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Nonnegative and Volume Constrained Image Deblurring

Lin, Lu (2016)
Honors Thesis (43 pages)
Committee Chair / Thesis Adviser: Nagy, James
Committee Members: DePasquale, Christina ; Duncan, John F
Research Fields: Applied mathematics
Keywords: image deblurring; iterative method
Program: College Honors Program, Mathematics
Permanent url: http://pid.emory.edu/ark:/25593/rhqcg

Abstract

In this thesis, we discuss iterative algorithms that can be used for constrained image deblurring. We mainly focus on the gradient projection method, which combines gradient descent with projections that implement constraints, such as nonnegative and volume constraints. Numerical experiments on three test problems using MATLAB illustrate the effctiveness and the efficiency of these methods.

Table of Contents

Table of Contents

1 Introduction

1.2 Iterative Methods................................................. 2

1.3 Image Deblurring................................................. 3

2 Gradient Projection Methods

2.1 Gradient Descent Method ..................................... 8

2.2 Nonnegative Projection........................................ 12

2.3 Conjugate Gradient Method for Least Squares ........ 13

3 Projection for Volume and Nonnegative Constraints

3.1 Nonnegative and Volume Projection....................... 15

3.1.1 Lagrange Multiplier Approach............................. 16

3.1.2 Newton's Method for finding ρ............................ 17

3.1.3 Initial Guess of ρ............................................. 17

4 Numerical Experiments

4.1 TestProblem: Satellite.......................................... 20

4.1.1 Methods Comparison................................ 20

4.1.2 Efficiency of the NNV Projection ................ 23

4.2 TestProblem: StarCluster .................................... 26

4.2.1 Methods Comparison................................ 26

4.2.2 Efficiency of the NNV Projection ................ 30

4.3 TestProblem: Grain ............................................. 31

4.3.1 Methods Comparison................................ 31

5 Conclusion and Discussion

Files

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