The literature listed below is by far not exhaustive, but it represents good starting points for further study.

**Lecture 1:**

E. Candes and M. Wakin. *An introduction to compressive sampling.*
IEEE Signal Process. Magazine, 25(2):21-30, 2008.

D. Donoho. * Compressed sensing. *
IEEE Trans. Inform. Theory 52, no.4, 1289--1306, 2006.

R. Baraniuk. *Compressive sensing.*
IEEE Signal Process. Magazine, 24(4):118-121, 2007.

J. Romberg.

**Lecture 2:**

S.S. Chen, D.L. Donoho, and M.A. Saunders. *Atomic decomposition by basis
pursuit*, SIAM J. Sci. Comput., 20:33-61, 1998.

A.M. Bruckstein, D. Donoho, and M. Elad.

S. Mallat.

**Lecture 3:**

D.L. Donoho and X. Huo. *Uncertainty principles and ideal atomic
decomposition*, IEEE Trans. Inform. Theory, 47:2845-2862, 1999.

O. Christensen. *An Introduction to Frames and Riesz Bases*. Applied and
Numerical Harmonic Analysis. Birkauser, Boston, 2003.

**Lecture 4:**

R. Gribonval and M. Nielsen. *Sparse representations in unions of
bases.* IEEE Trans. Inform. Theory, 49(12):3320-3325, 2003.

T. Strohmer and R. W. Heath. *Grassmannian frames with applications to
coding and communication*. Appl. Comput. Harmon. Anal., 14(3):257-275, 2003.

**Lecture 5:**

E. Candes, J. Romberg, and T. Tao. *Stable signal recovery from incomplete
and inaccurate measurements.* Comm. Pure Appl. Math., 59(8):1207-1223, 2006.

E. Candes and T. Tao. *Decoding by linear programming.* IEEE Trans.
Inform. Theory, 51(12):4203-4215, 2005.

D. Donoho and M. Elad. * Optimally Sparse Representation from
Overcomplete Dictionaries via l_1 norm minimization.*
Proc. Natl. Acad. Sci. USA, 100, no.5, 2197-2202, 2003.

**Lecture 6:**

E. Candes. *The restricted isometry property and its implications for
compressed sensing.* Compte Rendus de l'Academie des Sciences, Paris,
Serie I, 346 589--592.

**Lecture 7:**

J. Fuchs. *On Sparse Representations in Arbitrary Redundant Bases.*
IEEE Transactions on Information Theory, vol. 50, no. 6, 2004.

J. Tropp. * Recovery of short, complex linear combinations via l_1
minimization.*
IEEE Trans. Info. Theory, vol. 51, num. 4, pp. 1568-1570, 2005.

**Lecture 8:**

Two online introductions to probability theory

C.M.Grinstead and J.L.Snell, Introduction to Probability

Probability Theory course notes by Roman Vershynin

**Lecture 9:**

R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin. * A Simple Proof
of the Restricted Isometry Property for Random Matrices. *
Constructive Approximation, vol. 28, no. 3, pp. 253-263, 2008.

**Lecture 10:**

H. Rauhut.
Compressive sensing and structured random matrices. In
Theoretical Foundations and Numerical Methods for Sparse Recovery, Radon
Series Comp. Appl. Math. deGruyter, to appear. Version of April 5, 2010.

**Lecture 11:**

S. Boyd and L. Vandenberghe.
*Convex Optimization. *
Cambridge University Press.

S.S. Chen, D.L. Donoho, and M.A. Saunders. *Atomic decomposition by basis
pursuit*, SIAM J. Sci. Comput., 20:33-61, 1998.

**Lecture 12:**

J. Tropp. *Greed is good: Algorithmic results for sparse approximation.*
IEEE Trans. Info. Theory, vol. 50, num. 10, pp. 2231-2242, Oct. 2004.

D. Needell, J. A. Tropp, and R. Vershynin.
*Greedy signal recovery review*
In Proc. 42nd Asilomar Conf. Signals, Systems and Computers, Pacific Grove,
Oct. 2008.

W. Dai and O. Milenkovic.
* Subspace Pursuit for Compressive Sensing Signal Reconstruction.*

Several Matlab codes can be found here

**Lecture 13:**

E. J. Candès and B. Recht. * Exact matrix completion via convex
optimization.*
Found. of Comput. Math., 9 717--772.

Raghunandan H. Keshavan, Sewoong Oh and Andrea Montanari. *
Matrix Completion from a Few Entries.*
http://arxiv.org/abs/0901.3150, 2009.

**Lecture 14:**

E. J. Candes, X. Li, Y. Ma, and J. Wright. *Robust Principal Component
Analysis?* Preprint.

Benjamin Recht, Maryam Fazel, and Pablo A. Parrilo. * Guaranteed
Minimum Rank Solutions to Linear Matrix Equations via Nuclear Norm
Minimization.* To appear in SIAM Review.

**Lecture 15:**

M. Herman and T. Strohmer.
*High Resolution Radar via Compressed Sensing.*
IEEE Trans. Signal Processing, vol.57(6): 2275-2284, 2009.

**Lecture 16:**

D. Donoho. *
Neighborly Polytopes and Sparse Solutions of Underdetermined Linear
Equations. * 2005.

D. Donoho and J. Tanner. *
Exponential Bounds Implying Construction of Compressed Sensing Matrices,
Error-Correcting Codes and Neighborly Polytopes by Random
Sampling.* 2008.

R. G. Baraniuk, V. Cevher, M. Duarte, and C. Hegde. *
Model-based Compressive Sensing. *
To appear in IEEE Transactions on Information Theory, 2010.