520.648 - Sparse Recovery & Compressed Sensing

520.648 Sparse Recovery & Compressed Sensing

Department of Electrical and Computer Engineering
The Johns Hopkins University

Instructor
- Prof. Trac D. Tran
  Address: 215 Barton Hall
  Phone: (410) 516-7416
  Email: trac@jhu.edu
  Office Hours : Tues 11-1 or by appointment
- Prof. Sang (Peter) Chin
  Address: 320B Barton Hall
  Phone: (410) 516-7958
  Email: schin11@jhu.edu
  Office Hours : Thurs 3-4 or by appointment

Problem Sets
- Problem Set I, due Feb. 14 in class.
- Problem Set II, due Mar. 4 in TA or faculty office.
- Problem Set III, due Mar. 7 in class.
- Problem Set IV, due Mar. 14 in class.
- Problem Set V, due Mar. 28 in class.
  Code and Data Package.
- Problem Set VI, due Apr. 16 in class.

Course Description
- Sparsity has become a very important concept in recent years in applied mathematics, especially in mathematical signal and image processing, as in inverse problems. The key idea is that many classes of natural signals can be described by only a small number of significant degrees of freedom. This course offers a complete coverage of the recently emerged field of compressed sensing, which asserts that, if the true signal is sparse to begin with, accurate, robust, and even perfect signal recovery can be achieved from just a few randomized measurements. The focus is on describing the novel ideas that have emerged in sparse recovery with emphasis on theoretical foundations, practical numerical algorithms, and various related signal processing applications.

Syllabus
- Week 1: Introduction. Motivation. Mathematical Background
- Week 2: Traditional Sampling. Traditional Compression
- Week 3: Sparse Recovery. Restricted Isometry Property (RIP)
- Week 4: Coherence. Random Sampling. Johnson-Lindenstrauss
- Week 5: Stable Recovery. Number of Measurements
- Week 6: Sensing Matrix Design. Basis Pursuit Algorithms
- Week 7: Matching Pursuit Algorithms
- Spring Break
- Week 9: Robust PCA. Matrix Completion and Approximation
- Week 10: Applications to Medical Imaging
- Week 11: Applications to Sampling other RF Applications
- Week 12: Applications to Face Recognition & ATR
- Week 13: Applications in Computer Vision & Video Processing
- Week 14: In-class Final Project Presentations

Final Project
- Students are expected to work on a related topic of choice.
- The topic can be chosen from a list of suggestions provided by the instructor.
- A final project report and an oral demonstration/presentation are required from each project.

Important Dates
- First lecture: Tues, 01/29/2013, 1:30PM, Barton 117.
- Spring Break: 03/18/2013 -- 03/24/2013

Ethics Issues
- Please read the information provided by the Ethics Board.
- On homework and projects, you are permitted to discuss the problems for clarification purposes, and to help each other with specific points. However, the overall solution and write-up should be your own work.