ECE 513: Vector Space Signal Processing

Spring 2008

Lectures: Mondays, Wednesdays, 11-12:20 p.m.; 57 Everitt Lab.

Instructor: Prof. Yoram Bresler ( ybresler at uiuc.edu, 112 Coordinated Science Lab, 244-9660)

Office Hours:  Mondays 3:30-4:30 PM  (+ appointments by email).

Graders (for questions about grading):          Kiryung Lee,  kiryung at gmail.com;

Quang Nguyen, nguyenhuuquang at gmail.com

 


Overview:
Rigorous presentation of key mathematical tools in a vector space framework, and their applications in signal processing, including: finite and infinite dimensional vector spaces, Hilbert spaces, linear operators, inverse problems (e.g. deconvolution, tomography, Fourier imaging), least-squares methods, conditioning and regularization, matrix decompositions, subspace methods, bases and frames for signal representation (e.g. generalized Fourier series, wavelets, splines), Hilbert space of random variables, random processes, signal and spectral estimation.

Topics:

  • Inverse problems and matrix theory (12 hours): linear inverse problems; orthogonal projections; minimum-norm least squares solutions; Moore-Penrose pseudoinverse; singular value decomposition; matrix decomposition and approximation; conditioning and regularization.
  • General linear vector spaces (15 hours): finite and infinite dimensional vector spaces; Hilbert spaces; projection theorem; inverse problems in infinite dimensional vector spaces; approximation and Fourier series; pseudoinverse operators; iterative methods for optimization and inverse problems; bases and frames for signal representation;
  • Hilbert space of random variables (6 hours): random processes; least-squares estimation; Wiener filtering; Wold decomposition; discrete-time Kalman filter.
  • Applications in signal processing (12 hours, during the course): deconvolution, optimal filter design, temporal and spatial spectrum estimation, tomography, harmonic retrieval, subspace methods, sensor array processing, extrapolation of band-limited sequences, generalized sampling, wavelets, splines, subset selection, sparse approximation.


Handouts:


Lecture Notes: (access restricted to only people registered in the course)

 

Extra Notes:



Homework : (access restricted )

 

Problem Set #1: Due Wednesday, Jan 23, 2008.

Problem Set #2: Due Wednesday, Feb 13, 2008.

Problem Set #3: Due Wednesday, Feb 20, 2008.

Problem Set #4: Due Monday,      March 3, 2008.

Problem Set #5: Due Monday,      March 24, 2008.

Problem Set #6: Due Friday,         April 11, 2008.

 

Homework Solutions (access restricted)

Problem Set #1: Posted Wednesday, Feb 13, 2008.

Problem Set #2: Posted Thursday, Feb 21, 2008.

Problem Set #3: Posted Thursday, Feb 28, 2008.

Problem Set #4: Posted Tuesday, March4, 2008.

Problem Set #5: Posted Saturday, April 19, 2008.

Problem Set #6: Posted Sunday, April 20, 2008.

 


Exams (access restricted)

Midterm 1

Tuesday 3/4/08 7 – 9 PM. Location: 170 Everitt Lab

Coverage: Ch. 1 & Ch. 2 of BBC (incl. material on HWs 1- 4).

Closed book test. You are allowed one two-sided sheet of paper.

Midterm1 2008

Solutions to Midterm 1

Previous Exams

Midterm 2

Tuesday, April 22, 7 – 9 PM. Location: 163 Everitt Lab

Coverage: Ch. 1 - Ch. 7 of BBC (incl. material on HWs 1- 6).

Closed book test. You are allowed two two-sided sheet of paper.

Previous Exams

Midterm 2 2004

Midterm 2 2006 Solutions


Final Projects

  • Instructions
  • Project Proposals: Due Friday April 4, 5PM
  • Presentations: April 28-30
    • Deliver power point or PDF presentation
    • 20 minutes presentation, 5 minutes for questions
    • Must be present for all presentations, and participate in questions

Tuesday 4/29/08,   351 CSL

Wednesday 4/30/08, 141 CSL

4:00-4:30

Nghia

5:30-6:00

Arthur

4:30-5:00

Victor

6:00-6:30

Sanketh

5:00-5:30

Jun

6:30-7:00

Mert Dikmen

5:30-6:00

Anh

7:00-7:30

Loan

6:00-6:30

Mert Bay

7:30-8:00

Spencer

6:30-7:00

Bernard

 

 

 

·         General guidelines and criteria for evaluation of the presentations:

1.      Clear statement of the problem being addressed or of the main ideas and purpose of the theory being introduced.

2.      Precise statement of theoretical results (e.g., key theorem(s), key algorithm),
 and explanation of the significance and role of assumptions needed for these results to hold.

3.      Explanation of

a.       the meaning of the results

b.      their significance

c.       their implications (for applications, and/or for the development of additional theory)

d.      their limitations (when they break down, do not apply)

4.      Understanding and ability to explain (in a mathematically precise way, but also providing the intuition) the technical derivation of one of the key results.

a.        You need to be able to teach your audience something new they have not seen before in the course.

b.      Spend at least 5 minutes on this -- but remember to allocate your time to cover the other criteria/components.

5.      Clear illustration of the application of the results/theory by appropriate example(s) -- either your own simulation or analysis, or from the paper(s) you have read.

6.      Suggestions for future work (brief): what are open problem, or what extension/applications might be interesting to pursue.

7.      Ability to answer questions.

 

  • Project Report: Due in electronic form (WORD or PDF) by Midnight, May 5. Criteria: similar to the above, but greater focus on technical contents.
    • Include the key papers used as references, in electronic form