numerical experiments suggesting that these sufficient conditions are not optimal and the energy methods are quite robust for significant blurring.