## MTH 995-003: Introduction to Compressive Sensing and the Analysis of Big Data

Instructor: |
Mark Iwen |

Time and Place: |
T Th 12:30 pm -- 1:50 pm, in C304 WH |

E-mail: |
markiwen@math.msu.edu |

Office: |
C342 WH |

Office Hours: |
T 2:00 pm -- 3:00 pm, Th 2:00 pm -- 3:00 pm, and by appointment |

This class will focus on the rigorous analysis of practical algorithms for both compressive sensing, and the analysis of large and high dimensional data sets. Topics discussed will include (time permitting): Semidefinite programming, locally sensitive hashing, subspace approximation and n-widths, fast sparse Fourier transforms, the approximation of functions of many variables, metric space embeddings, and various applications of random matrices (including Johnson-Lindenstrauss embeddings, nearly-isometric embeddings of smooth submanifolds of **R**^{N}, and the restricted isometry property).

#### Course website for MTH995-003:

http://math.msu.edu/~markiwen/Teaching/MTH995/MTH995_S14.html

The course website has the course schedule, the syllabus, and supplementary reading. Papers covered in class will be posted there.

#### Textbook:

**A Mathematical Introduction to Compressive Sensing**, by Simon Foucart and Holger Rauhut. Springer, ISBN 978-0-8176-4947-0

This book is an excellent reference. I recommend it highly. In addition, we will be covering several papers during the semester. These papers will be posted on the course schedule before they are discussed.

#### Homework:

Exercises will be assigned in class most days. They will be collected and spot checked approximately once every two weeks.

Alternatively, students may elect to work on a research project (approved in advance by the instructor) instead of submitting all of the homework assignments. A written report on the project will then be required before the end of the semester. Project ideas will be presented occasionally during class. The written project report will count for all the homework assignments not submitted while the student is completing the research project.

You are encouraged to work with your peers on homework assignments. Math is a collaborative discipline and two or three minds are often better than one. However, your submitted homework assignments must be written up individually in your own words.

#### Scribing Lectures:

Each student should scribe 2 lectures. Pick two **unbolded** dates from the schedule when you are available to scribe, and then send your choices to the Instructor by e-mail. Dates will be distributed on a first-come, first-serve basis.

The scribed notes -- **both the .tex and .pdf files** -- should be e-mailed to the instructor **within 96 hours (i.e., 4 days)** after the end of the scribed lecture. The instructor will post the notes on the schedule **without review** immediately after receiving them. Students may be asked to make revisions later if mistakes are found by the class.

Students should use the following LaTeX template for typing up the notes. Several free LaTeX compilers (which compile .tex files into .pdf files) exist. I recommend MiKTeX for windows, and MacTeX for Macs.

#### Class Participation:

Please ask questions and make constructive comments during lecture. This course is for you: get the most out of it!

#### Grading:

Your final grade will be assigned based on the submitted homework (and/or project report), and the scribed lectures.

- Homework (and/or final project report) -- 90%
- Scribed Lectures -- 10%

Some of the homework exercises will be challenging -- it is only expected that the submitted homework demonstrates effort.