The Effects of Projection on Iterative Methods in Image Deblurring 公开
Herring, James Lincoln (2010)
Abstract
Abstract
The Effects of Projection on Iterative Methods in Image
Deblurring
By James L. Herring
Applications of iterative regularization methods encompass a broad
spectrum, in-
cluding image deblurring. One unique feature in image deblurring
problems is the
non-negativity of the solution. In light of this knowledge, this
thesis explores the
effectiveness of three projected iterative methods for image
deconvolution: projected
successive over-relaxation method (SOR), projected Landweber
method, and an in-
terior point gradient method. Specifically, this thesis compares
the effectiveness of
these methods to the standard un-projected SOR method, comparing
quality of image
reconstruction and the cost of each method. The thesis begins with
an introduction
to the field of image deblurring problems, iterative
regularization, and the methods
tested, and follows with experiments and analysis designed to
determine the useful-
ness of these methods for image deblurring.
Table of Contents
Contents
1 Introduction 1
1.1 Mathematical Background . . . . . . . . . . . . . . . . . . . .
. . . 3
1.2 Structure and Sparsity . . . . . . . . . . . . . . . . . . . .
. . . . . 7
1.3 Iterative Regularization . . . . . . . . . . . . . . . . . . .
. . . . . . 9
1.4 Projection: Additional Regularization . . . . . . . . . . . . .
. . . 11
1.5 Regularization Parameters and the Discrepancy Principle . .
12
2 Methods 14
2.1 Successive Over-Relaxation . . . . . . . . . . . . . . . . . .
. . . 14
2.2 Projected SOR . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 16
2.3 Projected Landweber Method . . . . . . . . . . . . . . . . . .
. . 17
2.4 Interior-Point Gradient Method . . . . . . . . . . . . . . . .
. . . 18
3 Filtering Properties 20
3.1 Filtering in Landweber . . . . . . . . . . . . . . . . . . . .
. . . . . 20
3.2 SOR Filtering . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 23
4 Numerical Experiments 25
4.1 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 26
4.2 Noise Level . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 28
4.3 Stopping Criterion . . . . . . . . . . . . . . . . . . . . . .
. . . . . .31
5 Experiments on Simulated Problems 35
5.1 Tests on Real Images . . . . . . . . . . . . . . . . . . . . .
. . . . 35
5.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . .39
About this Honors Thesis
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