Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Elective
Objectives of the Course The purpose of this course is to introduce some mathematical basics to remove blur of images and use MATLAB software to remove blur of images. In this lesson, after getting familiar with some concepts of image processing and the reasons for the existence of blur in images, students will solve image deblurring using mathematical methods that are mainly based on linear algebra.
Course Content The Image Deblurring Problem, A First Attempt at Deblurring, Deblurring Using a General Linear Model, Manipulating Images in MATLAB, The Blurring Function: Obtaining the PSF, Noise, Boundary Conditions, Structured Matrix Computations: 1D and 2D Problems, BCCB Matrices, BTTB + BTHB+BHTB + BHHB Matrices, Kronecker Product Matrices, Creating Realistic Test Data, Introduction to Spectral Filtering, SVD Analysis, The SVD Basis for Image Reconstruction, The DFT and DCT Bases, The Discrete Picard Condition, Regularization by Spectral Filtering, Implementation of Filtering Methods, Regularization Errors and Perturbation Errors, Color Images, A Blurring Model for Color Images, Tikhonov Regularization Revisited, Working with Partial Derivatives.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator Associate Prof.Dr. Nasser AGHAZADEH
Name of Lecturers Associate Prof.Dr. Nasser AGHAZADEH
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Hansen, Per Christian, James G. Nagy, and Dianne P. O'leary. Deblurring images: matrices, spectra, and filtering. Society for Industrial and Applied Mathematics, 2006.

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 1 % 30
Quizzes 0 % 0
Homeworks 2 % 10
Other activities 0 % 0
Laboratory works 0 % 0
Projects 2 % 20
Final examination 1 % 40
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 1 42 42
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 1 36 36
Laboratory 1 6 6
Exams and Exam Preparations 6 17 102
Total Work Load   Number of ECTS Credits 6 186

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 Understanding how images become arrays of numbers.
2 Ability to work with images in MATLAB.
3 Understanding the blurring function and different types of blurs.
4 Understanding some special matrices and Kronecker Product.
5 Understanding how singular value decomposition is related to deblurring.
6 Ability to work with color images.

Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 How Images Become Arrays of Numbers Deblurrinq Images (Hansen) - Chapter 1
2 A First Attempt at Deblurring Deblurrinq Images (Hansen) - Chapter 1
3 Images in MATLAB: Image, Reading, Displaying, and Writing Images, Performing Arithmetic on Images, Displaying and Writing Revisited Deblurrinq Images (Hansen) - Chapter 2
4 The Blurring Function: Taking Bad Pictures, The Matrix in the Mathematical Model, Obtaining the PSF, Conditions Deblurrinq Images (Hansen) - Chapter 3
5 Noise, Boundary Conditions Deblurrinq Images (Hansen) - Chapter 3
6 Basic Structures, One-Dimensional Problems, Two-Dimensional Problems, Separable Two-Dimensional Blurs, BCCB Matrices, Spectral Decomposition of a BCCB Matrix Deblurrinq Images (Hansen) - Chapter 4
7 Computations with BCCB Matrices, BTTB + BTHB+BHTB + BHHB Matrices Deblurrinq Images (Hansen) - Chapter 4
8 Kronecker Product Matrices, Constructing the Kronecker Product from the PSF, Matrix Computations with Kronecker Products Deblurrinq Images (Hansen) - Chapter 4
9 Summary of Fast Algorithms, Creating Realistic Test Data Deblurrinq Images (Hansen) - Chapter 4
10 Singular Value Decomposition and Spectral Analysis: Introduction to Spectral Filtering, Incorporating Boundary Conditions, SVD Analysis Deblurrinq Images (Hansen) - Chapter 5
11 The SVD Basis for Image Reconstruction, The DFT and DCT Bases, The Discrete Picard Condition Deblurrinq Images (Hansen) - Chapter 5
12 Regularization by Spectral Filtering: Two Important Methods, Implementation of Filtering Methods, Regularization Errors and Perturbation Errors, Parameter Choice Methods, Implementation of GCV, Estimating Noise Levels Deblurrinq Images (Hansen) - Chapter 6
13 Color Images: A Blurring Model for Color Images, Tikhonov Regularization Revisited Deblurrinq Images (Hansen) - Chapter 7
14 Color Images: Working with Partial Derivatives, Working with Other Smoothing Norms, Total Variation Deblurring, Blind Deconvolution Deblurrinq Images (Hansen) - Chapter 7

Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1 3 3 3
C2 3 3 4
C3 3 3 3
C4 3 3 3
C5 3 3 3
C6 3 3 4

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant