Statistical Methods in Signal and Image Analysis
Lectures 11:00-11:50 MWF
Place 1289 Comp S&St
noise brain surface mesh and its regulization via kernel smoothing
The course requirement is minimal and accessible for any graduate
students who knows multivariate normal distributions and
statistical inference and estimation. All topics will be self contained. Other
than undergraduate level mathematical statistics concepts, I will
introduce everything from scratch. For homework and projects,
you can use
any programming language such as R/Splus, MATLAB, JAVA, C++ but the
language of instruction will be in MATLAB due to its versatility of
Topics Covered: will not be covered in sequential order.
01. discrete and continuous random fields. simulation of random fields.
02. signal and image filtering and smoothing.
03. scale space. optimal filtering. bandwidth selection.
04. basics of Riemannian metric tensor geometry for image manipulation.
05. diffusion processes and diffusion equations. self-adjoint operators.
06. finite element methods and other numerical schemes.
07. smoothing scalar, vector and tensor data. smoothing manifolds.
08. stochastic optimization. EM algorithm.
09. Bayesian methods in image analysis. Gibbs sampler. image
10. functional data analysis: curve and image registration. deformation
11. shape analysis. directional statistics.
12. statistical inference, estimation and simulation in abstract space
Under no circumstance except medical or religious reasons, late
homeworks or projects will be accepted. It is encouraged to discuss
some hard problems with classmates only verbally but no plagiarism of
any sort will be permitted. Make sure you understand what is
plagiarism. You have an option of choosing
1. 20% class project + 30% independent project (your own research
area) + 50% biweekly homeworks.
2. 50% class project + 50% biweekly homeworks.
3. 30% class project + 70% biweekly homeworks.
Independent project should be based on techniques covered in the class
after consultation with the instructor. No credit will be given to a
project that has no connection with the course material. The first week
after spring break, please submit the title and abstract of project you
will be doing. There will be about 30 challenging homework problems.
You have an option of solving 2/3 of problems. So if you are more
theoretical person, you may skip some computation heavy problems. You
are required to submit homeworks biweekly. Most of problem will be
somewhat open ended and worth 5 points. Solving them correctly will
give you 4 points. To get an additional point, impress me by
doing something creative and inventive. Time consuming and difficult
homework problems will be usually assigned as class projects. To get
credit for project, submit typed project report of minimum 7pages
(20%),10pages (30%) or 15 pages (50%) excluding figures and
computer codes plus a disk containing working program. The deadline for
submitting the independent project is one week before the last lecture.
For class projects, the day of the last lecture.
Edward R. Dougherty, Random Processes for Image and Signal
Processing, IEEE Press 1999. ISBM: 0-8194-2513-3. It is not necessary
to buy this textbook but I recommend you to have one very good math
book on continuous stochastic processes.
Lecture Notes & Homeworks
Lecture 00. Image Analysis framework
01. Gaussian random fields
02. Linear operators on fields
03. Kernel smoothing I.
04. Numerical implementation of kernel smoothing
05. Diffusion equations
06. Iterated kernel smoothing
07. Isotropic kernels in manifolds
08. Kernel smoothing in manifolds
09. Simulating Gaussian fields
10. Hilbert Space.
11. Karhunen Loeve expansion I.
12. Karhunen Loeve expansion II.
13. Kernel Smoothing II.
14. Kernel Smoothing III.
15. Diffusion smoothing I.
16. Diffusion smoothing II.
17. Laplace Operator.
18. Multiple Comparisions I.
19. Multiple Comparisions II.
20. Bivariate smoothing on sphere I.
21. Bivariate smoothing on sphere II.
22. Brownian motion II.
23. Maxima of random fields I.
24. Maxima of random fields II.
25. Curve Modeling I.
26. Curve Modeling II.
27. Diffusion smoothing on manifolds II.
28. Diffusion smoothing on manifolds III.
29. Finite element method
30. Curve modeling III.
31. Curve modeling IV.
32. EM algorithm I.
33. EM algorithm II.
33. EM algorithm III appendum.
34. Anisotropic smoothing
35. Smoothing periodic functional data.
36. Smoothness of spatial noise.
37. Anisotropic smoothing II.
38. Image registration I.
39. EM algorithm IV..
40. Image registration II.