| Topic
+ Reading List |
Presenter |
Week/Date |
| Introduction
to Compressive
Sensing introductory slides, some old scanned notes |
Namrata Vaswani |
1 |
| Linear
Algebra Recap: Horn
and Johnson: parts of Chapter 0, 1, 2, 4, 5, 7 introduction, eigenvectors-eigenvalues, normal matrices and properties, Schur's result, eigenvector-eigenvalues of Hermitian matrices, variational characterization, Rayleigh-Ritz, Courant-Fisher, vector norms, dual norm, matrix norm (and sub-multiplicative property), induced norms, induced 1,2, infinity norm and their properties |
Namrata Vaswani |
1, 2 |
| Convex
Optimization Recap: Boyd and Vandenberghe's book + notes Boyd and Vandenberghe's book: pdf file Slides of Boyd and Vandenberghe: Introduction, Convex sets, Convex functions, Convex optimization problems, Duality, Subgradients (from EE 364b of Stanford) Convex Optimization S/W (Matlab): CVX |
Namrata Vaswani |
2,3 |
| Noiseless
Compressive Sensing: Exact Reconstruction Result Theorem 1.3 & Lemma 3.1 of Emmanuel Candès and Terence Tao, Decoding by linear programming. (IEEE Trans. on Information Theory, 51(12), pp. 4203 - 4215, December 2005) |
Namrata Vaswani | 3, 4 |
| Main
idea of different applications of CS (MRI/tomography, sensor networks, single-pixel camera, image compression) |
Namrata Vaswani | 4 |
| Noisy
Sparse Signals Emmanuel Candès and Terence Tao, The Dantzig Selector: Statistical estimation when p is much larger than n (To appear in Annals of Statistics) |
Namrata Vaswani | 4,5 |
| Compressible
or Noisy Sparse or
Noisy Compressible Signals Joel A. Tropp, Just Relax: Convex programming methods for identifying sparse signals, IEEE Trans. Info. Theory, vol. 51, num. 3, pp. 1030-1051, Mar. 2006 and its correction |
Namrata Vaswani | 6,7 (only 1 class in week 6) |
| Greedy
Approach to Compressive
Sensing (noiseless case) Joel Tropp and Anna Gilbert, Signal recovery from random measurements via orthogonal matching pursuit. (IEEE Trans. on Information Theory, 53(12) pp. 4655-4666, December 2007) |
Namrata Vaswani | 7, 8 |
| Brief
discussion of other greedy algorithms: Tree based OMP, Stagewise
OMP, CoSAMP, Subspace Pursuit Chinh La and Minh Do, Signal reconstruction using sparse tree representations. (SPIE Wavelets XI, San Diego, California, September 2005) David L. Donoho, Yaakov Tsaig, Iddo Drori, and Jean-Luc Starck, Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit. (Preprint, 2007) D. Needell and J. A. Tropp, CoSaMP: Iterative signal recovery from incomplete and inaccurate samples. (Preprint, 2008) Wei Dai and Olgica Milenkovic, Subspace pursuit for compressive sensing: Closing the gap between performance and complexity. (Preprint, 2008) |
March 3 |
|
| Guest lecture on John Wright, Allen Yang, Arvind Ganesh, Shankar Shastry, and Yi Ma, Robust face recognition via sparse representation. (To appear in IEEE Trans. on Pattern Analysis and Machine Intelligence) |
Xiaodong Yu |
|
| Compressible
Signals, Noiseless measurements + Discussion of UUP 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) |
Namrata Vaswani | March 10 |
| Brief discussion of measurement
matrices satisfying approximate orthogonality for sparse signals. Also
discussion of how to deal with large measurement matrices without
having to store them + More Applications E. Candes and J. Romberg, Robust Signal Recovery from Incomplete Observations, ICIP 2006 Thong T. Do, Trac D. Tran, and Lu Gan, Fast compressive sampling with structurally random matrices. (Preprint, 2007) Review paper (includes applications): A.M. Bruckstein, D.L. Donoho, and M. Elad, "From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images", SIAM Review, Vol. 51, No. 1, Pages 34-81, February 2009. |
Namrata Vaswani | March 12 |
| Spring Break |
March 17, 19 |
|
| Expansion-compression
Variance-component Based Sparse-signal Reconstruction from Noisy
Measurements Kun will also briefly discuss this: D.P. Wipf and B.D. Rao, Sparse bayesian learning for basis selection . (IEEE Trans. on Signal Processing, Special Issue on Machine Learning Methods in Signal Processing, 52, pp. 2153 - 2164, August 2004) |
Kun Qiu | March 24 |
| Guest lecture on David Donoho, Neighborly Polytopes and Sparse Solution of Underdetermined Linear Equations Reference article on Convex Polytopes |
Vamsi (Satya Andalam) |
March 26 |
| David Donoho, For most large underdetermined systems of linear equations, the minimal ell-1 norm solution is also the sparsest solution. (Communications on Pure and Applied Mathematics, 59(6), pp. 797-829, June 2006) | Wei Lu |
March 31 |
| Guest lecture on Wavelets.
Notes-1 Notes-2 Notes-3 |
Prof. Fritz Keinert (Math) |
April 2 |
| Holger Rauhut, Karin Schass, and
Pierre Vandergheynst, Compressed
sensing and redundant dictionaries.
(IEEE Trans. on Information Theory, 54(5), pp. 2210 - 2219, May 2008) M. Akçakaya and V. Tarokh, "A Frame Construction and A Universal Distortion Bound for Sparse Representations," IEEE Trans. on Signal Processing, June 2008. (pdf) |
Dominic Kramer |
April 7 |
| Project on CoSAMP and sequential CoSAMP. | Fardad Raisali |
April
8 (10-11:15 in Coover 1016) (make-up class) |
| Estimating Sparse Contour Deformations using Compressed Sensing : Applications to Deformable Contour Tracking | Samarjit Das |
April 9 |
| David Donoho, Compressed Sensing |
Yang Li |
April 14 |
| D. Needell and J. A. Tropp, CoSaMP: Iterative signal recovery from incomplete and inaccurate samples. (Preprint, 2008) | Chenlu Qiu |
April 16 |
| Martin Vetterli, Pina
Marziliano, and Thierry Blu, Sampling
signals with finite rate of innovation.
(IEEE Trans. on Signal Processing, 50(6), pp. 1417-1428, June 2002) Yue Lu and Minh Do, A theory for sampling signals from a union of subspaces. (IEEE Trans. on Signal Processing, 56(6), pp. 2334 - 2345, June 2008) |
Lu Dai |
April
17 (10-11:15 in Sweeney 1116) (make-up class) |
| Overview
of Analog CS: Yonina Eldar, Beyond bandlimited sampling: Nonideal sampling, smoothness, and sparsity (EUSIPCO, Lausanne, Switzerland, August 2008) Moshe Mishali and Yonina C. Eldar, Blind multi-band signal reconstruction: compressed sensing for analog signals. (IEEE Trans. on Signal Processing, 57(30), pp. 993-1009, March 2009) S. F. Cotter, B. D. Rao, K. Engan, and K. Kreutz-Delgado, Sparse solutions to linear inverse problems with multiple measurement vectors . (IEEE Trans. on Signal Processing, 53(9), pp. 2477 - 2488, July 2005) Yonina C. Eldar, Compressed sensing of analog signals. (Preprint, 2008) Yonina Eldar, Uncertainty relations for analog signals. (Preprint, 2008) New papers at ICASSP 2009: CS - 1 CS - 2 CS - 3 CS - 4 MRI |
Namrata Vaswani |
April 28 |
|
Elad,
M. and Bruckstein, A.M., A
generalized uncertainty principle and sparse representation in pairs of
bases, IEEE Trans. Info Theory, Sept 2002 |
Ahmet Alturk |
April 30 |
| Group
Presentations: Monday April 27, 1 -4pm |
everyone |
April
27, 1-4pm in Coover 1219 (make-up class) |
| Group
Presentations: 1. Distributed Compressed Sensing (Baron et al): Lu Dai and Kun Qiu 2. Remote Sening applications of CS: Yang Li 3. Compressive Imaging and Computer Vision: Samarjit Das 4. Convex Optimization Algorithms for Large Problems: Wei Lu and Fardad Raisali 5. Compressed Sensing and Redundant Dictionaries: Dominic Kramer 6. MRI applications of CS: Chenlu Qiu: over email before May 8 Some other interesting papers: 1. Wei Dai and Olgica Milenkovic, Subspace pursuit for compressive sensing: Closing the gap between performance and complexity. (Preprint, 2008) 2. Moshe Mishali and Yonina C. Eldar, Reduce and boost: Recovering arbitrary sets of jointly sparse vectors. (Preprint, February 2008) |