Error estimates for a bar code reconstruction method | Zendy

Selim Esedoḡlu | Zendy; Fadil Santosa | Zendy

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Error estimates for a bar code reconstruction method

Author(s) -

Selim Esedoḡlu,

Fadil Santosa

Publication year - 2012

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2012.17.1889

Subject(s) - bar (unit) , kernel (algebra) , code (set theory) , algorithm , gaussian function , error bar , gaussian , function (biology) , computer science , mathematics , binary number , variance (accounting) , noise (video) , artificial intelligence , statistics , discrete mathematics , physics , image (mathematics) , set (abstract data type) , programming language , arithmetic , accounting , quantum mechanics , evolutionary biology , biology , meteorology , business

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.

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