Deblurring of One Dimensional Bar Codes via Total Variation Energy Minimisation

TL;DR

This paper investigates the use of total variation energy minimisation to recover blurred 1D barcodes, establishing conditions for successful deblurring and demonstrating robustness through numerical experiments.

Contribution

It introduces a novel approach using total variation energy minimisation for 1D barcode deblurring, with theoretical conditions ensuring unique recovery.

Findings

Unique minimiser conditions for various blur regimes

Robustness of energy methods against significant blurring

Numerical evidence suggesting potential for improved conditions

Abstract

Using total variation based energy minimisation we address the recovery of a blurred (convoluted) one dimensional (1D) barcode. We consider functionals defined over all possible barcodes with fidelity to a convoluted signal of a barcode, and regularised 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 barcode, the size of the supports of the convolution and deconvolution kernels, and the fidelity parameter. For all functionals, we establish regimes (sufficient conditions) wherein the underlying barcode 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.