Research in Mathematical Image Processing, Lecture 1
The goal of this course is to give graduate students hands-on data-intensive research experience in medical image processing. Students will be encouraged to experiment with techniques found in recent literature on image processing, particularly algorithms involving variational methods, compressive sensing, and machine learning.
Possible Research Projects
i.) Similarity metrics for medical imagery
ii.) Change detection in MR brain images
iii.) Characterization of placental vascular networks
iv.) Sparse reconstruction in computerized tomography
v.) Contrast enhancement in MR images
vi.) Fusion of medical images from different imaging modalities
vii.) Automatic detection and segmentation of cells in bone marrow tissue.
The lectures will give an introduction to the mathematics of Image Processing. Topics will include:
-The Rudin-Osher-Fatemi Total Variation image model
-denoising by nonlocal means
-The Chan-Vese active contours segmentation model
-Introduction to Wavelets
-Introduction to Compressive sensing and L1 minimization by Bregman iteration.
There will be a discussion of medical image formats and programming with the Matlab Image Processing Toolbox. The lectures will alternate with a Matlab computer lab session where the students will be guided on programming the image processing algorithms discussed in the lecture.
Throughout the course, each team will have regular meetings with the instructor to update on their progress and obtain suggestions for further lines of inquiry.