P. Fieguth - SD770 Homepage
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

SD770 Home Page for Fall 2015

Multidimensional Signal Modeling and Estimation:

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


Course Overview

This course will study the statistical modeling, analysis, and numerical methods of data processing, especially multidimensional data processing, with problems in image processing serving as a motivating context throughout the term. Thus there will be relatively little overlap with other courses in image processing, although such courses would be excellent preparation for this course.

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

2015 Course Syllabus


Text

The text for the course is

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

There are two primary sources for the text:

There is a home page for the text, showing the table of contents and a few errata.


Audit Requirements

It will be difficult to get much out of this course without active participation and keeping up with the reading. The requirements for an audit are as follows: Students who are regularly attending the class should either register for credit or audit, as it is important for the department to receive credit for the number of students taking its courses.

Suggested Reading

An approximate outline of how we will move through the text.
  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

Course Projects:

A major part of the course grade is based on a project of each student's choosing. I will ask you to prepare a brief proposal (one or two paragraphs).

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:

Keep in mind that you can't ``re-use'' a project from another course, nor can you ``borrow'' part of existing thesis work for the project. Of course you are encouraged to look at something related to your research area, and maybe some of the insights you gain in doing your project will find their way into your thesis, however your work for the project needs to be something you haven't already done.

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:

If your English writing skills are a litle weak, you can at least eliminate some of the most common errors by looking at the following summary: If you would like more suggestions on books which talk about grammar / style, please talk to me.

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.


Assignment Handout and Due Dates:

TopicAssignmentDate DueUpload Link
Assign 1: Matrix ConditioningProblems 2.1-2.4Oct 1
Assign 2: Static Estimation, InterpolationProblems 3.4-3.7Oct 19Dropbox Link
Assign 3: Kalman FilteringProblems 3.8, 4.1, 4.4Oct 29Dropbox Link
Assign 4: 2D Surface ReconstructionProblems 5.3, 5.4Nov 9Dropbox Link
Assign 5: Random FieldsProblems 6.1, 6.2, 6.3, 7.1, 7.2Nov 19Dropbox Link
Assign 6: Computational MethodsProblems 9.1, 9.2, 9.3, 10.1Dec 3Dropbox Link
Project ProposalOct 25Dropbox Link
Project PresentationsDec 3Dropbox Link
Project SubmissionDec 16Dropbox Link

The assignments are due by midnight on the specified date.

Assignments and projects are to be submitted electronically:

  1. The assignment must be a PDF file.
  2. Attach only a single file, don't give me multiple files or a zip archive. Just a single PDF file.
  3. 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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