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課程名稱 |
影像處理
IMAGE PROCESSING |
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開課學期 |
98-2 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
陳宜良 |
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課號 |
MATH5408 |
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課程識別碼 |
221 U5570 |
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班次 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期三7,8,9(14:20~17:20) |
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上課地點 |
新404 |
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備註 |
總人數上限：50人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/982ip |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
Image processing is important in medical sciences such as computed tomography
(CT), magnetic resonance imaging (MRI), positron emission tomography (PET),
etc. It is also commonly seen in earth sciences, astrophysics, entertainment engineering,
etc. It is a fast growing field in applied mathematics. The SIAM has a
new journal on this subject. In this course, I will cover the following contents.
1. Sparse representation: Fourier and wavelet theory
2. Imaging and image models (covers blur model, CT, MRI, PET)
3. Image restoration
4. Numerical optimization
5. Compressed sensing |
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課程目標 |
1. To provide techniques for image modeling and medical imaging
2. To provide mathematical background for image analysis and restoration.
3. To have computational experience on handling real data. |
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課程要求 |
Linear Algebra, Advanced Calculus, a little bit probability, Introduction to
Computational Mathematics, Matlab or C Programming Language. |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
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參考書目 |
1. R. C. Gonzalez and R. E.Woods, Digital Signal Processing, (there is a
Chinese edition)
2. S. Mallat, A wavelet tool of Signal Processing
3. Ming Jiang’s lecture note on medical image restoration
4. F. Natterer and F. W¨ubbeling, Mathematical Methods in Image Reconstruction
5. Tony F. Chan, Jianhong Jackie Shen, Image Processing and Analysis:
Variational, PDE, Wavelet, and Stochastic Methods, SIAM, 2005
6. I. Daubechies’ Ten Lectures on Wavelets
7. Some notes will be provided in the class. |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
project 1 |
20% |
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2. |
project 2 |
20% |
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3. |
project 3 |
20% |
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4. |
project 4 |
20% |
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5. |
Final presentation |
20% |
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週次 |
日期 |
單元主題 |
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第1週 |
2/24 |
Introduction and Spatial Filters |
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第2週 |
3/03 |
Filter in frequency domain
Matlab experiments |
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第3週 |
3/10 |
I made some change on fast Fourier transform. Please download the fft.pdf again. |
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第4週 |
3/17 |
Filter in frequency domain, Lecture 3 is updated. |
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第5週 |
3/24 |
Filter in frequency domain, wavelets |
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第8週 |
4/14 |
Computer lab by TA. (I will go abroad for a meeting). |
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第9週 |
4/21 |
n1 is a brief overview.
IRIA is Jiang Ming's lecture note on image reconstruction. |
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第11週 |
5/05 |
(Updated) Function spaces and operators, Calculus of Variation |
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第13週 |
5/19 |
MRI, Radon |
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第14週 |
5/26 |
Final reports papers
I add two new paper: DMRI-Qball, GQI2010. |
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第16週 |
6/09 |
No class |
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第17週 |
6/19 |
Final report. Room 110, old math bldg.
Each one report 0.5 hour. 10 min or less for summary of projects 1, 2. |
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