Blind deconvolution of barcodesignals.pdfVIP

INSTITUTE OF PHYSICS PUBLISHING INVERSE PROBLEMS Inverse Problems 20 (2004) 121–135 PII: S0266-5611(04)60933-6 Blind deconvolution of bar code signals Selim Esedoglu Mathematics Department, University of California - Los Angeles, Box 951555, Los Angeles, CA 90095, USA Received 17 March 2003, in final form 9 October 2003 Published 21 November 2003 Online at stacks.iop.org/IP/20/ 121 (DOI: 10.1088/0266-5611/20/ 1/007) Abstract 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 analyse a total variation based variational model for the solution of this problem. This new technique models systematically the interaction of neighbouring 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. 1. Introduction We study the problem of recovering a bar code from the noisy signal detected by a bar code reader. Bar codes represent (finite) sequences of digits by (finite) sequences of dark parallel ‘bars’ of varying thickness, separated by ‘white spaces’ of varying size. As such, they can be conveniently modelled as characteristic functions of measurable subsets of R (see fig