Lecture 1

Lecture notes [link]
Supplemental material: the space BV [link]

Syllabus

Lecture 1: Image modeling
Image modeling for image display, lower-level image processing, and high-level computer graphics. Lower-level image processing models: Bounded variation (BV) images, statistical images, level sets, Markov random fields, etc. and their relations.

Lecture 2: Image processing and Matlab.

Lectures 3 and 4: Variational image processing models
Denoising models: the ROF model and its variants; Decomposition models: The Meyer, Vese-Osher, TV/L1 models; Inpainting models.

Lectures 5 and 6: Numerical methods for variational image processing
PDE and various optimization methods.

(1) PDE time stepping method based on Euler-Lagrange equations

(2) A. Chambolle's dual method

(3) Second-order cone programming (SOCP) methods using commercial solver Mosek

(4) Graph-cut and parametric maximum flow

Lecture 7: Student research proposals

Lectures 8-9: Advanced topics
(provisional) High dimensional geometry and image processing, metrics and regularization, iterative regularization, and inverse scale space.

Lectures 10-12: Student research presentations and discussions