Graduation Year


Date of Submission


Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Arts



Reader 1

Chiu-Yen Kao

Reader 2

Peter Uvin

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© 2017 Yizhou Tao


This thesis investigated a method of barcode reconstruction to address the recovery of a blurred and convoluted one-dimensional barcode. There are a lot of types of barcodes used today, such as Code 39, Code 93, Code 128, etc. Our algorithm applies to the universal barcode, EAN 13. We extend the methodologies proposed by Iwen et al. (2013) in the journal article "A Symbol-Based Algorithm for Decoding barcodes." The algorithm proposed in the paper requires a signal measured by a laser scanner as an input. The observed signal is modeled as a true signal corrupted by a Gaussian convolution, additional noises, and an unknown multiplier. The known barcode dictionaries were incorporated into the forward map between the true barcode and the observed barcode. Unlike the one proposed by Iwen et al., we take dictionaries of different patterns into account, specifically for decoding book barcodes from images which are captured with smartphones. We also presented numerical experiments that examined the performance of the proposed algorithm and illustrated that the unique determination of barcode digits is possible even in the presence of noise.


Best Senior Thesis in Mathematics