2024 Faculty Courses School of Engineering Department of Information and Communications Engineering Graduate major in Information and Communications Engineering
Multidimensional Information Processing
- Academic unit or major
- Graduate major in Information and Communications Engineering
- Instructor(s)
- Isao Yamada / Takamichi Miyata
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - Intensive
- Class
- -
- Course Code
- ICT.S403
- Number of credits
- 200
- Course offered
- 2024
- Offered quarter
- 2Q
- Syllabus updated
- Mar 14, 2025
- Language
- Japanese
Syllabus
Course overview and goals
This course focuses on the processing technologies for multi-dimensional information. Topics include sampling and quantization of multi-dimensional information, compression coding (entropy coding, quantization error analysis, orthogonal transform, Karhunen-Loeve transform (KLT), and Discrete Cosine Transform (DCT)), recent advances in image processing (image segmentation, colorization, image editing, and image retargeting), and image restoration via convex optimization (convex function/set, convex programming algorithms and regularization methods for image processing). The course enables students to understand the mathematical tools widely applicable to solve the real-world information processing problems. The lecture includes exercises using Numpy to deepen understanding of the algorithm through implementation.
Course description and aims
By the end of this course, students will:
1. Understand the fundamental of image coding methods.
2. Explain how to extract the essential and mathematical problems from real-world image processing problems.
3. Acquire the fundamentals of convex optimization
4. Ability to apply mathematical tools to various multidimensional information processing tasks and implement them.
Keywords
Signal processing, image processing, convex optimization
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
All lecture materials will be available to students in advance, and students are expected to prepare for the lecture. In the lectures, students are expected to deepen their understanding of the subject matter through a combination of classroom lectures and exercises.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Guidance, quantization, sampling, sampling theorem | Understand the course objectives and sampling theorem. |
| Class 2 | Entropy, source coding theorem | Undestand the fundamental of compression coding. |
| Class 3 | Exercise - Sampling Theorem | Understand the sampling theorem in depth through the exercise. |
| Class 4 | Quantization, analysis of quantization error | Understand the statistical analysis of quantization error. |
| Class 5 | Exercises - Quantization Error Estimation | Understand quantization error more deeply through the exercise. |
| Class 6 | Orthogonal transform，KLT (Karhunen-Loeve transform), DCT (Discrete Cosine Transform) | Understand the optimality of KLT and its relationship to DCT. |
| Class 7 | Application of eigenvalue problem，Locally linear embedding, Normalized cuts | Understand the applications of eigenvalue problem. |
| Class 8 | Exercise - Implementation of LLE | Through exercises, students will gain a deeper understanding of how to apply eigenvalue problems to signal processing. |
| Class 9 | Colorization using optimization, Poisson image editing | Understand that the simple system of linear equations can be used for solving the image processing problems. |
| Class 10 | Image recovery via convex optimization 1, Least square method，Tikhonov regularization | Understand the regulazaition technique and its necesity. |
| Class 11 | Exercises - Least Squares and Tikhonov Regularization | Understanding of least squares and Tikhonov's regularization through exercises. |
| Class 12 | Image recovery via convex optimization 2, convex function, convex set, gradient descent | Understand the fundamentals of convex optimization |
| Class 13 | Image recovery via convex optimization 3, TV regularization，norm，Legendre-Fenchel transform, mixed-norm，Chambolle's algorithm | Understand the complex regularization term and the numerical algorithms of convex optimization |
| Class 14 | Exercise - Implementation of Discrete Gradient Operators | Learn to implement discrete gradient actions through exercises. |
Study advice (preparation and review)
Textbook(s)
Not specified
Reference books, course materials, etc.
All course materials are provided on the lecturer's web-site.
Evaluation methods and criteria
The overall achievement of the learning objectives will be evaluated by multiple reports on the exercises (100%).
Related courses
- ICT.S206 ： Signal and System Analysis
- ZUS.F301 ： Foundations of Functional Analysis
- ICT.S414 ： Advanced Signal Processing (ICT)
Prerequisites
Not specified.
Other
In 2024, this course is to be presented as a 5 days intensive lecture (8/27[3-8], 8/28[3-8], 8/29[3-8], 9/2[3-8], 9/3[3-6]) in the summer vacation period.