Nonnegative and Volume Constrained Image Deblurring Open Access

Lin, Lu (2016)

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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

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

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