Sparse Representations and Compressive Sensing (Spring 2010)
Course: MAT 280
Title: Sparse Representations and Compressive Sensing
Class: MW 1:10pm-2:30pm, 2112 Math. Sci. Bldg.
Instructor: Thomas Strohmer
Office: 3144 MSB
Email:"my last name" at math.ucdavis.edu
Office Hours: M 3:10pm-4:00pm, or by appointment
This course will discuss the theoretical, numerical, and
practical foundations of sparse representations and compressive sensing.
Sparsity has become a very important concept in recent years in applied
mathematics. The key idea is that many types of functions and signals
arising naturally in applications can be described by only a small number of
significant degrees of freedom. Compressive sensing is a ingenius means to
exploit sparsity. Compressive sensing is not only one of the hottest topics
in mathematics in recent years, but it also has the potential to
revolutionize the technology of data acquisition and processing in a
broad sense. We will investigate the many fascinating connections between
these topics and other areas such as harmonic analysis, random matrix theory,
optimization, statistics, information theory and signal processing.
Furthermore, we will discuss matrix completion as well as applications
of compressive sensing in image processing, radar, and analog-to-digital
There is no required textbook (there is no textbook yet on compressive
sensing or on sparse representations).
- 50% Homework
- 50% Final Report
I will assign homework every other week, including both analytical and
programming exercises. A subset of these problems will be graded.
The homework will be announced at the
homework page. LATE HOMEWORK WILL NOT BE ACCEPTED.
The other half of your grade will be determined by your final report.
Here, you need to write a report on one of the following topics:
Describe how some of the methods you learned in this course will be
used in your research.
- Find a practical application yourself (not copying from
papers/books) using the methods you learned in this course; describe
how to use them; describe the importance of that application; what
impact would you expect if you are successful?
- A report describing a thorough numerical comparison of existing
algorithms for compressive sensing or matrix completion for a specific
application or problem.