C HRISTINE L EW D HEYANI M ALDE E VERARDO U RIBE Y IFAN Z HANG S UPERVISORS : E RNIE E SSER Y IFEI L OU BARCODE RECONITION TEAM

UPC B ARCODE What type of barcode? What is a barcode? Structure? Our barcode representation? Vector of 0s and 1s

M ATHEMATICAL R EPRESENTATION

0.2 S TANDARD D EVIATION

0.5 S TANDARD D EVIATION

0.9 S TANDARD D EVIATION

D ECONVOLUTION

S IMPLE M ETHODS OF D ECONVOLUTION Thresholding Basically converting signal to binary signal, seeing whether the amplitude at a specific point is closer to 0 or 1 and rounding to the value its closer to. Wiener filter Classical method of reconstructing a signal after being distorted, using known knowledge of kernel and noise.

W IENER F ILTER

0.7 S TANDARD D EVIATION, 0.05 S IGMA N OISE

0.7 S TANDARD D EVIATION, 0.2 S IGMA N OISE

0.7 S TANDARD D EVIATION, 0.5 S IGMA N OISE

Non-blind Deblurring using Yu Mao’s Method By: Christine Lew Dheyani Malde

Overview 2 general approaches: o -Yifei (blind: don’t know blur kernel) o -Yu Mao (non-blind: know blur kernel General goal: o -Taking a blurry barcode with noise and making it as clear as possible through gradient projection. o -Find method with best results and least error

Data Model

Classical Method

Comparisons for Yu Mao’s Method Yu Mao’s Gradient Projection Wiener Filter

Comparisons for Yu Mao’s Method (Cont.) Wiener Filter Yu Mao’s Gradient Projection

Jumps How does the number of jumps affect the result ? What happens if we apply the amount of jumps to the different methods of de-blurring? Compared Yu Mao’s method & Wiener Filter Created a code to calculate number of jumps 3 levels of jumps: o Easy: 4 jumps o Medium: 22 jumps o Hard: 45 jumps (regular barcode)

Created a code to calculate number of jumps: Jump: when the binary goes from 0 to 1 or 1 to 0 3 levels of jumps: o Easy: 4 jumps o Medium: 22 jumps o Hard: 45 jumps o (regular barcode) What are Jumps

How does the number of jumps affect the result (clear barcode)? Compare Yu Mao’s method & Weiner Filter Analyzing Jumps

Comparison for Small Jumps (4 jumps) Yu Mao’s Gradient Projection Wiener Filter

Comparison for Medium Jumps (22 jumps) Yu Mao’s Gradient Projection Wiener Filter

Comparison for Hard Jumps (45 jumps) Wiener Filter Yu Mao’s Gradient Projection

Wiener Filter with Varying Jumps - More jumps, greater error - Drastically gets worse with more jumps

Yu Mao's Gradient Projection with Varying Jumps - More jumps, greater error - Slightly gets worse with more jumps

Conclusion Yu Mao's method better overall: produces less error from jump cases: consistent error rate of 20%-30% Wiener filter did not have a consistent error rate: consistent only for small/medium jumps at 45 jumps, 40%- 50% error rate

B LIND D ECONVOLUTION Yifan Zhang Everardo Uribe

D ERIVATION OF M ODEL

Gradient Projection Projection of Gradient Descent ( first-order optimization) Advantage: Allows us to set a range Disadvantage: Takes very long time Not extremely accurate results Underestimate signal

Least Squares estimates unknown parameters minimizes sum of squares of errors considers observational errors

Least Squares (cont.) Advantages: return results faster than other methods easy to implement reasonably accurate results great results for low and high noise Disadvantage: doesn’t work well when there are errors in

Total Least Squares Least squares data modeling Also considers errors of SVD (C) Singular Value Decomposition Factorization

Total Least Squares (Cont.) Advantage: works on data in which others does not better than least squares when more errors in Disadvantages: doesn’t work for most data not in extremities overfits data not accurate takes a long time x