Medical imagings such as magnetic resonance imaging (MRI), computed tomog- raphy (CT), positron emission tomography (PET), are fast growing subjects in the field of applied mathematics. Especially the sparse representation and com- pressive sensing have attracted much attention from various disciplines in recent years. This course will focus on MRI with goals on innovative designs and ap- plications. In addition to the theory of MRI, this course will also have practical training provided by an MRI company CEMAR.
The structure of this course includes
• Basic image processing (6 hrs). I will use the book: Alasdair McAndrew, Introduction to digital image processing, Ch. 1-5. In this 6 hour lecture, stu- dents will learn how to use matlab to do point processing and filter processing. The applications include contrast enhancement, denoising and deblurring.
• Princeples of MRI (3 hrs): basic physics of MRI will be introduced. Bloch equation will be solved by matlab in order to know the excitation and relax- ation. The main reference of this lecture is Dwight Nishimura, Principles of Magnetic Resonance Imaging.
• Fourier transform (3 hrs): practice discrete Fourier transform
• MRI hardware introduction and working flow, MRI image acquisition. Stu- dents will go to CEMAR (No. 81, Zhongcheng Rd., Tucheng Dist., close to MRT Tucheng station) by 3:00 PM. Students will collect their own MRI images, if they want.
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• Modern image processing: this will include image and noise models, statistical approach, variational approach. I will also sketch some applications such as denoising, deblurring, inpainting, segmentation, compressive sensing.
• Various MRI image reconstruction. Students will play with their own row data. Here, the main reference book is Paul Suetens’ Fundamentals of Medical Imaging. These four lectures will be given by guest lecture Dr. Chien-Chih Huang from CEMAR.
The last three lectures will be focused on the recent progress of MRI. Students will give oral presentation on papers. These papers will be assigned in the middle of the semester. We will have a workshop at the end of this course. Some researchers will be invited to report on recent progress on MRI.