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 en-
gineering, etc. This subject is a fast growing eld in applied mathematics. The
SIAM has a new journal (Journal on Image Sciences) on this subject. Especially
the sparse representation and compressive sensing have attracted much attention
in recent years. In this course, I will mainly cover the following topics
1. Introduction: statistical approach, variational approach.
2. Some modern image analysis tools
3. Image modeling and representation
4. Image denoising
5. Image deblurring
6. Image inpainting
7. Image segmentation
8. Numerical optimization
9. Compressed sensing