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.
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
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||✔ Practical and/or problem-solving skills|
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|
|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.|
All course materials are provided on the lecturer's web-site.
Overall learning achievement is evaluated based on written report on the recent advances in image processing (100%).
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.