Blind deconvolution of bar code signals

Bar code reconstruction involves recovering a clean signal from an observed one that is corrupted by convolution with a kernel and additive noise. The precise form of the convolution kernel is also unknown, making reconstruction harder than in the case of standard deblurring. On the other hand, bar codes are functions that have a very special form -- this makes reconstruction feasible. We develop and analyze a total variation based variational model for the solution of this problem. This new technique models systematically the interaction of neighboring bars in the bar code under convolution with a kernel, as well as the estimation of the unknown parameters of the kernel from global information contained in the observed signal.