2023 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)
- 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
- 2023
- Offered quarter
- 2Q
- Syllabus updated
- Jul 8, 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.
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. Apply mathematical tools for wide variety of multi-dimensional information processing problems.
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
To allow students to get a good understanding of the course contents, all course materials are provided on the lecturer's web-site. The additonal description is provided at the lecture.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Guidance | Understand the course objectives. |
| Class 2 | Quantization, sampling, sampling theorem | Understand the sampling theorem |
| Class 3 | Entropy, source coding theorem | Undestand the fundamental of compression coding. |
| Class 4 | Quantization, analysis of quantization error | Understand the statistical analysis of quantization error. |
| Class 5 | Orthogonal transform，KLT (Karhunen-Loeve transform) | Understand the optimality of KLT |
| Class 6 | From KLT to DCT (Discrete Cosine Transform) | Understand the relationship between DCT and KLT. |
| Class 7 | Application of eigenvalue problem，Locally linear embedding, Normalized cuts | Understand the applications of eigenvalue problem. |
| Class 8 | Colorization using optimization, Poisson image editing | Understand that the simple system of linear equations can be used for solving the image processing problems. |
| Class 9 | Image retargetting，Seam carving, Bidirectional similarity | Understand the difficulties of image retargeting problem and how to solve them. |
| Class 10 | Image recovery via convex optimization 1, Least square method，Tikhonov regularization | Understand the regulazaition technique and its necesity. |
| Class 11 | Image recovery via convex optimization 2, convex function, convex set, gradient descent | Understand the fundamentals of convex optimization |
| Class 12 | Image recovery via convex optimization 3, TV regularization，norm，Legendre-Fenchel transform | Understand the complex regularization term. |
| Class 13 | Image recovery via convex optimization 4, mixed-norm ，Chambolle's algorithm | Understand the numerical algorithms of convex optimization |
| Class 14 | Image mosaicing and homography | Understand the basic 3D image transform. |
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
Overall learning achievement is evaluated based on written report on the recent advances in image processing (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 2023, this course is to be presented as a 5 days intensive lecture (8/21[3-8], 8/22[3-8], 8/28[3-8], 8/29[3-8], 9/6[3-6]) in the summer vacation period.