CSE 788.01 Spring 2012  Sparse representations and compressed sensing
Instructor: Luis Rademacher.
Lectures: TTh 11:00am12:18pm, Dreese Labs 480
Question:
Today's pointandshoot cameras collect a large amount of information
(say 12 megapixels) but a good fraction of it is immediately discarded
as the result is an image file in the lossy JPEG format. Can we collect
less information and still get the same output? Yes, provided the camera
uses a special mirror that mixes pixels and the image is sparse
in the right format, that is, it is a vector with few nonzero entries
in the right basis (In the case of JPEG compression, the DCT basis is
good for real world pictures).
In
this
course
we will understand how sparse representations help in reducing
collection of data, storage and computation. Among the topics the course
will include (tentatively) sparse representations in streaming
algorithms (can we keep statistics on network packets with very limited
storage?), data structures and machine learning, and compressed sensing,
which is a framework that studies how an unknown sparse vector can be
recovered with much fewer measurements than the length of the vector (as
in the camera example). Among the diverse applications we will discuss
some of: faster MRI, matrix completion (the Netflix problem), geometric
separation, image segmentation and radar imaging for oil prospecting.
The
emphasis
will
be more on the algorithmic aspects, theory and applications and only as
needed on signal processing.
Announcements:
No lecture on Thu 5/4/2012.
Problem sets:
PS1 (due lecture on April 17th).
Helpful courses/topics (NOT required):
The
following
topics are helpful but not required, as we will review them near the
beginning of the course as needed: linear algebra, linear and nonlinear
optimization, signal processing, advanced algorithms.
Office hours:
By instructor, by appointment.
Grading:
Depending on the number of students and interest, a combination of (some of,
but not necessarily all of) homework, paper presentations and working on a
research project (definitely no exams).
Precise details on group discussions, critiques, and inclass discussions here.
Recommended readings:
 Nuit Blanche, blog
including compressed sensing and matrix factorizations.
 An introduction to
compressive sensing. Richard Baraniuk, Mark A. Davenport, Marco F.
Duarte, Chinmay Hegde.
 Introduction
to
Compressed Sensing.
 M. Fornasier
and
H. Rauhut. Compressive
Sensing. In O. Scherzer, editor, Handbook
of
Mathematical Methods in Imaging,
pages 187228. Springer, 2011.
 Computational
methods for inverse problems. Curtis R. Vogel. Society for
Industrial and Applied Mathematics, c 2002. Philadelphia, PA. ISBN
0898715075.
List of papers (Warning: no guarantee that these are the latest
versions, search online)
 A remark on compressed sensing. Kashin and
Temlyakov.
 AlmostEuclidean Subspaces of l 1 N\ ell_1^ N
via Tensor Products: A Simple Approach to Randomness Reduction
Indyk and Szarek.
 Euclidean Sections of l 1 N\ ell_1^ N with
Sublinear Randomness and ErrorCorrection over the Reals
Guruswami, Lee, Wigderson.
 Optimal columnbased lowrank matrix
reconstruction Guruswami, Sinop.
 NearOptimal ColumnBased
Matrix Reconstruction Boutsidis, Drineas, MagdonIsmail.
 Restricted isometry property of matrices with
independent columns and neighborly polytopes by random
sampling Adamczak, Litvak, Pajor, TomczakJaegermann
 Graph Sparsification by Effective
Resistances (D. Spielman, N. Srivastava), [arXiv] [slides]
 TwiceRamanujan Sparsifiers (J.
Batson, D. Spielman, N. Srivastava), [arXiv] [slides] [video]
 Reconstruction from anisotropic random
measurements Rudelson, Zhou
 On
the power of adaptivity in sparse recovery Indyk, Prince,
Woodruff.
 Numerical Linear Algebra in the Streaming Model (full version) pdf
Ken Clarkson, David Woodruff.
 Fast Moment Estimation in Data Streams in Optimal Space pdf ,
Full version on ArXiv
(Daniel M. Kane, Jelani Nelson, Ely Porat, David Woodruff)
 Y. Plan, R. Vershynin, Robust
1bit
compressed sensing and sparse logistic regression: a convex
programming approach, submitted. [arXiv:1202.1212].
 Y. Plan, R. Vershynin, Onebit
compressed
sensing by linear programming, Communications on Pure and
Applied Mathematics, to appear. [arXiv:1109.4299].
See
also 1BitCompressiveSensing page
at
Rice.

 Compressive Dual Photography
Pradeep Sen and Soheil Darabi
Computer Graphics Forum, Vol. 28, No. 2, March 2009, (Proceedings of
Eurographics 2009) [pdf]
[bibtex]
 Compressive Rendering of Multidimensional Scenes
Pradeep Sen, Soheil Darabi, Lei Xiao to appear in Lecture Notes
in Computer Science, "Video Processing and Computational Video," Eds:
D. Cremers, M. Magnor, M. Oswald, L. ZelnikManor. Springer. [pdf]
[bibtex]
 The
Convex
Geometry of Linear Inverse Problems
Venkat Chandrasekaran, Benjamin Recht, Pablo A. Parrilo, and Alan S.
Willsky
 Simple Bounds for Recovering
Lowcomplexity Models
Emmanuel Candes, Benjamin Recht
 Nuclear norm penalization and
optimal rates for noisy low rank matrix completion
Vladimir Koltchinskii, Alexandre B. Tsybakov, Karim
Lounici
 MultiLabel
Prediction via Compressed Sensing
Daniel Hsu, Sham M. Kakade, John Langford, Tong Zhang
 Geometry of logconcave
ensembles of random matrices and approximate reconstruction.
ADAMCZAK, R., LATALA, R., LITVAK, A. E., , PAJOR, A. and
TOMCZAKJAEGERMANN, N. (2011)
 Nearly Optimal Sparse Fourier
Transform
Haitham Hassanieh, Piotr Indyk, Dina Katabi, Eric Price
 Gossip PCA
Satish Babu Korada, Andrea Montanari, Sewoong Oh
 The Power of Convex
Relaxation: NearOptimal Matrix Completion
Emmanuel J. Candes, Terence Tao
 A. d’Aspremont, F. Bach and L. El Ghaoui. Optimal
Solutions
for Sparse Principal Component Analysis. Journal of Machine
Learning Research, 9(Jul):1269–1294, 2008.
 Laurent El Ghaoui, GuanCheng Li, VietAn Duong, Vu Pham, Ashok
Srivastava, Kanishka Bhaduri. Sparse
Machine
Learning Methods for Understanding Large Text Corpora. Accepted
for publication in Proc. Conference
on Intelligent Data Understanding, 2011.
 Youwei Zhang and Laurent El Ghaoui. LargeScale
Sparse
Principal Component Analysis with Application to Text Data.
Schedule (tentative):