Lectures: Tuesdays, Wednesdays, 11-12:25 p.m.; 203 Transportation
Bldg.
Instructor: Prof. Yoram
Bresler (
ybresler
at illinois.edu, 112 Coordinated Science Lab, 244-9660)
Office Hours: Wed 3-4PM, 112 CSL (+ appointments by email).
TA: Nitin Aggarwal aggarwa1@illinois.edu
TA Office Hours: Tuesdays, 4:00-5:30pm; Everitt Lab 330L.
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:
Handouts:
Lecture Notes: (access restricted to only people registered in the
course)
Chapters 6-10 posted 4/5/09
Extra Notes:
Homework : (access restricted )
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Problem Set |
Date Posted |
Date Due |
Update/Comments |
Solutions |
Date Posted |
Update/Comments |
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1/29/09 |
2/5/09 |
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2/16/09 |
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2/10/09 |
2/17/09 |
Typo in Q2(b) corrected (Feb 16, 8:00pm) |
3/10/09 |
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2/19/09 |
2/26/09 |
Typos corrected (Feb 25, 4PM) |
3/10/09 |
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3/05/09 |
3/12/09 |
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4/02/09 |
4/9/09 |
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4/18 |
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4/15/09 |
4/22/09 |
Turn in to Nitin Aggarwal (CSL #339) By 5PM |
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Solutions to be posted on 4/22 5:10 PM, so no late HW can be accepted |
Exams (access restricted)
Midterm 1
Monday, March 16, 2009 7 – 9 PM. Location: 241 Everitt Lab.
Coverage: Ch. 1 – Ch. 4.3
Closed book test. You are allowed one two-sided sheet of paper.
· Grade Improvement Opportunity
You are being offered an opportunity to improve your grade on Midterm 1, by
re-working the problems of the midterm and turning the paper for grading by
Friday April 9, at 5 PM. Your final score on the midterm will be: in-class Exam
score + 0.3* (at home Exam score - in-class Exam score).
You may use the course notes and HW solutions handed out in the course, but no
other materials, in whatever form (printed, electronic, etc.). Also, you must
solve the problems yourself, and may not use any help in doing so.
On your paper include the following statement and sign:
“I certify that I did not use any materials, in whatever form, other than the
course notes and HW solutions handed out in the course, and did not receive any
help in preparing the solutions I am turning in for grading.
Signature:
--------------
........”
Previous Exams
Midterm 2
· Thursday, April 23, 2009, 7 – 9 PM. Location: 260 EVRT
·
Review Session: Wednesday, April 22,
2009, 7 – 9 PM. Location: 241 EVRT
·
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
Final Projects
|
Time |
Name |
Project Title |
|
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Tuesday Rm. 239 CSL* |
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6:00 PM |
Logan Niehaus |
Consistent Sampling and Signal Recovery |
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6:30 |
Sai Prasad R |
Sparse Representation
of data using a union of subspaces |
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7:00 |
Jeung Kim |
Signal Detection
through Projection |
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7:30 |
Onur Ertuk |
Restricted Orthogonality Property |
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Wednesday Rm.
239 CSL |
|
|
|
|
9:00 AM |
Myra Nam |
Shape metrics on the space of planar curves |
|
|
9:30 |
Bo Zhao |
Matrix Completion for Image Reconstruction in MRI Dynamic Imaging |
|
|
10:00 |
Shu Xinabiao |
Curvelets--A
Surprisingly Effective Nonadaptive Representation
for Objects with Edges |
|
|
Rm.
114 CSL |
|
|
|
|
2:00 PM |
Andrew Bean |
Signal sampling and
reconstruction |
|
|
2:30 |
Pilwon Hur |
Some mathematics in
learning theory and application |
|
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3:00 |
Chao Ma |
Simultaneous Sparse
Approximation and Its Application in MRI |
|
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3:30 |
Martin McCormick |
Brain Computer
Interfacing in the Context of Vector Space Signal Processing |
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4:00 |
Hoa Pham |
Greedy algorithms
for Sparse Approximation |
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4:30 |
Adam Gustafson |
Improvements of
Greedy Methods for Inverse Problems and Compressed Sensing |
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* CSL outside doors lock at 6PM.
·
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.
1. 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)
2. 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.
3. 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.
4. Suggestions for future work (brief): what are open problem, or what extension/applications might be interesting to pursue.
5. Ability to answer questions.