Paul Fieguth Dept. of Systems Design Engineering Faculty of Engineering University of Waterloo Waterloo, Ontario Canada N2L 3G1 |
pfieguth@uwaterloo.ca Tel: (519) 888-4567 x84970 FAX: (519) 746-4791 |

Your presentation will take place on Thursday, December 3rd:

- Please upload your slide(s) ahead of time, to this dropbox folder
- Please aim for about 3 minutes, and for sure no more than 5 minutes.
- Please prepare a one-page handout (one or two sides). Bring enough copies for the class (1 for yourself, 12 other students, 1 for me -- total of 14)
- The presentation and the handout are both associated with a modest grade. Not a large part of the course grade, but it is still worth doing a good job. Note that the presentation and handout are graded for engagement / interest / communications; I am not grading the problem you are working on itself.
- Please upload your project to this dropbox folder. The project is due by midnight on Wednesday, December 16th. Projects after that date are assessed a late penalty of 1% per day.

The course will begin with a linear systems and statistics review, followed by an overview of inverse problems, ill-posedness, estimation theory, and Kalman filtering.

The body of the course will examine specialized Kalman filtering algorithms, multi-dimensional estimation (marching methods, nested dissection, multigrid), conditional methods (coordinate descent, expectation-maximization), changes of bases (wavelets, radial basis functions, Gabor functions etc.), implicit models (Markov random fields, Gibbs random fields, simulated annealing), hypothesis testing, and hypothesis trees.

Models will be illustrated and motivated by examples from current literature and ongoing research, particularly in computer vision, remote sensing, and medical imaging.

Prerequisites: One of SD675, SD575, ECE603, ECE604

P. Fieguth, **Statistical Image Processing and Multidimensional Modeling**, Springer, 2010

There are two primary sources for the text:

- A printed, bound version from Amazon.ca.
- An electronic version, to which you have access from any UW computer, via Springer Link

- Do half of the first four assignments. The work does not need to be elegant or complete, but at least showing a bit of attention to the assignment questions.
- Submit a proposal (ie, pick some topic and do a little reading on it)
- Give a brief presentation at the end of the term, mainly discussing the topic and what it is that makes it interesting.

Period Reading Topics Week 1 (Sep 15): 1 Introduction Week 2 (Sep 22): 2.1 - 2.5 Inverse Problems, Regularization Week 3 (Sep 29): 3 Static Estimation Week 4 (Oct 6): 4.1 - 4.2 Dynamic Estimation, Kalman Filtering Week 5 (Oct 13): 4.2.2 - 4.2.4 Kalman Filter Methods Week 6 (Oct 20): 5.1 - 5.5 Determinisitic Modelling Week 7 (Oct 27): 5.6 - 5.7, 6.1 Statistical Modelling Week 8 (Nov 3): 6.2 - 6.7 Markov / Gibbs Random Fields Week 9 (Nov 10): 7 Hidden Markov models Week 10 (Nov 17): 8 Changes of Bases Week 11 (Nov 24): 9 Linear System Solvers Week 12 (Dec 1): 10 Large-Scale Kalman Filtering

**Project Proposal:** A project topic should be chosen by the middle of
October. This involves selecting a topic (ideally from the list
below, or from subjects in the course notes), and writing one or two
paragraphs, plus a reference or two, describing slightly more
specifically what you would like to look at.

This applies to both regular (credit) and audit students. Please begin thinking about possible project ideas. A piece of paper with your short proposal is due in class by Oct 22.

**Project Topics:**
I have a few
project suggestions here; I will work on adding to this list:

- Application of statistics to a problem in remote sensing
- A study of linear systems methods (CG, SOR, MG etc.)
- Spectral (eigenvalue distribution) issues in linear systems
- Application / survey of Markov random fields
- Application / survey of simulated annealing
- Application / survey of multigrid methods
- Application / survey of wavelet methods in large-scale processing, especially for estimation and statistics
- Krylov subspace methods (conj. gradient for statistics)
- Implementation of the marching methods algorithm, especially with smoothing
- FFT and Toroidal fields
- An experimental study of matrix conditioning
- Different Kalman filter algorithms (especially square-root and information forms)
- Nonlinear (extended) Kalman filters
- A study of any hierarchical change-of-basis method (Laplacian pyramids, Gabor functions, wavelets, hierarchical triangles etc.)
- A study of the mathematics of regularization and conditioning
- Applicability of robust statistics to large-scale problems

In general, because the concepts in this course are fairly advanced, I think that most of you would benefit more from implementing an algorithm and doing some simulations rather than trying to read some state-of-the-art journal papers.

**Project Writing:**
After grading a lot of assignments and course projects, I find myself
writing the same advice over and over again. All students in SD770
should take a look at the following:

**Project due date:**
Projects are due by midnight on Wednesday, December 16th. Projects submitted after that time are considered late, with a late penalty of 1% per day.

Topic | Assignment | Date Due | Upload Link |
---|---|---|---|

Assign 1: Matrix Conditioning | Problems 2.1-2.4 | Oct 1 | |

Assign 2: Static Estimation, Interpolation | Problems 3.4-3.7 | Oct 19 | Dropbox Link |

Assign 3: Kalman Filtering | Problems 3.8, 4.1, 4.4 | Oct 29 | Dropbox Link |

Assign 4: 2D Surface Reconstruction | Problems 5.3, 5.4 | Nov 9 | Dropbox Link |

Assign 5: Random Fields | Problems 6.1, 6.2, 6.3, 7.1, 7.2 | Nov 19 | Dropbox Link |

Assign 6: Computational Methods | Problems 9.1, 9.2, 9.3, 10.1 | Dec 3 | Dropbox Link |

Project Proposal | Oct 25 | Dropbox Link | |

Project Presentations | Dec 3 | Dropbox Link | |

Project Submission | Dec 16 | Dropbox Link |

The assignments are due by midnight on the specified date.

Assignments and projects are to be submitted electronically:

- The assignment must be a PDF file.
- Attach only a single file, don't give me multiple files or a zip archive. Just a single PDF file.
- Use the Dropbox upload link provided.

(The background to this web page is an example of a toroidally-periodic random field, generated using FFT methods, one of the approaches taught in SD770).

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