Error estimates for a bar code reconstruction method

Selim Esedoḡlu; Fadil Santosa

doi:10.3934/dcdsb.2012.17.1889

Article Contents

2012, Volume 17, Issue 6: 1889-1902. Doi: 10.3934/dcdsb.2012.17.1889

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Error estimates for a bar code reconstruction method

Selim Esedoḡlu^1, and
Fadil Santosa^2,

1.
Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48109
2.
School of Mathematics, University of Minnesota, Minneapolis, MN 55455

Received: August 2011

Revised: February 2012

Published: September 2012

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Abstract

We analyze a variational method for reconstructing a bar code signal from a blurry and noisy measurement. The bar code is modeled as a binary function with a finite number of transitions and a parameter controlling minimal feature size. The measured signal is the convolution of this binary function with a Gaussian kernel. In this work, we assume that the blur kernel is known and establish conditions (involving noise level and variance of the convolution kernel) under which the variational method considered recovers essentially the correct bar code.

Keywords:

Mathematics Subject Classification: Primary: 68U10, 65R20, 65R32; Secondary: 49K40, 49N45, 49N60.

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References

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