Introduction to Compressed Sensing

Instructor: Prof. Heung-No Lee

Email: heungno@gist.ac.kr

This course was offered in the Spring semester 2011 at GIST.

Here is the lecture note Book_CS.pdf for this course. Here is the presentation of professor Heung-No Lee presented at PSIVT 2011 Overview of Compressed Sensing

Course Syllabus

1	Introduction to Compressive Sensing, Shannon Nyquist Sampling Theorem l Richard Baraniuk, Compressive sensing. (IEEE Signal Processing Magazine, 24(4), pp. 118-121, July 2007) l Justin Romberg, Imaging via compressive sampling. (IEEE Signal Processing Magazine, 25(2), pp. 14 – 20, March 2008)
2	Comparison of L0, L1, L2 solutions, application of sparse representation theory in filter array based spectrometers	HW#1
3	Compressive Sensing Theory: L0 and L1 equivalence, The Spark = Dmin of parity check matrix, The Singleton bound, Givens Rotation based Matrix Design
4	Compressive Sensing Mathematics: Generalized Uncertainty Principle, Sparse Representation, conditions for the unique ell-0 solution, and the unique ell-1 solution, the Donoho approach 1. D. Donoho and X. Huo, “Uncertainty Principles and Ideal Atomic Decomposition,” IEEE Trans. on Info. Theory, vol.47, no.7, Nov. 2001. 2. M. Elad and A. Bruckstein, “A generalized uncertainty principle and sparse representation in pairs of bases,” IEEE Trans. Info. Theory, vol. 48, no. 9, Sept. 2002.	HW#2
5	Compressive Sensing Mathematics: conditions for the ell-0 solution, and the unique ell-1 solution, the Candes-Tao approach. 1. Emmanuel Candès and Terence Tao, Decoding by linear programming. (IEEE Trans. on Information Theory, 51(12), pp. 4203 – 4215, December 2005) 2. Emmanuel Candès, Justin Romberg, and Terence Tao, Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. (IEEE Trans. on Information Theory, 52(2) pp. 489 – 509, February 2006) 3. Emmanuel Candès and Terence Tao, “Near optimal signal recovery from random projections: Universal encoding strategies” (IEEE Trans. on Information Theory, 52(12), pp. 5406 – 5425, December 2006)
6	Compressive Sensing Mathematics: Sensing matrices and oversampling factors	HW#3
7	Stable Recovery
8	Midterm Exam
9	Recovery Algorithm I : Homotopy, LASSO, LARs , OMP.	HW#4
10	Recovery Algorithm II : ell-1 minimization , SOCP, Message Passing Algorithm s
11	Class Presentations #1/#2/#3	HW#5
12	Connection to the Shannon TheoryClass Presentations #4/#5/#6
13	The Rate Distortion TheoryClass Presentations #7/8/9	HW#6