2021 Multidimensional Information Processing

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Academic unit or major
Graduate major in Information and Communications Engineering
Miyata Takamichi  Yamada Isao 
Course component(s)
Lecture    (ZOOM)
Day/Period(Room No.)
Intensive ()  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
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Course description and aims

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.

Student learning outcomes

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.


Signal processing, image processing, convex optimization

Competencies that will be developed

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/Required learning

  Course schedule Required learning
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.


Not specified

Reference books, course materials, etc.

All course materials are provided on the lecturer's web-site.

Assessment criteria and methods

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 (i.e., required knowledge, skills, courses, etc.)

Not specified.


In 2021, this course is to be given as intensive lectures on Sep 1,2,3,9 (from 3rd to 8th classes) and on Sep 10 (from 3rd to 6th classes) in the summer vacation period.

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